%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU746^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/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 10:47:25 AM UTC 2026
% Result : Theorem 77.00s 13.12s
% Output : CNFRefutation 77.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 267
% Syntax : Number of formulae : 4844 (1735 unt; 0 typ; 266 def)
% Number of atoms : 41858 (16209 equ; 0 cnn)
% Maximal formula atoms : 268 ( 8 avg)
% Number of connectives : 91213 (16415 ~;15486 |; 215 &;56160 @)
% ( 56 <=>;2881 =>; 0 <=; 0 <~>)
% Maximal formula depth : 277 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2679 (2679 >; 0 *; 0 +; 0 <<)
% Number of symbols : 464 ( 461 usr; 271 con; 0-4 aty)
% Number of variables : 20190 (1377 ^;18634 !; 179 ?;20190 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_ap,type,
ap: $i > $i > $i > $i > $i ).
thf(tp_ap2apEq1,type,
ap2apEq1: $o ).
thf(tp_ap2apEq2,type,
ap2apEq2: $o ).
thf(tp_ap2p,type,
ap2p: $o ).
thf(tp_apProp,type,
apProp: $o ).
thf(tp_app,type,
app: $o ).
thf(tp_atleast2p,type,
atleast2p: $i > $o ).
thf(tp_atmost1p,type,
atmost1p: $i > $o ).
thf(tp_atmost2p,type,
atmost2p: $i > $o ).
thf(tp_beta1,type,
beta1: $o ).
thf(tp_beta2,type,
beta2: $o ).
thf(tp_binintersect,type,
binintersect: $i > $i > $i ).
thf(tp_binintersectEL,type,
binintersectEL: $o ).
thf(tp_binintersectER,type,
binintersectER: $o ).
thf(tp_binintersectI,type,
binintersectI: $o ).
thf(tp_binintersectLsub,type,
binintersectLsub: $o ).
thf(tp_binintersectRsub,type,
binintersectRsub: $o ).
thf(tp_binintersectSubset1,type,
binintersectSubset1: $o ).
thf(tp_binintersectSubset2,type,
binintersectSubset2: $o ).
thf(tp_binintersectSubset3,type,
binintersectSubset3: $o ).
thf(tp_binintersectSubset4,type,
binintersectSubset4: $o ).
thf(tp_binintersectSubset5,type,
binintersectSubset5: $o ).
thf(tp_binintersectTELcontra,type,
binintersectTELcontra: $o ).
thf(tp_binintersectTERcontra,type,
binintersectTERcontra: $o ).
thf(tp_binintersectT_lem,type,
binintersectT_lem: $o ).
thf(tp_binunion,type,
binunion: $i > $i > $i ).
thf(tp_binunionE,type,
binunionE: $o ).
thf(tp_binunionEcases,type,
binunionEcases: $o ).
thf(tp_binunionIL,type,
binunionIL: $o ).
thf(tp_binunionIR,type,
binunionIR: $o ).
thf(tp_binunionLsub,type,
binunionLsub: $o ).
thf(tp_binunionRsub,type,
binunionRsub: $o ).
thf(tp_binunionTILcontra,type,
binunionTILcontra: $o ).
thf(tp_binunionTIRcontra,type,
binunionTIRcontra: $o ).
thf(tp_binunionT_lem,type,
binunionT_lem: $o ).
thf(tp_breln,type,
breln: $i > $i > $i > $o ).
thf(tp_brelnall1,type,
brelnall1: $o ).
thf(tp_brelnall2,type,
brelnall2: $o ).
thf(tp_bs114d,type,
bs114d: $o ).
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_cartprodfstin,type,
cartprodfstin: $o ).
thf(tp_cartprodfstpairEq,type,
cartprodfstpairEq: $o ).
thf(tp_cartprodmempair,type,
cartprodmempair: $o ).
thf(tp_cartprodmempair1,type,
cartprodmempair1: $o ).
thf(tp_cartprodmempaircEq,type,
cartprodmempaircEq: $o ).
thf(tp_cartprodpairin,type,
cartprodpairin: $o ).
thf(tp_cartprodpairmemEL,type,
cartprodpairmemEL: $o ).
thf(tp_cartprodpairmemER,type,
cartprodpairmemER: $o ).
thf(tp_cartprodpairsurjEq,type,
cartprodpairsurjEq: $o ).
thf(tp_cartprodsndin,type,
cartprodsndin: $o ).
thf(tp_cartprodsndpairEq,type,
cartprodsndpairEq: $o ).
thf(tp_complementImpComplementIntersect,type,
complementImpComplementIntersect: $o ).
thf(tp_complementInPowersetComplementIntersect,type,
complementInPowersetComplementIntersect: $o ).
thf(tp_complementSubsetComplementIntersect,type,
complementSubsetComplementIntersect: $o ).
thf(tp_complementTE1,type,
complementTE1: $o ).
thf(tp_complementTI1,type,
complementTI1: $o ).
thf(tp_complementT_lem,type,
complementT_lem: $o ).
thf(tp_complementTcontraSubset,type,
complementTcontraSubset: $o ).
thf(tp_complementTnotintersectT,type,
complementTnotintersectT: $o ).
thf(tp_contraSubsetComplement,type,
contraSubsetComplement: $o ).
thf(tp_contrasubsetT,type,
contrasubsetT: $o ).
thf(tp_contrasubsetT1,type,
contrasubsetT1: $o ).
thf(tp_contrasubsetT2,type,
contrasubsetT2: $o ).
thf(tp_contrasubsetT3,type,
contrasubsetT3: $o ).
thf(tp_descr,type,
descr: ( $i > $o ) > $i ).
thf(tp_descr__Cong,type,
descr__Cong: $o ).
thf(tp_descrp,type,
descrp: $o ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_disjointsetsI1,type,
disjointsetsI1: $o ).
thf(tp_doubleComplementE1,type,
doubleComplementE1: $o ).
thf(tp_doubleComplementEq,type,
doubleComplementEq: $o ).
thf(tp_doubleComplementI1,type,
doubleComplementI1: $o ).
thf(tp_doubleComplementSub1,type,
doubleComplementSub1: $o ).
thf(tp_doubleComplementSub2,type,
doubleComplementSub2: $o ).
thf(tp_dpsetconstr,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_dpsetconstrEL1,type,
dpsetconstrEL1: $o ).
thf(tp_dpsetconstrEL2,type,
dpsetconstrEL2: $o ).
thf(tp_dpsetconstrER,type,
dpsetconstrER: $o ).
thf(tp_dpsetconstrERa,type,
dpsetconstrERa: $o ).
thf(tp_dpsetconstrI,type,
dpsetconstrI: $o ).
thf(tp_dpsetconstrSub,type,
dpsetconstrSub: $o ).
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrEL,type,
dsetconstrEL: $o ).
thf(tp_dsetconstrER,type,
dsetconstrER: $o ).
thf(tp_dsetconstrI,type,
dsetconstrI: $o ).
thf(tp_dsetconstr__Cong,type,
dsetconstr__Cong: $o ).
thf(tp_emptyE1,type,
emptyE1: $o ).
thf(tp_emptyI,type,
emptyI: $o ).
thf(tp_emptyInPowerset,type,
emptyInPowerset: $o ).
thf(tp_emptyinPowerset,type,
emptyinPowerset: $o ).
thf(tp_emptyinunitempty,type,
emptyinunitempty: $o ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_emptysetAx,type,
emptysetAx: $o ).
thf(tp_emptysetE,type,
emptysetE: $o ).
thf(tp_emptyset__Cong,type,
emptyset__Cong: $o ).
thf(tp_emptysetimpfalse,type,
emptysetimpfalse: $o ).
thf(tp_emptysetsubset,type,
emptysetsubset: $o ).
thf(tp_eqbreln,type,
eqbreln: $o ).
thf(tp_eqimpsubset1,type,
eqimpsubset1: $o ).
thf(tp_eqimpsubset2,type,
eqimpsubset2: $o ).
thf(tp_eqinunit,type,
eqinunit: $o ).
thf(tp_eta1,type,
eta1: $o ).
thf(tp_eta2,type,
eta2: $o ).
thf(tp_ex1,type,
ex1: $i > ( $i > $o ) > $o ).
thf(tp_ex1E1,type,
ex1E1: $o ).
thf(tp_ex1E2,type,
ex1E2: $o ).
thf(tp_ex1I,type,
ex1I: $o ).
thf(tp_ex1I2,type,
ex1I2: $o ).
thf(tp_exu,type,
exu: ( $i > $o ) > $o ).
thf(tp_exuE1,type,
exuE1: $o ).
thf(tp_exuE2,type,
exuE2: $o ).
thf(tp_exuE3e,type,
exuE3e: $o ).
thf(tp_exuE3u,type,
exuE3u: $o ).
thf(tp_exuEu,type,
exuEu: $o ).
thf(tp_exuI1,type,
exuI1: $o ).
thf(tp_exuI2,type,
exuI2: $o ).
thf(tp_exuI3,type,
exuI3: $o ).
thf(tp_exu__Cong,type,
exu__Cong: $o ).
thf(tp_foundationAx,type,
foundationAx: $o ).
thf(tp_func,type,
func: $i > $i > $i > $o ).
thf(tp_funcGraphProp1,type,
funcGraphProp1: $o ).
thf(tp_funcGraphProp2,type,
funcGraphProp2: $o ).
thf(tp_funcGraphProp3,type,
funcGraphProp3: $o ).
thf(tp_funcGraphProp4,type,
funcGraphProp4: $o ).
thf(tp_funcImageSingleton,type,
funcImageSingleton: $o ).
thf(tp_funcSet,type,
funcSet: $i > $i > $i ).
thf(tp_funcext,type,
funcext: $o ).
thf(tp_funcext2,type,
funcext2: $o ).
thf(tp_funcextLem,type,
funcextLem: $o ).
thf(tp_funcinfuncset,type,
funcinfuncset: $o ).
thf(tp_if,type,
if: $i > $o > $i > $i > $i ).
thf(tp_ifSingleton,type,
ifSingleton: $o ).
thf(tp_iffalse,type,
iffalse: $o ).
thf(tp_iffalseProp1,type,
iffalseProp1: $o ).
thf(tp_iffalseProp2,type,
iffalseProp2: $o ).
thf(tp_ifp,type,
ifp: $o ).
thf(tp_iftrue,type,
iftrue: $o ).
thf(tp_iftrueProp1,type,
iftrueProp1: $o ).
thf(tp_iftrueProp2,type,
iftrueProp2: $o ).
thf(tp_iftrueorfalse,type,
iftrueorfalse: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_inComplementUnionImpInComplement1,type,
inComplementUnionImpInComplement1: $o ).
thf(tp_inComplementUnionImpNotIn1,type,
inComplementUnionImpNotIn1: $o ).
thf(tp_inCongP,type,
inCongP: $o ).
thf(tp_inIntersectImpInIntersectUnions,type,
inIntersectImpInIntersectUnions: $o ).
thf(tp_inIntersectImpInUnion,type,
inIntersectImpInUnion: $o ).
thf(tp_inIntersectImpInUnion2,type,
inIntersectImpInUnion2: $o ).
thf(tp_inPowerset,type,
inPowerset: $o ).
thf(tp_in__Cong,type,
in__Cong: $o ).
thf(tp_infuncsetfunc,type,
infuncsetfunc: $o ).
thf(tp_intersectInPowersetIntersectUnions,type,
intersectInPowersetIntersectUnions: $o ).
thf(tp_iskpair,type,
iskpair: $i > $o ).
thf(tp_kfst,type,
kfst: $i > $i ).
thf(tp_kfstpairEq,type,
kfstpairEq: $o ).
thf(tp_kfstsingleton,type,
kfstsingleton: $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_kpairiskpair,type,
kpairiskpair: $o ).
thf(tp_kpairp,type,
kpairp: $o ).
thf(tp_kpairsurjEq,type,
kpairsurjEq: $o ).
thf(tp_ksnd,type,
ksnd: $i > $i ).
thf(tp_ksndpairEq,type,
ksndpairEq: $o ).
thf(tp_ksndsingleton,type,
ksndsingleton: $o ).
thf(tp_lam,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(tp_lam2lamEq,type,
lam2lamEq: $o ).
thf(tp_lam2p,type,
lam2p: $o ).
thf(tp_lamProp,type,
lamProp: $o ).
thf(tp_lamp,type,
lamp: $o ).
thf(tp_noeltsimpempty,type,
noeltsimpempty: $o ).
thf(tp_nonempty,type,
nonempty: $i > $o ).
thf(tp_nonemptyE1,type,
nonemptyE1: $o ).
thf(tp_nonemptyI,type,
nonemptyI: $o ).
thf(tp_nonemptyI1,type,
nonemptyI1: $o ).
thf(tp_nonemptyImpWitness,type,
nonemptyImpWitness: $o ).
thf(tp_notdallE,type,
notdallE: $o ).
thf(tp_notdexE,type,
notdexE: $o ).
thf(tp_notequalI1,type,
notequalI1: $o ).
thf(tp_notequalI2,type,
notequalI2: $o ).
thf(tp_notinemptyset,type,
notinemptyset: $o ).
thf(tp_notinsingleton,type,
notinsingleton: $o ).
thf(tp_notsubsetI,type,
notsubsetI: $o ).
thf(tp_omega,type,
omega: $i ).
thf(tp_omega0Ax,type,
omega0Ax: $o ).
thf(tp_omegaIndAx,type,
omegaIndAx: $o ).
thf(tp_omegaSAx,type,
omegaSAx: $o ).
thf(tp_omega__Cong,type,
omega__Cong: $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetAx,type,
powersetAx: $o ).
thf(tp_powersetE,type,
powersetE: $o ).
thf(tp_powersetE1,type,
powersetE1: $o ).
thf(tp_powersetI,type,
powersetI: $o ).
thf(tp_powersetI1,type,
powersetI1: $o ).
thf(tp_powersetTE1,type,
powersetTE1: $o ).
thf(tp_powersetTI1,type,
powersetTI1: $o ).
thf(tp_powersetT_lem,type,
powersetT_lem: $o ).
thf(tp_powerset__Cong,type,
powerset__Cong: $o ).
thf(tp_powersetsubset,type,
powersetsubset: $o ).
thf(tp_prop2set,type,
prop2set: $o > $i ).
thf(tp_prop2set2propI,type,
prop2set2propI: $o ).
thf(tp_prop2setE,type,
prop2setE: $o ).
thf(tp_prop2setI,type,
prop2setI: $o ).
thf(tp_quantDeMorgan1,type,
quantDeMorgan1: $o ).
thf(tp_quantDeMorgan2,type,
quantDeMorgan2: $o ).
thf(tp_quantDeMorgan3,type,
quantDeMorgan3: $o ).
thf(tp_quantDeMorgan4,type,
quantDeMorgan4: $o ).
thf(tp_regular,type,
regular: $i > $o ).
thf(tp_replAx,type,
replAx: $o ).
thf(tp_sK100_SY2874,type,
sK100_SY2874: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK101_SY3206,type,
sK101_SY3206: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK102_SY3231,type,
sK102_SY3231: $i > $i > $i > $i > $i ).
thf(tp_sK103_SY3153,type,
sK103_SY3153: $i > $i > $i > $i > $i ).
thf(tp_sK104_SY3153,type,
sK104_SY3153: $i > $i > $i > $i > $i ).
thf(tp_sK105_SY3202,type,
sK105_SY3202: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK106_SY2874,type,
sK106_SY2874: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK107_SY3153,type,
sK107_SY3153: $i > $i > $i > $i > $i ).
thf(tp_sK108_SY3239,type,
sK108_SY3239: $i > $i > $i > $i > $i ).
thf(tp_sK109_SY3240,type,
sK109_SY3240: $i > $i > $i > $i > $i ).
thf(tp_sK10_SY2649,type,
sK10_SY2649: ( $i > $o ) > $i > $i ).
thf(tp_sK110_SY3178,type,
sK110_SY3178: $i > $i > $i > $i ).
thf(tp_sK111_SY3226,type,
sK111_SY3226: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK112_SY3227,type,
sK112_SY3227: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK113_SY3245,type,
sK113_SY3245: $i > $i > $i > $i > $i ).
thf(tp_sK114_SY3178,type,
sK114_SY3178: $i > $i > $i > $i ).
thf(tp_sK115_SY3233,type,
sK115_SY3233: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK116_SY3223,type,
sK116_SY3223: $i > $i > $i > $i ).
thf(tp_sK117_SY3252,type,
sK117_SY3252: $i > $i > $i > $i ).
thf(tp_sK118_SY3237,type,
sK118_SY3237: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK119_SY3238,type,
sK119_SY3238: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK11_SY2701,type,
sK11_SY2701: $i > $i > $i ).
thf(tp_sK120_SY2770,type,
sK120_SY2770: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK121_SY2337,type,
sK121_SY2337: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK122_SY3260,type,
sK122_SY3260: $i > $i > $i > $i ).
thf(tp_sK123_SY3244,type,
sK123_SY3244: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK124_SY2770,type,
sK124_SY2770: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK125_SY2337,type,
sK125_SY2337: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK126_SY3248,type,
sK126_SY3248: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK127_SY3249,type,
sK127_SY3249: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK128_SY3246,type,
sK128_SY3246: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK129_SY3256,type,
sK129_SY3256: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK12_SY2740,type,
sK12_SY2740: ( $i > $o ) > $i > $i ).
thf(tp_sK130_SY3257,type,
sK130_SY3257: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK131_SY3258,type,
sK131_SY3258: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK132_SY3259,type,
sK132_SY3259: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK133_SY3250,type,
sK133_SY3250: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK134_SY3264,type,
sK134_SY3264: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK135_SY3265,type,
sK135_SY3265: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK136_SY3266,type,
sK136_SY3266: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK137_SY2770,type,
sK137_SY2770: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK138_SY2337,type,
sK138_SY2337: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK139_SY3270,type,
sK139_SY3270: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK13_SY2744,type,
sK13_SY2744: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK140_SY2770,type,
sK140_SY2770: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK141_SY2337,type,
sK141_SY2337: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK142_SY2770,type,
sK142_SY2770: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK143_SY2337,type,
sK143_SY2337: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK144_SY2770,type,
sK144_SY2770: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK145_SY2337,type,
sK145_SY2337: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK146_SY2770,type,
sK146_SY2770: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK147_SY2337,type,
sK147_SY2337: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK148_SY2770,type,
sK148_SY2770: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK149_SY2337,type,
sK149_SY2337: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK14_SY2766,type,
sK14_SY2766: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK150_SY2770,type,
sK150_SY2770: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK151_SY2337,type,
sK151_SY2337: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK152_SY2770,type,
sK152_SY2770: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK153_SY2337,type,
sK153_SY2337: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK154_SY3278,type,
sK154_SY3278: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK155_SY3280,type,
sK155_SY3280: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK156_SY3281,type,
sK156_SY3281: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK157_SY3282,type,
sK157_SY3282: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK158_SY3286,type,
sK158_SY3286: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK159_SY3287,type,
sK159_SY3287: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK15_SY2806,type,
sK15_SY2806: ( $i > $o ) > $i > $i ).
thf(tp_sK160_SY3288,type,
sK160_SY3288: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK161_SY3295,type,
sK161_SY3295: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK16_SY2834,type,
sK16_SY2834: $i > $i > $i ).
thf(tp_sK17_SY2871,type,
sK17_SY2871: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK18_SY2009,type,
sK18_SY2009: $i > $i ).
thf(tp_sK19_SY2610,type,
sK19_SY2610: $i > $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK20_SY2946,type,
sK20_SY2946: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK21_SY2977,type,
sK21_SY2977: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK22_SY3113,type,
sK22_SY3113: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK23_SY3119,type,
sK23_SY3119: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK24_SY3007,type,
sK24_SY3007: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK25_SY3010,type,
sK25_SY3010: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK26_SY2833,type,
sK26_SY2833: ( $i > $o ) > $i > $i ).
thf(tp_sK27_SY2440,type,
sK27_SY2440: $i > $i ).
thf(tp_sK28_SY3036,type,
sK28_SY3036: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK29_SY3041,type,
sK29_SY3041: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK2_SY2624,type,
sK2_SY2624: $i ).
thf(tp_sK30_SY2541,type,
sK30_SY2541: ( $i > $o ) > $i > $i ).
thf(tp_sK31_SY3079,type,
sK31_SY3079: $i > ( $i > $o ) > $i ).
thf(tp_sK32_SY2591,type,
sK32_SY2591: ( $i > $o ) > $i > $i ).
thf(tp_sK33_SY3090,type,
sK33_SY3090: $o ).
thf(tp_sK34_SY3112,type,
sK34_SY3112: ( $i > $o ) > $i > $i ).
thf(tp_sK35_SY2993,type,
sK35_SY2993: $i > $i > $i > $i ).
thf(tp_sK36_SY3121,type,
sK36_SY3121: ( $i > $o ) > $i > $i ).
thf(tp_sK37_SY2850,type,
sK37_SY2850: $i > $i > $i ).
thf(tp_sK38_SY2017,type,
sK38_SY2017: $i > $i > $i ).
thf(tp_sK39_SY3168,type,
sK39_SY3168: $i ).
thf(tp_sK3_SY2186,type,
sK3_SY2186: $i > $i ).
thf(tp_sK40_SY3104,type,
sK40_SY3104: $o > $i > $i > $i ).
thf(tp_sK41_SX0,type,
sK41_SX0: $i > $i > $i ).
thf(tp_sK42_SX0,type,
sK42_SX0: $i > $i > $i ).
thf(tp_sK43_SY2728,type,
sK43_SY2728: $i > $i > $i ).
thf(tp_sK44_SY2395,type,
sK44_SY2395: $i > $i ).
thf(tp_sK45_SY3132,type,
sK45_SY3132: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(tp_sK46_SY2574,type,
sK46_SY2574: $i > $i > $i ).
thf(tp_sK47_SY2601,type,
sK47_SY2601: $i > $i > $i ).
thf(tp_sK48_SY3143,type,
sK48_SY3143: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK49_SY2231,type,
sK49_SY2231: $i > ( $i > $o ) > $i ).
thf(tp_sK4_SY2000,type,
sK4_SY2000: $i > $i ).
thf(tp_sK50_SY3155,type,
sK50_SY3155: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK51_SY2874,type,
sK51_SY2874: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK52_SY3083,type,
sK52_SY3083: $i > $i > $i > $i ).
thf(tp_sK53_SY2599,type,
sK53_SY2599: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK54_SY2601,type,
sK54_SY2601: $i > $i > $i ).
thf(tp_sK55_SY2926,type,
sK55_SY2926: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK56_SY2652,type,
sK56_SY2652: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK57_SY3106,type,
sK57_SY3106: $i > $i > $i > $i ).
thf(tp_sK58_SY3190,type,
sK58_SY3190: $i > ( $i > $o ) > $i ).
thf(tp_sK59_SY3114,type,
sK59_SY3114: $i > $i > $i > $i ).
thf(tp_sK5_SY2101,type,
sK5_SY2101: $i > $i ).
thf(tp_sK60_SY3073,type,
sK60_SY3073: $i > ( $i > $o ) > $i ).
thf(tp_sK61_SY3188,type,
sK61_SY3188: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(tp_sK62_SY3087,type,
sK62_SY3087: $i > ( $i > $o ) > $i ).
thf(tp_sK63_SY3141,type,
sK63_SY3141: $i > $i > $i > $i > $i ).
thf(tp_sK64_SY3189,type,
sK64_SY3189: $i > $i > ( $i > $o ) > $i > $i ).
thf(tp_sK65_SY3092,type,
sK65_SY3092: $i > ( $i > $o ) > $i ).
thf(tp_sK66_SY3093,type,
sK66_SY3093: $i > ( $i > $o ) > $i ).
thf(tp_sK67_SY3096,type,
sK67_SY3096: $i > ( $i > $o ) > $i ).
thf(tp_sK68_SY3146,type,
sK68_SY3146: $i > $i > $i > $i > $i ).
thf(tp_sK69_SY3116,type,
sK69_SY3116: $i > ( $i > $o ) > $i ).
thf(tp_sK6_SY2578,type,
sK6_SY2578: $i > $i > $i ).
thf(tp_sK70_SY3151,type,
sK70_SY3151: $i > $i > $i > $i > $i ).
thf(tp_sK71_SY3191,type,
sK71_SY3191: $i > $i > ( $i > $o ) > $i > $i ).
thf(tp_sK72_SY3158,type,
sK72_SY3158: $i > $i > $i > $i > $i ).
thf(tp_sK73_SY3165,type,
sK73_SY3165: $i > $i > $i > $i > $i ).
thf(tp_sK74_SY3127,type,
sK74_SY3127: $i > ( $i > $o ) > $i ).
thf(tp_sK75_SY3197,type,
sK75_SY3197: $i > $i > $i > $i > $i ).
thf(tp_sK76_SY3169,type,
sK76_SY3169: $i > $i > $i > $i ).
thf(tp_sK77_SY3201,type,
sK77_SY3201: $i > $i > $i > $i > $i ).
thf(tp_sK78_SY1902,type,
sK78_SY1902: $i > ( $i > $o ) > $i ).
thf(tp_sK79_SY2107,type,
sK79_SY2107: $i > ( $i > $o ) > $i ).
thf(tp_sK7_SY2600,type,
sK7_SY2600: $i > $i > $i ).
thf(tp_sK80_SY3176,type,
sK80_SY3176: $i > $i > $i ).
thf(tp_sK81_SY2233,type,
sK81_SY2233: $i > ( $i > $o ) > $i ).
thf(tp_sK82_SY2233,type,
sK82_SY2233: $i > ( $i > $o ) > $i ).
thf(tp_sK83_SY2316,type,
sK83_SY2316: $i > ( $i > $o ) > $i ).
thf(tp_sK84_SY2794,type,
sK84_SY2794: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK85_SY3187,type,
sK85_SY3187: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK86_SY2511,type,
sK86_SY2511: $i > ( $i > $o ) > $i ).
thf(tp_sK87_SY1902,type,
sK87_SY1902: $i > ( $i > $o ) > $i ).
thf(tp_sK88_SY1929,type,
sK88_SY1929: $i > ( $i > $o ) > $i ).
thf(tp_sK89_SY2107,type,
sK89_SY2107: $i > ( $i > $o ) > $i ).
thf(tp_sK8_SY2615,type,
sK8_SY2615: $i > $i > $i ).
thf(tp_sK90_SY2233,type,
sK90_SY2233: $i > ( $i > $o ) > $i ).
thf(tp_sK91_SY3115,type,
sK91_SY3115: $i > $i > $i > $i ).
thf(tp_sK92_SY3115,type,
sK92_SY3115: $i > $i > $i > $i ).
thf(tp_sK93_SY2316,type,
sK93_SY2316: $i > ( $i > $o ) > $i ).
thf(tp_sK94_SY2511,type,
sK94_SY2511: $i > ( $i > $o ) > $i ).
thf(tp_sK95_SY1929,type,
sK95_SY1929: $i > ( $i > $o ) > $i ).
thf(tp_sK96_SY1929,type,
sK96_SY1929: $i > ( $i > $o ) > $i ).
thf(tp_sK97_SY3115,type,
sK97_SY3115: $i > $i > $i > $i ).
thf(tp_sK98_SY3153,type,
sK98_SY3153: $i > $i > $i > $i > $i ).
thf(tp_sK99_SY1929,type,
sK99_SY1929: $i > ( $i > $o ) > $i ).
thf(tp_sK9_SY2932,type,
sK9_SY2932: $i ).
thf(tp_secondinupair,type,
secondinupair: $o ).
thf(tp_sepInPowerset,type,
sepInPowerset: $o ).
thf(tp_sepSubset,type,
sepSubset: $o ).
thf(tp_set2prop,type,
set2prop: $i > $o ).
thf(tp_setOfPairsIsBReln,type,
setOfPairsIsBReln: $o ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinAx,type,
setadjoinAx: $o ).
thf(tp_setadjoinE,type,
setadjoinE: $o ).
thf(tp_setadjoinIL,type,
setadjoinIL: $o ).
thf(tp_setadjoinIR,type,
setadjoinIR: $o ).
thf(tp_setadjoinOr,type,
setadjoinOr: $o ).
thf(tp_setadjoinSub,type,
setadjoinSub: $o ).
thf(tp_setadjoinSub2,type,
setadjoinSub2: $o ).
thf(tp_setadjoin__Cong,type,
setadjoin__Cong: $o ).
thf(tp_setbeta,type,
setbeta: $o ).
thf(tp_setext,type,
setext: $o ).
thf(tp_setextAx,type,
setextAx: $o ).
thf(tp_setextT,type,
setextT: $o ).
thf(tp_setextsub,type,
setextsub: $o ).
thf(tp_setminus,type,
setminus: $i > $i > $i ).
thf(tp_setminusEL,type,
setminusEL: $o ).
thf(tp_setminusELneg,type,
setminusELneg: $o ).
thf(tp_setminusER,type,
setminusER: $o ).
thf(tp_setminusERneg,type,
setminusERneg: $o ).
thf(tp_setminusI,type,
setminusI: $o ).
thf(tp_setminusILneg,type,
setminusILneg: $o ).
thf(tp_setminusIRneg,type,
setminusIRneg: $o ).
thf(tp_setminusLsub,type,
setminusLsub: $o ).
thf(tp_setminusSubset1,type,
setminusSubset1: $o ).
thf(tp_setminusSubset2,type,
setminusSubset2: $o ).
thf(tp_setminusT_lem,type,
setminusT_lem: $o ).
thf(tp_setoftrueEq,type,
setoftrueEq: $o ).
thf(tp_setsmeet,type,
setsmeet: $i > $i > $o ).
thf(tp_setukpairIL,type,
setukpairIL: $o ).
thf(tp_setukpairIR,type,
setukpairIR: $o ).
thf(tp_setukpairinjL,type,
setukpairinjL: $o ).
thf(tp_setukpairinjL1,type,
setukpairinjL1: $o ).
thf(tp_setukpairinjL2,type,
setukpairinjL2: $o ).
thf(tp_setukpairinjR,type,
setukpairinjR: $o ).
thf(tp_setukpairinjR1,type,
setukpairinjR1: $o ).
thf(tp_setukpairinjR11,type,
setukpairinjR11: $o ).
thf(tp_setukpairinjR12,type,
setukpairinjR12: $o ).
thf(tp_setukpairinjR2,type,
setukpairinjR2: $o ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunionAx,type,
setunionAx: $o ).
thf(tp_setunionE,type,
setunionE: $o ).
thf(tp_setunionE2,type,
setunionE2: $o ).
thf(tp_setunionI,type,
setunionI: $o ).
thf(tp_setunion__Cong,type,
setunion__Cong: $o ).
thf(tp_setunionsingleton,type,
setunionsingleton: $o ).
thf(tp_setunionsingleton1,type,
setunionsingleton1: $o ).
thf(tp_setunionsingleton2,type,
setunionsingleton2: $o ).
thf(tp_singleton,type,
singleton: $i > $o ).
thf(tp_singletoninpowerset,type,
singletoninpowerset: $o ).
thf(tp_singletoninpowunion,type,
singletoninpowunion: $o ).
thf(tp_singletonprop,type,
singletonprop: $o ).
thf(tp_singletonsswitch,type,
singletonsswitch: $o ).
thf(tp_singletonsubset,type,
singletonsubset: $o ).
thf(tp_singletonsuniq,type,
singletonsuniq: $o ).
thf(tp_subPowSU,type,
subPowSU: $o ).
thf(tp_subbreln,type,
subbreln: $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset2powerset,type,
subset2powerset: $o ).
thf(tp_subsetE,type,
subsetE: $o ).
thf(tp_subsetE2,type,
subsetE2: $o ).
thf(tp_subsetI1,type,
subsetI1: $o ).
thf(tp_subsetI2,type,
subsetI2: $o ).
thf(tp_subsetRefl,type,
subsetRefl: $o ).
thf(tp_subsetTI,type,
subsetTI: $o ).
thf(tp_subsetTrans,type,
subsetTrans: $o ).
thf(tp_subsetemptysetimpeq,type,
subsetemptysetimpeq: $o ).
thf(tp_symdiff,type,
symdiff: $i > $i > $i ).
thf(tp_symdiffE,type,
symdiffE: $o ).
thf(tp_symdiffI1,type,
symdiffI1: $o ).
thf(tp_symdiffI2,type,
symdiffI2: $o ).
thf(tp_symdiffIneg1,type,
symdiffIneg1: $o ).
thf(tp_symdiffIneg2,type,
symdiffIneg2: $o ).
thf(tp_theeq,type,
theeq: $o ).
thf(tp_theprop,type,
theprop: $o ).
thf(tp_ubforcartprodlem1,type,
ubforcartprodlem1: $o ).
thf(tp_ubforcartprodlem2,type,
ubforcartprodlem2: $o ).
thf(tp_ubforcartprodlem3,type,
ubforcartprodlem3: $o ).
thf(tp_uniqinunit,type,
uniqinunit: $o ).
thf(tp_upairequniteq,type,
upairequniteq: $o ).
thf(tp_upairinpowunion,type,
upairinpowunion: $o ).
thf(tp_upairset2E,type,
upairset2E: $o ).
thf(tp_upairset2IR,type,
upairset2IR: $o ).
thf(tp_upairsetE,type,
upairsetE: $o ).
thf(tp_upairsetIL,type,
upairsetIL: $o ).
thf(tp_upairsetIR,type,
upairsetIR: $o ).
thf(tp_upairsetp,type,
upairsetp: $i > $o ).
thf(tp_upairsubunion,type,
upairsubunion: $o ).
thf(tp_vacuousDall,type,
vacuousDall: $o ).
thf(tp_wellorderingAx,type,
wellorderingAx: $o ).
thf(ap2apEq1,definition,
( ap2apEq1
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectLsub,definition,
( binintersectLsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectRsub,definition,
( binintersectRsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset1,definition,
( binintersectSubset1
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(binintersectSubset2,definition,
( binintersectSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,definition,
( binintersectSubset3
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectSubset4,definition,
( binintersectSubset4
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionLsub,definition,
( binunionLsub
= ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,definition,
( binunionRsub
= ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',binunionT_lem) ).
thf(breln,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).
thf(brelnall1,definition,
( brelnall1
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodmempair,definition,
( cartprodmempair
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(complementImpComplementIntersect,definition,
( complementImpComplementIntersect
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ X ) )
=> ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',complementTnotintersectT) ).
thf(contraSubsetComplement,definition,
( contraSubsetComplement
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ Y )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',contrasubsetT3) ).
thf(descr__Cong,definition,
( descr__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) )
=> ( ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',emptyE1) ).
thf(emptyI,definition,
( emptyI
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
thf(emptyInPowerset,definition,
( emptyInPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,definition,
( emptyinPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyinunitempty,definition,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(emptyset__Cong,definition,
( emptyset__Cong
= ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetsubset,definition,
( emptysetsubset
= ( ! [A: $i] : ( subset @ emptyset @ A ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',eqbreln) ).
thf(eqimpsubset1,definition,
( eqimpsubset1
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,definition,
( eqimpsubset2
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqinunit,definition,
( eqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',eta2) ).
thf(ex1,definition,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(ex1E1,definition,
( ex1E1
= ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ex1I2) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',exuE2) ).
thf(exuE3e,definition,
( exuE3e
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] : ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',inIntersectImpInUnion2) ).
thf(inPowerset,definition,
( inPowerset
= ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',intersectInPowersetIntersectUnions) ).
thf(kfstpairEq,definition,
( kfstpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,definition,
( kpairp
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
thf(kpairsurjEq,definition,
( kpairsurjEq
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(ksndpairEq,definition,
( ksndpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',lamp) ).
thf(noeltsimpempty,definition,
( noeltsimpempty
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyE1,definition,
( nonemptyE1
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] : ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(nonemptyI1,definition,
( nonemptyI1
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ( nonempty @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyImpWitness,definition,
( nonemptyImpWitness
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& $true ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',notdexE) ).
thf(notequalI1,definition,
( notequalI1
= ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',notequalI2) ).
thf(notinemptyset,definition,
( notinemptyset
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(notinsingleton,definition,
( notinsingleton
= ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega__Cong,definition,
( omega__Cong
= ( omega = omega ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',powersetE) ).
thf(powersetE1,definition,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(powersetI1,definition,
( powersetI1
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',powersetT_lem) ).
thf(powerset__Cong,definition,
( powerset__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(powersetsubset,definition,
( powersetsubset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset) ).
thf(prop2set2propI,definition,
( prop2set2propI
= ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set2propI) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(prop2setI,definition,
( prop2setI
= ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',replAx) ).
thf(secondinupair,definition,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,definition,
( sepSubset
= ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinSub,definition,
( setadjoinSub
= ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setextT) ).
thf(setextsub,definition,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,definition,
( setminusLsub
= ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,definition,
( setminusSubset1
= ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1) ).
thf(setminusSubset2,definition,
( setminusSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setminusT_lem) ).
thf(setoftrueEq,definition,
( setoftrueEq
= ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setunionI) ).
thf(setunion__Cong,definition,
( setunion__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(setunionsingleton,definition,
( setunionsingleton
= ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton) ).
thf(setunionsingleton1,definition,
( setunionsingleton1
= ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,definition,
( setunionsingleton2
= ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(singletoninpowerset,definition,
( singletoninpowerset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',singletonsswitch) ).
thf(singletonsubset,definition,
( singletonsubset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletonsuniq,definition,
( singletonsuniq
= ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsuniq) ).
thf(subPowSU,definition,
( subPowSU
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',subbreln) ).
thf(subset2powerset,definition,
( subset2powerset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(subsetRefl,definition,
( subsetRefl
= ( ! [A: $i] : ( subset @ A @ A ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).
thf(subsetemptysetimpeq,definition,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(theeq,definition,
( theeq
= ( ! [X: $i] :
( ( singleton @ X )
=> ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ( setunion @ X )
= Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theeq) ).
thf(theprop,definition,
( theprop
= ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',upairset2E) ).
thf(upairset2IR,definition,
( upairset2IR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,definition,
( upairsetIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,definition,
( upairsetIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',upairsubunion) ).
thf(vacuousDall,definition,
( vacuousDall
= ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',wellorderingAx) ).
thf(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ! [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/sandbox2/benchmark/theBenchmark.p',binunionTE) ).
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
=> ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $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 ) ) ) ) )
=> ( ! [SY479: $i,SY480: $i > $o] :
( ( singleton
@ ( dsetconstr @ SY479
@ ^ [SY484: $i] : ( SY480 @ SY484 ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY479 )
& ( SY480 @ Xx ) ) )
=> ( ! [SY486: $i,SY487: $i > $o,SY488: $i] :
( ( in @ SY488 @ SY486 )
=> ( ( SY487 @ SY488 )
=> ( ! [Xy: $i] :
( ( in @ Xy @ SY486 )
=> ( ( SY487 @ Xy )
=> ( Xy = SY488 ) ) )
=> ( singleton
@ ( dsetconstr @ SY486
@ ^ [SY493: $i] : ( SY487 @ SY493 ) ) ) ) ) )
=> ( ! [SY494: $i,SY495: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY494 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY494 )
=> ( ( SY495 @ Xx )
=> ( ( SY495 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY494 )
& ( SY495 @ Xx ) )
=> ( singleton
@ ( dsetconstr @ SY494
@ ^ [SY502: $i] : ( SY495 @ SY502 ) ) ) ) )
=> ( ! [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 ) )
=> ( ! [SY586: $i,SY587: $i,SY588: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SY586 @ SY587
@ ^ [Xx: $i,Xy: $i] : ( SY588 @ Xx @ Xy ) )
@ ( cartprod @ SY586 @ SY587 ) )
=> ( ! [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 ) ) )
=> ( ! [SY662: $i,SY663: $i,SY664: $i] :
( ( subset @ SY664 @ ( cartprod @ SY662 @ SY663 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY662 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY663 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY664 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY664 )
=> ( Xphi @ Xx ) ) ) )
=> ( ! [SY672: $i,SY673: $i,SY674: $i] :
( ( subset @ SY674 @ ( cartprod @ SY672 @ SY673 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY672 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY673 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY674 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY674 )
=> ( Xphi @ Xx ) ) ) )
=> ( ! [SY682: $i,SY683: $i > $o] :
( ( singleton
@ ( dsetconstr @ SY682
@ ^ [SY687: $i] : ( SY683 @ SY687 ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY682 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY682 )
=> ( ( SY683 @ Xx )
=> ( ( SY683 @ 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 ) ) ) ) )
=> ( ! [SY715: $i,SY716: $i,SY717: $i] :
( ( subset @ SY717 @ ( cartprod @ SY715 @ SY716 ) )
=> ! [SY721: $i] :
( ( subset @ SY721 @ ( cartprod @ SY715 @ SY716 ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY715 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY716 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY717 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY721 ) ) ) )
=> ( subset @ SY717 @ SY721 ) ) ) )
=> ( ! [SY727: $i,SY728: $i,SY729: $i] :
( ( subset @ SY729 @ ( cartprod @ SY727 @ SY728 ) )
=> ! [SY733: $i] :
( ( subset @ SY733 @ ( cartprod @ SY727 @ SY728 ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY727 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY728 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY729 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY733 ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY727 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY728 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY733 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY729 ) ) ) )
=> ( SY729 = SY733 ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
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,
( ( ! [SY479: $i,SY480: $i > $o] :
( ( singleton
@ ( dsetconstr @ SY479
@ ^ [SY484: $i] : ( SY480 @ SY484 ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY479 )
& ( SY480 @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(159,plain,
( ( ! [SY486: $i,SY487: $i > $o,SY488: $i] :
( ( in @ SY488 @ SY486 )
=> ( ( SY487 @ SY488 )
=> ( ! [Xy: $i] :
( ( in @ Xy @ SY486 )
=> ( ( SY487 @ Xy )
=> ( Xy = SY488 ) ) )
=> ( singleton
@ ( dsetconstr @ SY486
@ ^ [SY493: $i] : ( SY487 @ SY493 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(160,plain,
( ( ! [SY494: $i,SY495: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY494 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY494 )
=> ( ( SY495 @ Xx )
=> ( ( SY495 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY494 )
& ( SY495 @ Xx ) )
=> ( singleton
@ ( dsetconstr @ SY494
@ ^ [SY502: $i] : ( SY495 @ SY502 ) ) ) ) ) )
= $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,
( ( ! [SY586: $i,SY587: $i,SY588: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SY586 @ SY587
@ ^ [Xx: $i,Xy: $i] : ( SY588 @ Xx @ Xy ) )
@ ( cartprod @ SY586 @ SY587 ) ) )
= $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,
( ( ! [SY662: $i,SY663: $i,SY664: $i] :
( ( subset @ SY664 @ ( cartprod @ SY662 @ SY663 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY662 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY663 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY664 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY664 )
=> ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(202,plain,
( ( ! [SY672: $i,SY673: $i,SY674: $i] :
( ( subset @ SY674 @ ( cartprod @ SY672 @ SY673 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY672 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY673 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY674 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY674 )
=> ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(203,plain,
( ( ! [SY682: $i,SY683: $i > $o] :
( ( singleton
@ ( dsetconstr @ SY682
@ ^ [SY687: $i] : ( SY683 @ SY687 ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY682 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY682 )
=> ( ( SY683 @ Xx )
=> ( ( SY683 @ 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,
( ( ! [SY715: $i,SY716: $i,SY717: $i] :
( ( subset @ SY717 @ ( cartprod @ SY715 @ SY716 ) )
=> ! [SY721: $i] :
( ( subset @ SY721 @ ( cartprod @ SY715 @ SY716 ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY715 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY716 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY717 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY721 ) ) ) )
=> ( subset @ SY717 @ SY721 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(210,plain,
( ( ! [SY727: $i,SY728: $i,SY729: $i] :
( ( subset @ SY729 @ ( cartprod @ SY727 @ SY728 ) )
=> ! [SY733: $i] :
( ( subset @ SY733 @ ( cartprod @ SY727 @ SY728 ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY727 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY728 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY729 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY733 ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY727 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY728 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY733 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY729 ) ) ) )
=> ( SY729 = SY733 ) ) ) ) ) )
= $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 ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(267,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(polarity_switch,[status(thm)],[266]) ).
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(copy,[status(thm)],[265]) ).
thf(269,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(270,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(271,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(272,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(273,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(274,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(275,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(276,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(277,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(278,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(279,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(280,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(281,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(282,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( X
= ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(283,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(284,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(285,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(286,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(287,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(288,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(289,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(290,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(291,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(292,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(293,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(294,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(295,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(296,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(297,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(298,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(299,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(300,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(301,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(302,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(303,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(304,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(305,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(306,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(307,plain,
( ( ! [X: $i] :
( ( singleton @ X )
=> ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ( setunion @ X )
= Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(308,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(309,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(310,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(311,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(312,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(313,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(314,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(315,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(316,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(317,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(318,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(319,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(320,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(321,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(322,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(323,plain,
( ( ! [SY727: $i,SY728: $i,SY729: $i] :
( ( subset @ SY729 @ ( cartprod @ SY727 @ SY728 ) )
=> ! [SY733: $i] :
( ( subset @ SY733 @ ( cartprod @ SY727 @ SY728 ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY727 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY728 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY729 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY733 ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY727 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY728 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY733 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY729 ) ) ) )
=> ( SY729 = SY733 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(324,plain,
( ( ! [SY715: $i,SY716: $i,SY717: $i] :
( ( subset @ SY717 @ ( cartprod @ SY715 @ SY716 ) )
=> ! [SY721: $i] :
( ( subset @ SY721 @ ( cartprod @ SY715 @ SY716 ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY715 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY716 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY717 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY721 ) ) ) )
=> ( subset @ SY717 @ SY721 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(325,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(326,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(327,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(328,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(329,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(330,plain,
( ( ! [SY682: $i,SY683: $i > $o] :
( ( singleton
@ ( dsetconstr @ SY682
@ ^ [SY687: $i] : ( SY683 @ SY687 ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY682 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY682 )
=> ( ( SY683 @ Xx )
=> ( ( SY683 @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(331,plain,
( ( ! [SY672: $i,SY673: $i,SY674: $i] :
( ( subset @ SY674 @ ( cartprod @ SY672 @ SY673 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY672 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY673 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY674 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY674 )
=> ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(332,plain,
( ( ! [SY662: $i,SY663: $i,SY664: $i] :
( ( subset @ SY664 @ ( cartprod @ SY662 @ SY663 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY662 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY663 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY664 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY664 )
=> ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(333,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(334,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(335,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(336,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(337,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(338,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(339,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(340,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(341,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(342,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(343,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(344,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(345,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(346,plain,
( ( ! [SY586: $i,SY587: $i,SY588: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SY586 @ SY587
@ ^ [Xx: $i,Xy: $i] : ( SY588 @ Xx @ Xy ) )
@ ( cartprod @ SY586 @ SY587 ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(347,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(348,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(349,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(350,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(351,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(352,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(353,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(354,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(355,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( ksnd @ Xu ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(356,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(357,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(358,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(359,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(360,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(361,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(362,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(363,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(364,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(365,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(366,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(367,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(368,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(369,plain,
( ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(370,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(371,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(372,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(373,plain,
( ( ! [SY494: $i,SY495: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY494 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY494 )
=> ( ( SY495 @ Xx )
=> ( ( SY495 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY494 )
& ( SY495 @ Xx ) )
=> ( singleton
@ ( dsetconstr @ SY494
@ ^ [SY502: $i] : ( SY495 @ SY502 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(374,plain,
( ( ! [SY486: $i,SY487: $i > $o,SY488: $i] :
( ( in @ SY488 @ SY486 )
=> ( ( SY487 @ SY488 )
=> ( ! [Xy: $i] :
( ( in @ Xy @ SY486 )
=> ( ( SY487 @ Xy )
=> ( Xy = SY488 ) ) )
=> ( singleton
@ ( dsetconstr @ SY486
@ ^ [SY493: $i] : ( SY487 @ SY493 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(375,plain,
( ( ! [SY479: $i,SY480: $i > $o] :
( ( singleton
@ ( dsetconstr @ SY479
@ ^ [SY484: $i] : ( SY480 @ SY484 ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY479 )
& ( SY480 @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(376,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(377,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(378,plain,
( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(379,plain,
( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(380,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(381,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(382,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(383,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(384,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(385,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(386,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(387,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(388,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(389,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(390,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(391,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(392,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(393,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(394,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(395,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(396,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(397,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(398,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(399,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(400,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(401,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(402,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(403,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(404,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(405,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(406,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(407,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(408,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(409,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(410,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(411,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(412,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(413,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(414,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(415,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(416,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(417,plain,
( ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(418,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(419,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(420,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(421,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(422,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(423,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(424,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(425,plain,
( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(426,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(427,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(428,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(429,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(430,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(431,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(432,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(433,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(434,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(435,plain,
( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(436,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(437,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(438,plain,
( ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(439,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(440,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(441,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(442,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(443,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(444,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(445,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(446,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(447,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(448,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(449,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(450,plain,
( ( ! [A: $i] : ( subset @ emptyset @ A ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(451,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(452,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(453,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(454,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(455,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(456,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(457,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(458,plain,
( ( omega = omega )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(459,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(460,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(461,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(462,plain,
( ( emptyset = emptyset )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(463,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(464,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(465,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(466,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(467,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(468,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(469,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(470,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(471,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(472,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(473,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(474,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(475,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(476,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(477,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(478,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(479,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(480,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(481,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(482,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(483,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(484,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(485,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(486,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(487,plain,
( ( ! [SY145: $i] :
( ( SY145 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY145 )
& $true ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(488,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(489,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(490,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(491,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(492,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(493,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(494,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(495,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(496,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(497,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(498,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(499,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(500,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(501,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(502,plain,
( ( ! [SY106: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY106 )
=> ( SY106 != emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(503,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(504,plain,
( ( ! [SY100: $i] :
( ( SY100 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY100 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(505,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(506,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(507,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(508,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(509,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(510,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(511,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(512,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(513,plain,
( ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(514,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(515,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(516,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(517,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(518,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(519,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(520,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(521,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(522,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(523,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(524,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(525,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(526,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(527,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(528,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(529,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(530,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)],[267]) ).
thf(531,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(532,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)],[469,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(533,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)],[287,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(534,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(535,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(536,plain,
( ( ! [SX0: $i,SX1: $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(537,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( 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)],[455,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(538,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(539,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( set2prop @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(540,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(541,plain,
( ( ! [SX0: $i > $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(542,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(543,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(544,plain,
( ( ! [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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(545,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( in @ emptyset @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(546,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( in @ ( setminus @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(547,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(548,plain,
( ( ! [SX0: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(549,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(550,plain,
( ( ! [SX0: $i] :
( ~ ( singleton @ SX0 )
| ( in @ ( setunion @ SX0 ) @ SX0 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(551,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX1: $i] :
( SX0
= ( kpair @ ( kfst @ 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(552,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( ( kpair @ SX2 @ SX3 )
= ( kpair @ SX2 @ SX3 ) ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(553,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( ( ksnd @ ( kpair @ SX2 @ SX3 ) )
= SX3 ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(554,plain,
( ( ! [SX0: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(555,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ ( kfst @ SX2 ) @ SX0 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(556,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
!= ( setadjoin @ SX2 @ emptyset ) )
| ( SX0 = 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(557,plain,
( ( ! [SX0: $i,SX1: $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(558,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ( func @ SX0 @ SX1 @ 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(559,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(560,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ~ ( subset @ SX2 @ SX1 )
| ( subset @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(561,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[281,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(562,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(563,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[274,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(564,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( 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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(565,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(566,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( 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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(567,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[269,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(568,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(569,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(570,plain,
( ( ! [SX0: $i,SX1: $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)],[296,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(571,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( 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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(572,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(573,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(574,plain,
( ( ! [SX0: $i,SX1: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(575,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(576,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(577,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ ( binunion @ SX0 @ 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(578,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(579,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(580,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX0 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(581,plain,
( ( ! [SX0: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(582,plain,
( ( ! [SX0: $i,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)],[275,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(583,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ( in @ SX1 @ emptyset )
| ( SX0 @ SX1 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(584,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( SX1 @ SX2 ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(585,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(586,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(587,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( powerset @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(588,plain,
( ( ! [SX0: $i > $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(589,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in
@ ( setunion
@ ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) ) )
@ 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(590,plain,
( ( ! [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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(591,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX0 @ SX1 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(592,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( subset @ SX3 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
| ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 ) ) )
| ( subset @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(593,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(594,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(595,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ 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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(596,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(597,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX3 )
| ( SX3 = SX2 ) )
| ( singleton
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(598,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(599,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(600,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(601,plain,
( ( ! [SX0: $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(602,plain,
( ( ! [SX0: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(603,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i > $o] :
( ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
| ( SX3 @ ( kpair @ SX4 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(604,plain,
( ( ! [SX0: $i > $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(605,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(606,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ( SX0
@ ( descr
@ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(607,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(608,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( binintersect @ SX0 @ SX1 )
= 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(609,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(610,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( ( binintersect @ SX0 @ SX1 )
= 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(611,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(612,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(613,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[273,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(614,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( ( kpair @ ( kfst @ SX0 ) @ ( ksnd @ SX0 ) )
= SX0 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(615,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( binintersect @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(616,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(617,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(618,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[291,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(619,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( 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)],[277,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(620,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(621,plain,
( ( ! [SX0: $i,SX1: $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(622,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(623,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) )
| ( SX0 = 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(624,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ! [SX3: $o] :
( ~ ( ( SX2 != SX0 )
| SX3 )
| ~ ( ~ ( in @ SX2 @ SX1 )
| SX3 )
| SX3 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(625,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(626,plain,
( ( ! [SX0: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(627,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[276,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(628,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[292,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(629,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[280,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(630,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ ( ksnd @ SX2 ) @ SX1 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(631,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[286,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(632,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ( ( lam @ SX0 @ SX1
@ ^ [SX3: $i] : ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) )
= SX2 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(633,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( singleton
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(634,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ! [SX2: $o] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX1 @ SX3 )
| ~ ( in @ SX3 @ SX0 )
| SX2 )
| SX2 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(635,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [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)],[289,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(636,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(637,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[511,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(638,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( iskpair @ SX2 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(639,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(640,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ SX3 @ 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(641,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( 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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(642,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( powerset @ SX0 ) @ ( powerset @ 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(643,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( ( kpair @ ( kfst @ SX2 ) @ ( ksnd @ SX2 ) )
= SX2 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(644,plain,
( ( ! [SX0: $i,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)],[297,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(645,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(646,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(647,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(648,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(649,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [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)],[272,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(650,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setunion @ SX0 )
= ( setunion @ 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(651,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(652,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(653,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(654,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[290,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(655,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( in @ SX2 @ SX0 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(656,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(657,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( SX1
= ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(658,plain,
( ( ! [SX0: $i > $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(659,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( setminus @ SX0 @ SX1 ) @ ( powerset @ ( setminus @ SX0 @ ( binintersect @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(660,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( setminus @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(661,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ emptyset )
| ( SX0 = emptyset ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(662,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(663,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(664,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( SX0 != SX1 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(665,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[268,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(666,plain,
( ( ! [SX0: $i,SX1: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(667,plain,
( ( ! [SX0: $i,SX1: $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)],[304,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(668,plain,
( ( ! [SX0: $i,SX1: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(669,plain,
( ( ! [SX0: $i,SX1: $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(670,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( 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)],[526,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(671,plain,
( ( ! [SX0: $i,SX1: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(672,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( ( kfst @ ( kpair @ SX2 @ SX3 ) )
= SX2 ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(673,plain,
( ( ! [SX0: $i,SX1: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(674,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[288,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(675,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 )
| ( subset @ SX0 @ SX2 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(676,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(677,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ SX1 @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(678,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ( ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
!= emptyset )
| $false ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(679,plain,
( ( ! [SX0: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(680,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( setminus @ SX0 @ SX1 )
= emptyset ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(681,plain,
( ( ! [SX0: $i > $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(682,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( in @ SX0 @ ( powerset @ SX1 ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(683,plain,
( ( ! [SX0: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(684,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(685,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= emptyset ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(686,plain,
( ( ! [SX0: $i > $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(687,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(688,plain,
( ( ! [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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(689,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[271,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(690,plain,
( ( ! [SX0: $o,SX1: $i] :
( ~ ( in @ SX1 @ ( prop2set @ SX0 ) )
| 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(691,plain,
( ( ! [SX0: $i > $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(692,plain,
( ( ! [SX0: $i] :
( ~ ( singleton @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( ( setunion @ SX0 )
= SX1 ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(693,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setminus @ 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(694,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( 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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(695,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ SX1
| ( ( if @ SX0 @ SX1 @ SX2 @ SX3 )
= 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(696,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( subset @ SX3 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
| ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 ) ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 )
| ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(697,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(698,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i > $o] :
( ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
| ( SX3 @ ( kpair @ SX4 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(699,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(700,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX1: $i] : ( in @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(701,plain,
( ( ! [SX0: $i,SX1: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(702,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 != emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(703,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(704,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(705,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(706,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| ! [SX1: $o] : SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[512,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(707,plain,
( ( ! [SX0: $i,SX1: $i,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)],[318,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(708,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(709,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ( ( setadjoin @ SX0 @ SX2 )
= ( setadjoin @ SX1 @ SX3 ) ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(710,plain,
( ( ! [SX0: $i,SX1: $i > $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(711,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setadjoin @ SX0 @ emptyset )
!= ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(712,plain,
( ( ! [SX0: $i,SX1: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(713,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( 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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(714,plain,
( ( ! [SX0: $i,SX1: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(715,plain,
( ( ! [SX0: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(716,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( if @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX0 ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(717,plain,
( ( ! [SX0: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(718,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(719,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX1 ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(720,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( setadjoin @ SX2 @ emptyset ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(721,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( singleton
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(722,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( in @ SX1 @ ( setadjoin @ SX0 @ 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(723,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(724,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(725,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(726,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(727,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[270,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(728,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ $true ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(729,plain,
( ( ! [SX0: $i,SX1: $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(730,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(731,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(732,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(733,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ( ( binintersect @ SX0 @ SX1 )
= emptyset ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(734,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(735,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX2 )
| ( subset @ SX0 @ ( setadjoin @ SX1 @ 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(736,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(737,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(738,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(739,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( powerset @ SX0 )
= ( powerset @ 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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(740,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(741,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[295,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(742,plain,
( ( ! [SX0: $i,SX1: $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(743,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ ( setadjoin @ SX1 @ emptyset ) @ ( powerset @ SX0 ) ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(744,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(745,plain,
( ( ! [SX0: $i,SX1: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(746,plain,
( ( ! [SX0: $i,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)],[279,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(747,plain,
( ( ! [SX0: $i > $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(748,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(749,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setminus @ SX0 @ SX1 )
!= emptyset )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(750,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ~ SX1
| ( ( if @ SX0 @ SX1 @ SX2 @ SX3 )
= SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(751,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( 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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(752,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( 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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(753,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(754,plain,
( ( ! [SX0: $i > $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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(755,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( binunion @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(756,plain,
( ( ! [SX0: $i,SX1: $i,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)],[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,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(757,plain,
! [SV1: $i] :
( ( ! [SY1866: $i,SY1867: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV1 @ SY1866
@ ^ [Xx: $i,Xy: $i] : ( SY1867 @ Xx @ Xy ) )
@ ( cartprod @ SV1 @ SY1866 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(758,plain,
! [SV2: $i] :
( ( ! [SY1870: $i,SY1871: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV2 @ SY1870
@ ^ [Xx: $i,Xy: $i] : ( SY1871 @ Xx @ Xy ) )
@ ( cartprod @ SV2 @ SY1870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(759,plain,
! [SV3: $i] :
( ( ! [SY1874: $i] :
( ( ksnd @ ( kpair @ SV3 @ SY1874 ) )
= SY1874 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(760,plain,
! [SV4: $i] :
( ( ! [SY1875: $i] :
( ( kfst @ ( kpair @ SV4 @ SY1875 ) )
= SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(761,plain,
! [SV5: $i] :
( ( ( setunion @ ( setadjoin @ SV5 @ emptyset ) )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(762,plain,
! [SV6: $i] :
( ( subset @ SV6 @ ( setunion @ ( setadjoin @ SV6 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(763,plain,
! [SV7: $i] :
( ( subset @ ( setunion @ ( setadjoin @ SV7 @ emptyset ) ) @ SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(764,plain,
! [SV8: $i] :
( ( ! [SY1876: $i] : ( iskpair @ ( kpair @ SV8 @ SY1876 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(765,plain,
! [SV9: $i] :
( ( ! [SY1877: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ SV9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV9 @ ( setadjoin @ SY1877 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(766,plain,
! [SV10: $i] :
( ( ! [SY1878: $i] : ( in @ SY1878 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV10 @ ( setadjoin @ SY1878 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(767,plain,
! [SV11: $i] :
( ( ! [SY1879: $i] : ( in @ SV11 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV11 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV11 @ ( setadjoin @ SY1879 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(768,plain,
! [SV12: $i] :
( ( ! [SY1880: $i] : ( in @ SY1880 @ ( setadjoin @ SV12 @ ( setadjoin @ SY1880 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(769,plain,
! [SV13: $i] :
( ( ! [SY1881: $i] : ( subset @ ( setminus @ SV13 @ SY1881 ) @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(770,plain,
! [SV14: $i] :
( ( ! [SY1882: $i,SY1883: $i] :
( ( binintersect @ SV14 @ ( binunion @ SY1882 @ SY1883 ) )
= ( binunion @ ( binintersect @ SV14 @ SY1882 ) @ ( binintersect @ SV14 @ SY1883 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(771,plain,
! [SV15: $i] :
( ( ! [SY1884: $i] : ( subset @ ( binintersect @ SV15 @ SY1884 ) @ SY1884 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(772,plain,
! [SV16: $i] :
( ( ! [SY1885: $i] : ( subset @ ( binintersect @ SV16 @ SY1885 ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(773,plain,
! [SV17: $i] :
( ( ! [SY1886: $i] : ( subset @ SY1886 @ ( binunion @ SV17 @ SY1886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(774,plain,
! [SV18: $i] :
( ( ! [SY1887: $i] : ( subset @ SV18 @ ( binunion @ SV18 @ SY1887 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(775,plain,
! [SV19: $i] :
( ( ! [SY1888: $i] : ( in @ SY1888 @ ( setadjoin @ SV19 @ ( setadjoin @ SY1888 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(776,plain,
! [SV20: $i] :
( ( ! [SY1889: $i > $o] :
( subset
@ ( dsetconstr @ SV20
@ ^ [Xx: $i] : ( SY1889 @ Xx ) )
@ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(777,plain,
! [SV21: $i] :
( ( ! [SY1891: $i > $o] :
( in
@ ( dsetconstr @ SV21
@ ^ [Xx: $i] : ( SY1891 @ Xx ) )
@ ( powerset @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(778,plain,
! [SV22: $i] :
( ( in @ SV22 @ ( powerset @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(779,plain,
! [SV23: $i] :
( ( ! [SY1893: $i] : ( subset @ SY1893 @ ( setadjoin @ SV23 @ SY1893 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(780,plain,
! [SV24: $i] :
( ( subset @ SV24 @ SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(781,plain,
! [SV25: $i] :
( ( subset @ emptyset @ SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(782,plain,
! [SV26: $i] :
( ( ! [SY1894: $i] : ( in @ SY1894 @ ( setadjoin @ SV26 @ ( setadjoin @ SY1894 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(783,plain,
! [SV27: $i] :
( ( ! [SY1895: $i] : ( in @ SV27 @ ( setadjoin @ SV27 @ ( setadjoin @ SY1895 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(784,plain,
! [SV28: $i] :
( ( in @ emptyset @ ( powerset @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(785,plain,
! [SV29: $i] :
( ( in @ emptyset @ ( powerset @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(786,plain,
! [SV30: $i] :
( ( ( dsetconstr @ SV30
@ ^ [Xx: $i] : $true )
= SV30 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(787,plain,
! [SV31: $i] :
( ( ! [SY1897: $i] : ( in @ SV31 @ ( setadjoin @ SV31 @ SY1897 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(788,plain,
! [SV32: $i] :
( ( ~ ( in @ SV32 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(789,plain,
! [SV33: $i] :
( ( ~ ( in @ SV33 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(790,plain,
! [SV34: $i] :
( ( ! [SY1898: $i,SY1899: $i] :
( ~ ( func @ SV34 @ SY1898 @ SY1899 )
| ( in @ SY1899 @ ( funcSet @ SV34 @ SY1898 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(791,plain,
! [SV35: $i > $o] :
( ( ~ ~ ! [SY1900: $i] :
~ ~ ( ~ ( SV35 @ SY1900 )
| ~ ! [SY1901: $i] :
( ~ ( SV35 @ SY1901 )
| ( SY1900 = SY1901 ) ) )
| ~ ! [SY1902: $i] :
~ ~ ( ~ ( SV35 @ SY1902 )
| ~ ! [SY1903: $i] :
( ~ ( SV35 @ SY1903 )
| ( SY1902 = SY1903 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(792,plain,
! [SV36: $i] :
( ( ! [SY1904: $i] :
( ~ ( in @ SY1904 @ ( powerset @ SV36 ) )
| ! [SY1905: $i] :
( ~ ( in @ SY1905 @ ( powerset @ SV36 ) )
| ~ ( subset @ ( setminus @ SV36 @ SY1905 ) @ ( setminus @ SV36 @ SY1904 ) )
| ( subset @ SY1904 @ SY1905 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(793,plain,
! [SV37: $i] :
( ( ! [SY1906: $i] :
( ~ ( in @ SV37 @ ( setadjoin @ SY1906 @ emptyset ) )
| ( SV37 = SY1906 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(794,plain,
! [SV38: $i] :
( ( ! [SY1907: $i,SY1908: $i] :
( ~ ( func @ SV38 @ SY1907 @ SY1908 )
| ! [SY1909: $i] :
( ~ ( in @ SY1909 @ SV38 )
| ! [SY1910: $i] :
( ~ ( in @ SY1910 @ SY1907 )
| ~ ( in @ ( kpair @ SY1909 @ SY1910 ) @ SY1908 )
| ( ( ap @ SV38 @ SY1907 @ SY1908 @ SY1909 )
= SY1910 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(795,plain,
! [SV39: $i] :
( ( ! [SY1911: $o,SY1912: $i] :
( ~ ( in @ SY1912 @ SV39 )
| ! [SY1913: $i] :
( ~ ( in @ SY1913 @ SV39 )
| ~ SY1911
| ( in @ SY1912
@ ( dsetconstr @ SV39
@ ^ [SX4: $i] :
( ~ ( ~ SY1911
| ( SX4 != SY1912 ) )
| ~ ( ~ ~ SY1911
| ( SX4 != SY1913 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(796,plain,
! [SV40: $i] :
( ( ! [SY1915: $i] :
( ( SV40 != SY1915 )
| ! [SY1916: $i > $o,SY1917: $i > $o] :
( ~ ! [SY1918: $i] :
( ~ ( in @ SY1918 @ SV40 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY1915 )
| ( SY1918 != SX5 )
| ~ ( ~ ( ~ ( SY1916 @ SY1918 )
| ( SY1917 @ SX5 ) )
| ~ ( ~ ( SY1917 @ SX5 )
| ( SY1916 @ SY1918 ) ) ) ) )
| ( ( dsetconstr @ SV40
@ ^ [SX4: $i] : ( SY1916 @ SX4 ) )
= ( dsetconstr @ SY1915
@ ^ [SX4: $i] : ( SY1917 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(797,plain,
! [SV41: $i] :
( ( ! [SY1922: $i > $o] :
( ~ ~ ~ ! [SY1923: $i] :
~ ~ ( ~ ( in @ SY1923 @ SV41 )
| ~ ( SY1922 @ SY1923 ) )
| ! [SY1924: $i] :
( ~ ( in @ SY1924 @ SV41 )
| ~ ( SY1922 @ SY1924 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(798,plain,
! [SV42: $o] :
( ( ~ SV42
| ( set2prop @ ( prop2set @ SV42 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[539]) ).
thf(799,plain,
( ( ~ $true
| ( set2prop @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[539]) ).
thf(800,plain,
( ( ~ $false
| ( set2prop @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[539]) ).
thf(801,plain,
! [SV43: $i] :
( ( ! [SY1925: $i,SY1926: $i] :
( ~ ~ ( in @ SY1926 @ SV43 )
| ~ ( in @ SY1926 @ ( setminus @ SV43 @ SY1925 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(802,plain,
! [SV44: $i > $o] :
( ( ~ ~ ! [SY1927: $i] :
~ ! [SY1928: $i] :
~ ( ~ ( ~ ( SV44 @ SY1928 )
| ( SY1928 = SY1927 ) )
| ~ ( ( SY1928 != SY1927 )
| ( SV44 @ SY1928 ) ) )
| ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(803,plain,
! [SV45: $i] :
( ( ! [SY1931: $i,SY1932: $i] :
( ~ ( in @ SY1932 @ ( setminus @ SV45 @ SY1931 ) )
| ~ ( in @ SY1932 @ SY1931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(804,plain,
! [SV46: $i] :
( ( ! [SY1933: $i,SY1934: $i] :
( ~ ( in @ SY1934 @ SV46 )
| ! [SY1935: $i] :
( ~ ( in @ SY1935 @ SY1933 )
| ( in @ ( kpair @ SY1934 @ SY1935 ) @ ( cartprod @ SV46 @ SY1933 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(805,plain,
! [SV47: $i] :
( ( ! [SY1936: $i,SY1937: $i] :
~ ( ~ ( ~ ( in @ SY1937 @ ( setadjoin @ SV47 @ SY1936 ) )
| ( SY1937 = SV47 )
| ( in @ SY1937 @ SY1936 ) )
| ~ ( ~ ( ( SY1937 = SV47 )
| ( in @ SY1937 @ SY1936 ) )
| ( in @ SY1937 @ ( setadjoin @ SV47 @ SY1936 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(806,plain,
! [SV48: $o] :
( ( ~ SV48
| ( in @ emptyset @ ( prop2set @ SV48 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[545]) ).
thf(807,plain,
( ( ~ $true
| ( in @ emptyset @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[545]) ).
thf(808,plain,
( ( ~ $false
| ( in @ emptyset @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[545]) ).
thf(809,plain,
! [SV49: $i] :
( ( ! [SY1938: $i] :
( ~ ( in @ SY1938 @ ( powerset @ SV49 ) )
| ( in @ ( setminus @ SV49 @ SY1938 ) @ ( powerset @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(810,plain,
! [SV50: $i] :
( ( ! [SY1939: $i,SY1940: $i] :
( ~ ( in @ SY1940 @ ( setminus @ SV50 @ SY1939 ) )
| ( in @ SY1940 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(811,plain,
! [SV51: $i] :
( ( ! [SY1941: $i,SY1942: $i] :
( ~ ( func @ SV51 @ SY1941 @ SY1942 )
| ! [SY1943: $i] :
( ~ ( in @ SY1943 @ SV51 )
| ( singleton
@ ( dsetconstr @ SY1941
@ ^ [SX4: $i] : ( in @ ( kpair @ SY1943 @ SX4 ) @ SY1942 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(812,plain,
! [SV52: $i] :
( ( ! [SY1945: $i] :
( ~ ( in @ SY1945 @ ( powerset @ SV52 ) )
| ( subset @ SY1945 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(813,plain,
! [SV53: $i] :
( ( ~ ( singleton @ SV53 )
| ( in @ ( setunion @ SV53 ) @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(814,plain,
! [SV54: $i] :
( ( ~ ( iskpair @ SV54 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SV54 )
@ ^ [SY1946: $i] :
( SV54
= ( kpair @ ( kfst @ SV54 ) @ SY1946 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(815,plain,
! [SV55: $i] :
( ( ! [SY1947: $i,SY1948: $i] :
( ~ ( in @ SY1948 @ SV55 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1947 )
| ( ( kpair @ SY1948 @ SX3 )
= ( kpair @ SY1948 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(816,plain,
! [SV56: $i] :
( ( ! [SY1950: $i,SY1951: $i] :
( ~ ( in @ SY1951 @ SV56 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1950 )
| ( ( ksnd @ ( kpair @ SY1951 @ SX3 ) )
= SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(817,plain,
! [SV57: $i] :
( ( ! [SY1953: $i,SY1954: $i] :
( ~ ( func @ SV57 @ SY1953 @ SY1954 )
| ! [SY1955: $i] :
( ~ ( in @ SY1955 @ SV57 )
| ( in @ ( kpair @ SY1955 @ ( ap @ SV57 @ SY1953 @ SY1954 @ SY1955 ) ) @ SY1954 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(818,plain,
! [SV58: $i] :
( ( ! [SY1956: $i,SY1957: $i] :
( ~ ( in @ SY1957 @ ( cartprod @ SV58 @ SY1956 ) )
| ( in @ ( kfst @ SY1957 ) @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(819,plain,
! [SV59: $i] :
( ( ! [SY1958: $i,SY1959: $i] :
( ( ( setadjoin @ SV59 @ ( setadjoin @ SY1958 @ emptyset ) )
!= ( setadjoin @ SY1959 @ emptyset ) )
| ( SV59 = SY1958 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(820,plain,
! [SV60: $i] :
( ( ! [SY1960: $o,SY1961: $i] :
( ~ ( in @ SY1961 @ SV60 )
| ! [SY1962: $i] :
( ~ ( in @ SY1962 @ SV60 )
| ( singleton
@ ( dsetconstr @ SV60
@ ^ [SX4: $i] :
( ~ ( ~ SY1960
| ( SX4 != SY1961 ) )
| ~ ( ~ ~ SY1960
| ( SX4 != SY1962 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(821,plain,
! [SV61: $i] :
( ( ! [SY1964: $i,SY1965: $i] :
( ~ ( in @ SY1965 @ ( funcSet @ SV61 @ SY1964 ) )
| ( func @ SV61 @ SY1964 @ SY1965 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(822,plain,
! [SV62: $i] :
( ( ! [SY1966: $i,SY1967: $i] :
( ~ ( in @ SY1967 @ SV62 )
| ~ ( in @ SY1967 @ SY1966 )
| ( in @ SY1967 @ ( binintersect @ SV62 @ SY1966 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(823,plain,
! [SV63: $i] :
( ( ! [SY1968: $i,SY1969: $i] :
( ~ ( subset @ SY1969 @ SV63 )
| ~ ( subset @ SY1969 @ SY1968 )
| ( subset @ SY1969 @ ( binintersect @ SV63 @ SY1968 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(824,plain,
! [SV64: $i] :
( ( ! [SY1970: $i] :
( ~ ( in @ SY1970 @ ( powerset @ SV64 ) )
| ! [SY1971: $i] :
( ~ ( in @ SY1971 @ ( powerset @ SV64 ) )
| ! [SY1972: $i] :
( ~ ( in @ SY1972 @ SV64 )
| ~ ( in @ SY1972 @ ( setminus @ SV64 @ SY1970 ) )
| ~ ( in @ SY1972 @ ( binintersect @ SY1970 @ SY1971 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(825,plain,
! [SV65: $i] :
( ( ! [SY1973: $i,SY1974: $i] :
( ~ ( in @ SY1974 @ ( binintersect @ SV65 @ SY1973 ) )
| ( in @ SY1974 @ SY1973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(826,plain,
! [SV66: $i] :
( ( ! [SY1975: $i] :
( ~ ( in @ SY1975 @ ( powerset @ SV66 ) )
| ! [SY1976: $i] :
( ~ ( in @ SY1976 @ ( powerset @ SV66 ) )
| ! [SY1977: $i] :
( ~ ( in @ SY1977 @ SV66 )
| ~ ~ ( in @ SY1977 @ ( binunion @ SY1975 @ SY1976 ) )
| ~ ( in @ SY1977 @ SY1976 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(827,plain,
! [SV67: $i] :
( ( ! [SY1978: $i,SY1979: $i] :
( ~ ( func @ SV67 @ SY1978 @ SY1979 )
| ! [SY1980: $i] :
( ~ ( in @ SY1980 @ SV67 )
| ( ( ap @ SV67 @ SY1978 @ SY1979 @ SY1980 )
= ( ap @ SV67 @ SY1978 @ SY1979 @ SY1980 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(828,plain,
! [SV68: $i] :
( ( ! [SY1981: $i,SY1982: $i] :
( ~ ( in @ SY1982 @ SY1981 )
| ~ ( in @ SY1982 @ ( setminus @ SV68 @ SY1981 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(829,plain,
! [SV69: $i] :
( ( ! [SY1983: $i] :
~ ( ~ ( ~ ( in @ SY1983 @ ( setunion @ SV69 ) )
| ~ ! [SY1984: $i] :
~ ~ ( ~ ( in @ SY1983 @ SY1984 )
| ~ ( in @ SY1984 @ SV69 ) ) )
| ~ ( ~ ~ ! [SY1985: $i] :
~ ~ ( ~ ( in @ SY1983 @ SY1985 )
| ~ ( in @ SY1985 @ SV69 ) )
| ( in @ SY1983 @ ( setunion @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(830,plain,
! [SV70: $i] :
( ( ! [SY1986: $i] :
( ~ ( in @ SY1986 @ ( powerset @ SV70 ) )
| ! [SY1987: $i] :
( ~ ( in @ SY1987 @ ( powerset @ SV70 ) )
| ! [SY1988: $i] :
( ~ ( in @ SY1988 @ SV70 )
| ~ ( in @ SY1988 @ ( setminus @ SV70 @ ( binunion @ SY1986 @ SY1987 ) ) )
| ~ ( in @ SY1988 @ SY1986 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(831,plain,
! [SV71: $i] :
( ( ! [SY1989: $i] :
( ~ ! [SY1990: $i] :
( ~ ( in @ SY1990 @ SV71 )
| ( in @ SY1990 @ SY1989 ) )
| ( subset @ SV71 @ SY1989 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(832,plain,
! [SV72: $i] :
( ( ! [SY1991: $i > $o,SY1992: $i] :
( ~ ( in @ SY1992
@ ( dsetconstr @ SV72
@ ^ [SX3: $i] : ( SY1991 @ SX3 ) ) )
| ( SY1991 @ SY1992 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(833,plain,
! [SV73: $i] :
( ( ! [SY1994: $i] :
( ~ ( in @ SY1994 @ ( powerset @ SV73 ) )
| ! [SY1995: $i] :
( ~ ( in @ SY1995 @ ( powerset @ SV73 ) )
| ~ ! [SY1996: $i] :
( ~ ( in @ SY1996 @ SV73 )
| ~ ( in @ SY1996 @ SY1994 )
| ( in @ SY1996 @ SY1995 ) )
| ( in @ SY1994 @ ( powerset @ SY1995 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(834,plain,
! [SV74: $i] :
( ( ! [SY1997: $i,SY1998: $i] :
( ~ ( in @ SY1998 @ ( symdiff @ SV74 @ SY1997 ) )
| ! [SY1999: $o] :
( ~ ( ~ ( in @ SY1998 @ SV74 )
| ~ ~ ( in @ SY1998 @ SY1997 )
| SY1999 )
| ~ ( ~ ~ ( in @ SY1998 @ SV74 )
| ~ ( in @ SY1998 @ SY1997 )
| SY1999 )
| SY1999 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(835,plain,
! [SV75: $i] :
( ( ~ ! [SY2000: $i] :
~ ( in @ SY2000 @ SV75 )
| ( SV75 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(836,plain,
! [SV76: $i] :
( ( ! [SY2001: $i,SY2002: $i] :
( ~ ( subset @ SV76 @ SY2001 )
| ~ ~ ( in @ SY2002 @ SY2001 )
| ~ ( in @ SY2002 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(837,plain,
! [SV77: $i] :
( ( ! [SY2003: $i,SY2004: $i > $i > $o,SY2005: $i,SY2006: $i] :
( ~ ( in @ ( kpair @ SY2005 @ SY2006 )
@ ( dpsetconstr @ SV77 @ SY2003
@ ^ [SX5: $i,SX6: $i] : ( SY2004 @ SX5 @ SX6 ) ) )
| ( in @ SY2006 @ SY2003 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(838,plain,
! [SV78: $i] :
( ( ~ ( ( SV78 != emptyset ) )
| ~ ! [SY2009: $i] :
~ ( in @ SY2009 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(839,plain,
! [SV79: $i] :
( ( ! [SY2010: $i > $o] :
( ~ ~ ~ ! [SY2011: $i] :
~ ~ ( ~ ( in @ SY2011 @ SV79 )
| ~ ( SY2010 @ SY2011 ) )
| ! [SY2012: $i] :
( ~ ( in @ SY2012 @ SV79 )
| ~ ( SY2010 @ SY2012 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(840,plain,
! [SV80: $i] :
( ( ! [SY2013: $i,SY2014: $i] :
( ~ ( in @ SY2014 @ SV80 )
| ( in @ SY2014 @ ( binunion @ SV80 @ SY2013 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(841,plain,
! [SV81: $i] :
( ( ! [SY2015: $i] :
( ~ ( in @ SY2015 @ SV81 )
| ( in @ SY2015 @ ( powerset @ ( setunion @ SV81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(842,plain,
! [SV82: $i] :
( ( ~ ~ ! [SY2016: $i] :
~ ( in @ SY2016 @ SV82 )
| ~ ! [SY2017: $i] :
~ ~ ( ~ ( in @ SY2017 @ SV82 )
| ~ ~ ~ ! [SY2018: $i] :
~ ~ ( ~ ( in @ SY2018 @ SY2017 )
| ~ ( in @ SY2018 @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(843,plain,
! [SV83: $i] :
( ( ! [SY2019: $i] :
( ( ( binintersect @ SV83 @ SY2019 )
!= SV83 )
| ( subset @ SV83 @ SY2019 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(844,plain,
! [SV84: $i] :
( ( ! [SY2020: $i,SY2021: $i,SY2022: $o] :
( ~ ( in @ SY2021 @ ( binunion @ SV84 @ SY2020 ) )
| ~ ( ~ ( in @ SY2021 @ SV84 )
| SY2022 )
| ~ ( ~ ( in @ SY2021 @ SY2020 )
| SY2022 )
| SY2022 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(845,plain,
! [SV85: $i] :
( ( ! [SY2023: $i] :
( ~ ( in @ SY2023 @ ( powerset @ SV85 ) )
| ! [SY2024: $i] :
( ~ ( in @ SY2024 @ ( powerset @ SV85 ) )
| ! [SY2025: $i] :
( ~ ( in @ SY2025 @ SV85 )
| ~ ~ ( in @ SY2025 @ ( binunion @ SY2023 @ SY2024 ) )
| ~ ( in @ SY2025 @ SY2023 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(846,plain,
! [SV86: $i > $o] :
( ( ! [SY2026: $i] :
( ~ ( in @ SY2026 @ emptyset )
| ( SV86 @ SY2026 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(847,plain,
! [SV87: $i] :
( ( ! [SY2027: $i > $o] :
( ~ ~ ! [SY2028: $i] :
( ~ ( in @ SY2028 @ SV87 )
| ( SY2027 @ SY2028 ) )
| ~ ! [SY2029: $i] :
~ ~ ( ~ ( in @ SY2029 @ SV87 )
| ~ ~ ( SY2027 @ SY2029 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(848,plain,
! [SV88: $i] :
( ( ! [SY2030: $i] :
( ~ ! [SY2031: $i] :
( ~ ( in @ SY2031 @ SV88 )
| ( in @ SY2031 @ SY2030 ) )
| ~ ! [SY2032: $i] :
( ~ ( in @ SY2032 @ SY2030 )
| ( in @ SY2032 @ SV88 ) )
| ( SV88 = SY2030 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(849,plain,
! [SV89: $i] :
( ( ! [SY2033: $i] :
( ( SV89 != SY2033 )
| ( subset @ SV89 @ SY2033 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(850,plain,
! [SV90: $i] :
( ( ! [SY2034: $i] :
( ~ ( in @ SY2034 @ ( powerset @ SV90 ) )
| ( in @ ( powerset @ SY2034 ) @ ( powerset @ ( powerset @ SV90 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(851,plain,
! [SV91: $i > $o] :
( ( ~ ~ ! [SY2035: $i] :
~ ~ ( ~ ( SV91 @ SY2035 )
| ~ ! [SY2036: $i] :
( ~ ( SV91 @ SY2036 )
| ( SY2035 = SY2036 ) ) )
| ! [SY2037: $i,SY2038: $i] :
( ~ ( SV91 @ SY2037 )
| ~ ( SV91 @ SY2038 )
| ( SY2037 = SY2038 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(852,plain,
! [SV92: $i] :
( ( ! [SY2039: $i,SY2040: $i] :
( ~ ( func @ SV92 @ SY2039 @ SY2040 )
| ! [SY2041: $i] :
( ~ ( in @ SY2041 @ SV92 )
| ( in
@ ( setunion
@ ( dsetconstr @ SY2039
@ ^ [SX4: $i] : ( in @ ( kpair @ SY2041 @ SX4 ) @ SY2040 ) ) )
@ SY2039 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(853,plain,
! [SV93: $i] :
( ( ! [SY2043: $i] :
( ( SV93 != SY2043 )
| ( ( setadjoin @ ( setadjoin @ SV93 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV93 @ ( setadjoin @ SY2043 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV93 @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(854,plain,
! [SV94: $i] :
( ( ! [SY2044: $i,SY2045: $i] :
( ~ ( in @ SY2045 @ SV94 )
| ~ ~ ( in @ SY2045 @ SY2044 )
| ~ ( subset @ SV94 @ SY2044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(855,plain,
! [SV95: $i] :
( ( ! [SY2046: $i,SY2047: $i] :
( ~ ( subset @ SY2047 @ ( cartprod @ SV95 @ SY2046 ) )
| ! [SY2048: $i] :
( ~ ( subset @ SY2048 @ ( cartprod @ SV95 @ SY2046 ) )
| ~ ! [SY2049: $i] :
( ~ ( in @ SY2049 @ SV95 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2046 )
| ~ ( in @ ( kpair @ SY2049 @ SX5 ) @ SY2047 )
| ( in @ ( kpair @ SY2049 @ SX5 ) @ SY2048 ) ) )
| ( subset @ SY2047 @ SY2048 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(856,plain,
! [SV96: $i] :
( ( ! [SY2051: $i] :
( ~ ( in @ SY2051 @ ( setunion @ SV96 ) )
| ~ ! [SY2052: $i] :
~ ~ ( ~ ( in @ SY2052 @ SV96 )
| ~ ( in @ SY2051 @ SY2052 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(857,plain,
! [SV97: $i] :
( ( ! [SY2053: $i] :
( ~ ( in @ SY2053 @ ( powerset @ SV97 ) )
| ! [SY2054: $i] :
( ~ ( in @ SY2054 @ SV97 )
| ~ ~ ( in @ SY2054 @ ( setminus @ SV97 @ SY2053 ) )
| ( in @ SY2054 @ SY2053 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(858,plain,
! [SV98: $i] :
( ( ! [SY2055: $i > $o,SY2056: $i] :
( ~ ( in @ SY2056 @ SV98 )
| ~ ( ~ ( ~ ( in @ SY2056
@ ( dsetconstr @ SV98
@ ^ [SX3: $i] : ( SY2055 @ SX3 ) ) )
| ( SY2055 @ SY2056 ) )
| ~ ( ~ ( SY2055 @ SY2056 )
| ( in @ SY2056
@ ( dsetconstr @ SV98
@ ^ [SX3: $i] : ( SY2055 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(859,plain,
! [SV99: $i] :
( ( ! [SY2059: $i] :
( ~ ! [SY2060: $i] :
( ~ ( in @ SY2060 @ SY2059 )
| ( in @ SY2060 @ SV99 ) )
| ( in @ SY2059 @ ( powerset @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(860,plain,
! [SV100: $i] :
( ( ! [SY2061: $i > $o,SY2062: $i] :
( ~ ( in @ SY2062 @ SV100 )
| ~ ( SY2061 @ SY2062 )
| ~ ! [SY2063: $i] :
( ~ ( in @ SY2063 @ SV100 )
| ~ ( SY2061 @ SY2063 )
| ( SY2063 = SY2062 ) )
| ( singleton
@ ( dsetconstr @ SV100
@ ^ [SX3: $i] : ( SY2061 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(861,plain,
! [SV101: $i] :
( ( ! [SY2065: $i,SY2066: $i > $i > $o,SY2067: $i,SY2068: $i] :
( ~ ( in @ ( kpair @ SY2067 @ SY2068 )
@ ( dpsetconstr @ SV101 @ SY2065
@ ^ [SX5: $i,SX6: $i] : ( SY2066 @ SX5 @ SX6 ) ) )
| ( SY2066 @ SY2067 @ SY2068 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(862,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 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(863,plain,
! [SV102: $i] :
( ( ! [SY2071: $i] :
( ~ ( in @ SV102 @ ( setadjoin @ SY2071 @ emptyset ) )
| ( in @ SY2071 @ ( setadjoin @ SV102 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(864,plain,
! [SV103: $i] :
( ( ! [SY2072: $i,SY2073: $i] :
( ~ ( in @ SY2073 @ ( funcSet @ SV103 @ SY2072 ) )
| ( ( lam @ SV103 @ SY2072
@ ^ [SY2074: $i] : ( ap @ SV103 @ SY2072 @ SY2073 @ SY2074 ) )
= SY2073 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(865,plain,
! [SV104: $i] :
( ( ! [SY2075: $i,SY2076: $i] :
( ~ ( in @ SY2076 @ SV104 )
| ! [SY2077: $i] :
( ~ ( in @ SY2077 @ SY2075 )
| ( subset @ ( setadjoin @ SY2076 @ ( setadjoin @ SY2077 @ emptyset ) ) @ ( binunion @ SV104 @ SY2075 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(866,plain,
! [SV105: $i] :
( ( ! [SY2078: $i,SY2079: $i] :
( ~ ( subset @ SY2079 @ ( cartprod @ SV105 @ SY2078 ) )
| ! [SY2080: $i > $o] :
( ~ ! [SY2081: $i] :
( ~ ( in @ SY2081 @ SV105 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2078 )
| ~ ( in @ ( kpair @ SY2081 @ SX5 ) @ SY2079 )
| ( SY2080 @ ( kpair @ SY2081 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2079 )
| ( SY2080 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(867,plain,
! [SV106: $i > $o] :
( ( ~ ~ ! [SY2084: $i] :
~ ~ ( ~ ( SV106 @ SY2084 )
| ~ ! [SY2085: $i] :
( ~ ( SV106 @ SY2085 )
| ( SY2084 = SY2085 ) ) )
| ! [SY2086: $i,SY2087: $i] :
( ~ ( SV106 @ SY2086 )
| ~ ( SV106 @ SY2087 )
| ( SY2086 = SY2087 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(868,plain,
! [SV107: $i] :
( ( ! [SY2088: $i > $o,SY2089: $i] :
( ~ ( in @ SY2089 @ SV107 )
| ~ ( SY2088 @ SY2089 )
| ( in @ SY2089
@ ( dsetconstr @ SV107
@ ^ [SX3: $i] : ( SY2088 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(869,plain,
! [SV108: $i > $o] :
( ( ~ ~ ! [SY2091: $i] :
~ ~ ( ~ ( SV108 @ SY2091 )
| ~ ! [SY2092: $i] :
( ~ ( SV108 @ SY2092 )
| ( SY2091 = SY2092 ) ) )
| ( SV108
@ ( descr
@ ^ [SY2093: $i] : ( SV108 @ SY2093 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(870,plain,
! [SV109: $i] :
( ( ! [SY2094: $i,SY2095: $i > $i > $o,SY2096: $i,SY2097: $i] :
( ~ ( in @ ( kpair @ SY2096 @ SY2097 )
@ ( dpsetconstr @ SV109 @ SY2094
@ ^ [SX5: $i,SX6: $i] : ( SY2095 @ SX5 @ SX6 ) ) )
| ( in @ SY2096 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(871,plain,
! [SV110: $i] :
( ( ! [SY2100: $i] :
( ~ ( subset @ SV110 @ SY2100 )
| ( ( binintersect @ SV110 @ SY2100 )
= SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(872,plain,
! [SV111: $i] :
( ( ~ ! [SY2101: $i] :
~ ( in @ SY2101 @ SV111 )
| ( SV111 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(873,plain,
! [SV112: $i] :
( ( ! [SY2102: $i] :
( ~ ( subset @ SY2102 @ SV112 )
| ( ( binintersect @ SV112 @ SY2102 )
= SY2102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(874,plain,
! [SV113: $i] :
( ( ! [SY2103: $i,SY2104: $i] :
( ~ ~ ( in @ SY2104 @ ( setminus @ SV113 @ SY2103 ) )
| ~ ~ ( in @ SY2104 @ SY2103 )
| ~ ( in @ SY2104 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(875,plain,
! [SV114: $i > $o] :
( ( ~ ~ ! [SY2105: $i] :
~ ~ ( ~ ( SV114 @ SY2105 )
| ~ ! [SY2106: $i] :
( ~ ( SV114 @ SY2106 )
| ( SY2105 = SY2106 ) ) )
| ~ ! [SY2107: $i] :
~ ( SV114 @ SY2107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(876,plain,
! [SV115: $i] :
( ( ! [SY2108: $i] :
( ~ ( in @ SY2108 @ ( powerset @ SV115 ) )
| ! [SY2109: $i] :
( ~ ( in @ SY2109 @ ( powerset @ SV115 ) )
| ! [SY2110: $i] :
( ~ ( in @ SY2110 @ ( powerset @ SV115 ) )
| ! [SY2111: $i] :
( ~ ( in @ SY2111 @ SV115 )
| ~ ( in @ SY2111 @ ( binintersect @ SY2108 @ SY2109 ) )
| ( in @ SY2111 @ ( binunion @ SY2108 @ SY2110 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(877,plain,
! [SV116: $i] :
( ( ~ ( iskpair @ SV116 )
| ( ( kpair @ ( kfst @ SV116 ) @ ( ksnd @ SV116 ) )
= SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(878,plain,
! [SV117: $i] :
( ( ! [SY2112: $i] :
( ~ ( in @ SY2112 @ ( powerset @ SV117 ) )
| ! [SY2113: $i] :
( ~ ( in @ SY2113 @ ( powerset @ SV117 ) )
| ( in @ ( binintersect @ SY2112 @ SY2113 ) @ ( powerset @ SV117 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(879,plain,
! [SV118: $i] :
( ( ! [SY2114: $i > $o] :
( ~ ! [SY2115: $i] :
( ~ ( in @ SY2115 @ SV118 )
| ~ ( SY2114 @ SY2115 ) )
| ~ ~ ! [SY2116: $i] :
~ ~ ( ~ ( in @ SY2116 @ SV118 )
| ~ ( SY2114 @ SY2116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(880,plain,
! [SV119: $i] :
( ( ! [SY2117: $i > $o] :
( ~ ~ ! [SY2118: $i] :
( ~ ( in @ SY2118 @ SV119 )
| ( SY2117 @ SY2118 ) )
| ~ ! [SY2119: $i] :
~ ~ ( ~ ( in @ SY2119 @ SV119 )
| ~ ~ ( SY2117 @ SY2119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(881,plain,
! [SV120: $i] :
( ( ! [SY2120: $i] :
( ~ ( in @ SY2120 @ ( powerset @ SV120 ) )
| ! [SY2121: $i] :
( ~ ( in @ SY2121 @ ( powerset @ SV120 ) )
| ! [SY2122: $i] :
( ~ ( in @ SY2122 @ SV120 )
| ~ ~ ( in @ SY2122 @ SY2121 )
| ~ ( in @ SY2122 @ ( binintersect @ SY2120 @ SY2121 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(882,plain,
! [SV121: $i] :
( ( ! [SY2123: $i] :
( ~ ( in @ SY2123 @ ( powerset @ SV121 ) )
| ! [SY2124: $i] :
( ~ ( in @ SY2124 @ ( powerset @ SV121 ) )
| ~ ( subset @ SY2123 @ ( setminus @ SV121 @ SY2124 ) )
| ! [SY2125: $i] :
( ~ ( in @ SY2125 @ SV121 )
| ~ ( in @ SY2125 @ SY2124 )
| ( in @ SY2125 @ ( setminus @ SV121 @ SY2123 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(883,plain,
! [SV122: $i] :
( ( ! [SY2126: $i] :
( ~ ~ ( subset @ SV122 @ SY2126 )
| ( SV122 != SY2126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(884,plain,
! [SV123: $i] :
( ( ! [SY2127: $i,SY2128: $i > $i] :
( ~ ! [SY2129: $i] :
( ~ ( in @ SY2129 @ SV123 )
| ( in @ ( SY2128 @ SY2129 ) @ SY2127 ) )
| ( in
@ ( lam @ SV123 @ SY2127
@ ^ [SX3: $i] : ( SY2128 @ SX3 ) )
@ ( funcSet @ SV123 @ SY2127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(885,plain,
! [SV124: $i] :
( ( ! [SY2131: $i,SY2132: $i] :
( ~ ( in @ SY2131 @ SY2132 )
| ~ ( in @ SY2132 @ SV124 )
| ( in @ SY2131 @ ( setunion @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(886,plain,
! [SV125: $i] :
( ( ! [SY2133: $i,SY2134: $i] :
( ~ ( in @ ( setadjoin @ SY2134 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV125 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV125 @ ( setadjoin @ SY2133 @ emptyset ) ) @ emptyset ) ) )
| ( SV125 = SY2134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(887,plain,
! [SV126: $i] :
( ( ! [SY2135: $i,SY2136: $i] :
( ~ ( in @ SY2136 @ ( setadjoin @ SV126 @ SY2135 ) )
| ! [SY2137: $o] :
( ~ ( ( SY2136 != SV126 )
| SY2137 )
| ~ ( ~ ( in @ SY2136 @ SY2135 )
| SY2137 )
| SY2137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(888,plain,
! [SV127: $i] :
( ( ! [SY2138: $i,SY2139: $i] :
( ~ ~ ( in @ SY2139 @ SV127 )
| ~ ~ ( in @ SY2139 @ SY2138 )
| ~ ( in @ SY2139 @ ( symdiff @ SV127 @ SY2138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(889,plain,
! [SV128: $i] :
( ( ! [SY2140: $i,SY2141: $i] :
( ~ ( in @ SY2141 @ SV128 )
| ! [SY2142: $i] :
( ~ ( in @ SY2142 @ SY2140 )
| ( in @ ( setadjoin @ SY2141 @ ( setadjoin @ SY2142 @ emptyset ) ) @ ( powerset @ ( binunion @ SV128 @ SY2140 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(890,plain,
! [SV129: $i] :
( ( ! [SY2143: $i] :
( ~ ( in @ SY2143 @ ( powerset @ SV129 ) )
| ! [SY2144: $i] :
( ~ ( in @ SY2144 @ ( powerset @ SV129 ) )
| ~ ( subset @ SY2143 @ ( setminus @ SV129 @ SY2144 ) )
| ( subset @ SY2144 @ ( setminus @ SV129 @ SY2143 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(891,plain,
! [SV130: $i] :
( ( ! [SY2145: $i] :
( ~ ( in @ SY2145 @ ( powerset @ SV130 ) )
| ! [SY2146: $i] :
( ~ ( in @ SY2146 @ ( powerset @ SV130 ) )
| ! [SY2147: $i] :
( ~ ( in @ SY2147 @ SV130 )
| ~ ~ ( in @ SY2147 @ SY2145 )
| ~ ( in @ SY2147 @ ( binintersect @ SY2145 @ SY2146 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(892,plain,
! [SV131: $i] :
( ( ! [SY2148: $i] :
( ~ ( in @ SY2148 @ ( powerset @ SV131 ) )
| ! [SY2149: $i] :
( ~ ( in @ SY2149 @ ( powerset @ SV131 ) )
| ! [SY2150: $i] :
( ~ ( in @ SY2150 @ SV131 )
| ~ ( in @ SY2150 @ ( setminus @ SV131 @ SY2148 ) )
| ( in @ SY2150 @ ( setminus @ SV131 @ ( binintersect @ SY2148 @ SY2149 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(893,plain,
! [SV132: $i] :
( ( ! [SY2151: $i,SY2152: $i] :
( ~ ( in @ SY2152 @ ( cartprod @ SV132 @ SY2151 ) )
| ( in @ ( ksnd @ SY2152 ) @ SY2151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(894,plain,
! [SV133: $i] :
( ( ! [SY2153: $i] :
( ~ ( in @ SY2153 @ ( powerset @ SV133 ) )
| ! [SY2154: $i] :
( ~ ( in @ SY2154 @ SV133 )
| ~ ( in @ SY2154 @ SY2153 )
| ( in @ SY2154 @ ( setminus @ SV133 @ ( setminus @ SV133 @ SY2153 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(895,plain,
! [SV134: $i] :
( ( ! [SY2155: $i,SY2156: $i] :
( ~ ( func @ SV134 @ SY2155 @ SY2156 )
| ( ( lam @ SV134 @ SY2155
@ ^ [SY2157: $i] : ( ap @ SV134 @ SY2155 @ SY2156 @ SY2157 ) )
= SY2156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(896,plain,
! [SV135: $i] :
( ( ! [SY2158: $i > $o] :
( ~ ( singleton
@ ( dsetconstr @ SV135
@ ^ [SX2: $i] : ( SY2158 @ SX2 ) ) )
| ! [SY2160: $i] :
( ~ ( in @ SY2160 @ SV135 )
| ! [SY2161: $i] :
( ~ ( in @ SY2161 @ SV135 )
| ~ ( SY2158 @ SY2160 )
| ~ ( SY2158 @ SY2161 )
| ( SY2160 = SY2161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(897,plain,
! [SV136: $i] :
( ( ! [SY2162: $i] :
( ~ ( in @ SY2162 @ ( setunion @ SV136 ) )
| ! [SY2163: $o] :
( ~ ! [SY2164: $i] :
( ~ ( in @ SY2162 @ SY2164 )
| ~ ( in @ SY2164 @ SV136 )
| SY2163 )
| SY2163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(898,plain,
! [SV137: $i] :
( ( ! [SY2165: $i] :
( ~ ( in @ SY2165 @ ( powerset @ SV137 ) )
| ! [SY2166: $i] :
( ~ ( in @ SY2166 @ ( powerset @ SV137 ) )
| ! [SY2167: $i] :
( ~ ( in @ SY2167 @ SV137 )
| ~ ( subset @ SY2165 @ SY2166 )
| ~ ~ ( in @ SY2167 @ SY2166 )
| ~ ( in @ SY2167 @ SY2165 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(899,plain,
! [SV138: $i] :
( ( ! [SY2168: $i,SY2169: $i] :
( ~ ( in @ SY2169 @ ( setadjoin @ SV138 @ ( setadjoin @ SY2168 @ emptyset ) ) )
| ( SY2169 = SV138 )
| ( SY2169 = SY2168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(900,plain,
! [SV139: $i] :
( ( ~ ( in @ SV139 @ emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(901,plain,
! [SV140: $i] :
( ( ! [SY2170: $i,SY2171: $i] :
( ~ ( in @ SY2171 @ ( cartprod @ SV140 @ SY2170 ) )
| ( iskpair @ SY2171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(902,plain,
! [SV141: $i] :
( ( ! [SY2172: $i,SY2173: $i] :
( ~ ( in @ SY2173 @ SY2172 )
| ( in @ SY2173 @ ( setadjoin @ SV141 @ SY2172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(903,plain,
! [SV142: $i] :
( ( ! [SY2174: $i,SY2175: $i,SY2176: $i] :
( ~ ( in @ ( kpair @ SY2175 @ SY2176 ) @ ( cartprod @ SV142 @ SY2174 ) )
| ( in @ SY2176 @ SY2174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(904,plain,
! [SV143: $i] :
( ( ! [SY2177: $i,SY2178: $i] :
( ~ ( in @ SY2178 @ ( funcSet @ SV143 @ SY2177 ) )
| ! [SY2179: $i] :
( ~ ( in @ SY2179 @ SV143 )
| ( in @ ( kpair @ SY2179 @ ( ap @ SV143 @ SY2177 @ SY2178 @ SY2179 ) ) @ SY2178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(905,plain,
! [SV144: $i] :
( ( ! [SY2180: $i] :
( ~ ( subset @ SV144 @ SY2180 )
| ( subset @ ( powerset @ SV144 ) @ ( powerset @ SY2180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(906,plain,
! [SV145: $i] :
( ( ! [SY2181: $i,SY2182: $i] :
( ~ ( in @ SY2182 @ ( cartprod @ SV145 @ SY2181 ) )
| ( ( kpair @ ( kfst @ SY2182 ) @ ( ksnd @ SY2182 ) )
= SY2182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(907,plain,
! [SV146: $i] :
( ( ! [SY2183: $i] :
( ~ ( in @ SY2183 @ ( powerset @ SV146 ) )
| ! [SY2184: $i] :
( ~ ( in @ SY2184 @ ( powerset @ SV146 ) )
| ~ ! [SY2185: $i] :
( ~ ( in @ SY2185 @ SV146 )
| ~ ( in @ SY2185 @ SY2183 )
| ( in @ SY2185 @ SY2184 ) )
| ( subset @ SY2183 @ SY2184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(908,plain,
! [SV147: $i] :
( ( ~ ! [SY2186: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY2187: $i] :
( ~ ( in @ SY2187 @ SY2186 )
| ! [SY2188: $i] :
( ~ ( in @ SY2188 @ SY2187 )
| ( in @ SY2188 @ SV147 ) ) )
| ~ ! [SY2189: $i,SY2190: $i] :
( ~ ~ ( ~ ( in @ SY2189 @ SV147 )
| ~ ( in @ SY2190 @ SV147 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2186 )
| ~ ( ~ ( ~ ( in @ SY2189 @ SX4 )
| ( in @ SY2190 @ SX4 ) )
| ~ ( ~ ( in @ SY2190 @ SX4 )
| ( in @ SY2189 @ SX4 ) ) ) )
| ( SY2189 = SY2190 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY2186 )
| ~ ( in @ SX3 @ SY2186 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY2196: $i] :
( ~ ~ ( ~ ! [SY2197: $i] :
( ~ ( in @ SY2197 @ SY2196 )
| ( in @ SY2197 @ SV147 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY2196 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY2186 )
| ~ ( in @ SX4 @ SY2196 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY2196 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2186 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(909,plain,
! [SV148: $i] :
( ( ! [SY2204: $i,SY2205: $i] :
( ~ ( subset @ SV148 @ SY2204 )
| ~ ( in @ SY2205 @ SV148 )
| ( in @ SY2205 @ SY2204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(910,plain,
! [SV149: $i] :
( ( ! [SY2206: $i] :
( ~ ( subset @ SY2206 @ SV149 )
| ( in @ SY2206 @ ( powerset @ SV149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(911,plain,
! [SV150: $i] :
( ( ! [SY2207: $i,SY2208: $i] :
( ~ ( in @ SY2208 @ SY2207 )
| ( in @ SY2208 @ ( binunion @ SV150 @ SY2207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(912,plain,
! [SV151: $i] :
( ( ! [SY2209: $i] :
( ~ ( in @ SY2209 @ ( powerset @ SV151 ) )
| ! [SY2210: $i] :
( ~ ( in @ SY2210 @ ( powerset @ SV151 ) )
| ! [SY2211: $i] :
( ~ ( in @ SY2211 @ ( powerset @ SV151 ) )
| ! [SY2212: $i] :
( ~ ( in @ SY2212 @ SV151 )
| ~ ( in @ SY2212 @ ( binintersect @ SY2209 @ SY2210 ) )
| ( in @ SY2212 @ ( binunion @ SY2210 @ SY2211 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(913,plain,
! [SV152: $i] :
( ( ! [SY2213: $i] :
( ( SV152 != SY2213 )
| ( ( setunion @ SV152 )
= ( setunion @ SY2213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(914,plain,
! [SV153: $i] :
( ( ! [SY2214: $i,SY2215: $i,SY2216: $i] :
( ~ ( in @ ( kpair @ SY2215 @ SY2216 ) @ ( cartprod @ SV153 @ SY2214 ) )
| ( in @ SY2215 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(915,plain,
! [SV154: $i] :
( ( ! [SY2217: $i,SY2218: $i] :
( ~ ( in @ SY2218 @ ( binunion @ SV154 @ SY2217 ) )
| ( in @ SY2218 @ SV154 )
| ( in @ SY2218 @ SY2217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(916,plain,
! [SV155: $i] :
( ( ! [SY2219: $i] :
( ~ ! [SY2220: $i] :
( ~ ( in @ SY2220 @ SV155 )
| ( in @ SY2220 @ SY2219 ) )
| ( subset @ SV155 @ SY2219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(917,plain,
! [SV156: $i] :
( ( ! [SY2221: $i] :
( ~ ( in @ SY2221 @ ( powerset @ SV156 ) )
| ! [SY2222: $i] :
( ~ ( in @ SY2222 @ ( powerset @ SV156 ) )
| ! [SY2223: $i] :
( ~ ( in @ SY2223 @ SV156 )
| ~ ( subset @ SY2221 @ ( setminus @ SV156 @ SY2222 ) )
| ~ ( in @ SY2223 @ SY2222 )
| ~ ( in @ SY2223 @ SY2221 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(918,plain,
! [SV157: $i] :
( ( ! [SY2224: $i > $o,SY2225: $i] :
( ~ ( in @ SY2225
@ ( dsetconstr @ SV157
@ ^ [SX3: $i] : ( SY2224 @ SX3 ) ) )
| ( in @ SY2225 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(919,plain,
! [SV158: $i] :
( ( ! [SY2227: $i,SY2228: $i] :
( ~ ~ ( in @ SY2228 @ ( setminus @ SV158 @ SY2227 ) )
| ~ ( in @ SY2228 @ SV158 )
| ( in @ SY2228 @ SY2227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(920,plain,
! [SV159: $i] :
( ( ! [SY2229: $i] :
( ~ ( in @ SY2229 @ ( powerset @ SV159 ) )
| ( SY2229
= ( setminus @ SV159 @ ( setminus @ SV159 @ SY2229 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(921,plain,
! [SV160: $i > $o] :
( ( ~ ~ ! [SY2230: $i] :
~ ( SV160 @ SY2230 )
| ~ ! [SY2231: $i,SY2232: $i] :
( ~ ( SV160 @ SY2231 )
| ~ ( SV160 @ SY2232 )
| ( SY2231 = SY2232 ) )
| ~ ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(922,plain,
! [SV161: $i] :
( ( ! [SY2235: $i] :
( ~ ( in @ SY2235 @ ( powerset @ SV161 ) )
| ! [SY2236: $i] :
( ~ ( in @ SY2236 @ ( powerset @ SV161 ) )
| ( in @ ( setminus @ SV161 @ SY2235 ) @ ( powerset @ ( setminus @ SV161 @ ( binintersect @ SY2235 @ SY2236 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(923,plain,
! [SV162: $i] :
( ( ! [SY2237: $i] :
( ~ ( in @ SY2237 @ ( powerset @ SV162 ) )
| ! [SY2238: $i] :
( ~ ( in @ SY2238 @ ( powerset @ SV162 ) )
| ( in @ ( setminus @ SY2237 @ SY2238 ) @ ( powerset @ SV162 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(924,plain,
! [SV163: $i] :
( ( ~ ( subset @ SV163 @ emptyset )
| ( SV163 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(925,plain,
! [SV164: $i] :
( ( ! [SY2239: $i,SY2240: $i] :
( ~ ( in @ SY2240 @ SV164 )
| ~ ~ ( in @ SY2240 @ SY2239 )
| ( in @ SY2240 @ ( symdiff @ SV164 @ SY2239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(926,plain,
! [SV165: $i] :
( ( ! [SY2241: $i] :
( ( SV165 != SY2241 )
| ! [SY2242: $i,SY2243: $i] :
( ( SY2242 != SY2243 )
| ~ ( in @ SY2242 @ SV165 )
| ( in @ SY2243 @ SY2241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(927,plain,
! [SV166: $i] :
( ( ! [SY2244: $i,SY2245: $i] :
( ~ ( in @ SY2245 @ SV166 )
| ~ ~ ( in @ SY2245 @ SY2244 )
| ( SV166 != SY2244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(928,plain,
! [SV167: $i] :
( ( ! [SY2246: $i] :
( ~ ( in @ SY2246 @ ( powerset @ SV167 ) )
| ! [SY2247: $i] :
( ~ ( in @ SY2247 @ ( powerset @ SV167 ) )
| ! [SY2248: $i] :
( ~ ( in @ SY2248 @ SV167 )
| ~ ( in @ SY2248 @ ( setminus @ SV167 @ ( binunion @ SY2246 @ SY2247 ) ) )
| ( in @ SY2248 @ ( setminus @ SV167 @ SY2246 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(929,plain,
! [SV168: $i] :
( ( ! [SY2249: $i,SY2250: $i] :
( ~ ( func @ SV168 @ SY2249 @ SY2250 )
| ! [SY2251: $i] :
( ~ ( func @ SV168 @ SY2249 @ SY2251 )
| ~ ! [SY2252: $i] :
( ~ ( in @ SY2252 @ SV168 )
| ( ( ap @ SV168 @ SY2249 @ SY2250 @ SY2252 )
= ( ap @ SV168 @ SY2249 @ SY2251 @ SY2252 ) ) )
| ( SY2250 = SY2251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(930,plain,
! [SV169: $i] :
( ( ! [SY2253: $o,SY2254: $i] :
( ~ ( in @ SY2254 @ SV169 )
| ! [SY2255: $i] :
( ~ ( in @ SY2255 @ SV169 )
| ( in @ ( if @ SV169 @ SY2253 @ SY2254 @ SY2255 ) @ ( setadjoin @ SY2254 @ ( setadjoin @ SY2255 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(931,plain,
! [SV170: $i] :
( ( ! [SY2256: $i,SY2257: $i > $i] :
( ~ ! [SY2258: $i] :
( ~ ( in @ SY2258 @ SV170 )
| ( in @ ( SY2257 @ SY2258 ) @ SY2256 ) )
| ( ( lam @ SV170 @ SY2256
@ ^ [SX3: $i] : ( SY2257 @ SX3 ) )
= ( lam @ SV170 @ SY2256
@ ^ [SX3: $i] : ( SY2257 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(932,plain,
! [SV171: $i] :
( ( ! [SY2261: $o,SY2262: $i] :
( ~ ( in @ SY2262 @ SV171 )
| ! [SY2263: $i] :
( ~ ( in @ SY2263 @ SV171 )
| ~ ~ SY2261
| ( ( dsetconstr @ SV171
@ ^ [SX4: $i] :
( ~ ( ~ SY2261
| ( SX4 != SY2262 ) )
| ~ ( ~ ~ SY2261
| ( SX4 != SY2263 ) ) ) )
= ( setadjoin @ SY2263 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(933,plain,
! [SV172: $i] :
( ( ! [SY2265: $i] :
~ ( ~ ( ~ ( in @ SY2265 @ ( powerset @ SV172 ) )
| ! [SY2266: $i] :
( ~ ( in @ SY2266 @ SY2265 )
| ( in @ SY2266 @ SV172 ) ) )
| ~ ( ~ ! [SY2267: $i] :
( ~ ( in @ SY2267 @ SY2265 )
| ( in @ SY2267 @ SV172 ) )
| ( in @ SY2265 @ ( powerset @ SV172 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(934,plain,
! [SV173: $i] :
( ( ! [SY2268: $i,SY2269: $i,SY2270: $i] :
( ( ( setadjoin @ ( setadjoin @ SV173 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV173 @ ( setadjoin @ SY2268 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY2269 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2269 @ ( setadjoin @ SY2270 @ emptyset ) ) @ emptyset ) ) )
| ( SY2268 = SY2270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(935,plain,
! [SV174: $i] :
( ( ! [SY2271: $i,SY2272: $i] :
( ~ ( in @ SY2272 @ SV174 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2271 )
| ( ( kfst @ ( kpair @ SY2272 @ SX3 ) )
= SY2272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(936,plain,
! [SV175: $i] :
( ( ! [SY2274: $i,SY2275: $i] :
( ~ ( in @ SY2275 @ ( funcSet @ SV175 @ SY2274 ) )
| ! [SY2276: $i] :
( ~ ( in @ SY2276 @ SV175 )
| ( in @ ( ap @ SV175 @ SY2274 @ SY2275 @ SY2276 ) @ SY2274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(937,plain,
! [SV176: $i] :
( ( ! [SY2277: $i] :
( ~ ( in @ SY2277 @ ( powerset @ SV176 ) )
| ! [SY2278: $i] :
( ~ ( in @ SY2278 @ ( powerset @ SV176 ) )
| ~ ( subset @ SY2277 @ SY2278 )
| ( subset @ ( setminus @ SV176 @ SY2278 ) @ ( setminus @ SV176 @ SY2277 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(938,plain,
! [SV177: $i] :
( ( ! [SY2279: $i,SY2280: $i] :
( ~ ( subset @ SV177 @ SY2279 )
| ~ ( subset @ SY2279 @ SY2280 )
| ( subset @ SV177 @ SY2280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(939,plain,
! [SV178: $i] :
( ( ! [SY2281: $i,SY2282: $i] :
( ~ ( in @ SY2282 @ ( binintersect @ SV178 @ SY2281 ) )
| ( in @ SY2282 @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(940,plain,
! [SV179: $i] :
( ( ! [SY2283: $i] :
( ~ ( in @ SY2283 @ ( powerset @ SV179 ) )
| ( subset @ SY2283 @ ( setminus @ SV179 @ ( setminus @ SV179 @ SY2283 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(941,plain,
! [SV180: $i] :
( ( ! [SY2284: $i > $o] :
( ~ ~ ! [SY2285: $i] :
~ ~ ( ~ ( in @ SY2285 @ SV180 )
| ~ ( SY2284 @ SY2285 ) )
| ( ( dsetconstr @ SV180
@ ^ [SX2: $i] : ( SY2284 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(942,plain,
! [SV181: $i] :
( ( ! [SY2287: $i > $o] :
( ~ ! [SY2288: $i] :
( ~ ( in @ SY2288 @ SV181 )
| ! [SY2289: $i] :
( ~ ( in @ SY2289 @ SV181 )
| ~ ( SY2287 @ SY2288 )
| ~ ( SY2287 @ SY2289 )
| ( SY2288 = SY2289 ) ) )
| ~ ~ ! [SY2290: $i] :
~ ~ ( ~ ( in @ SY2290 @ SV181 )
| ~ ( SY2287 @ SY2290 ) )
| ( singleton
@ ( dsetconstr @ SV181
@ ^ [SX2: $i] : ( SY2287 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(943,plain,
! [SV182: $i] :
( ( ! [SY2292: $i] :
( ~ ( subset @ SV182 @ SY2292 )
| ( ( setminus @ SV182 @ SY2292 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(944,plain,
! [SV183: $i > $o] :
( ( ! [SY2293: $i > $o] :
( ~ ! [SY2294: $i,SY2295: $i] :
( ( SY2294 != SY2295 )
| ~ ( ~ ( ~ ( SV183 @ SY2294 )
| ( SY2293 @ SY2295 ) )
| ~ ( ~ ( SY2293 @ SY2295 )
| ( SV183 @ SY2294 ) ) ) )
| ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY2293 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY2293 @ SX3 )
| ( SX2 = SX3 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SX2: $i] : ( SY2293 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(945,plain,
! [SV184: $i] :
( ( ! [SY2302: $i] :
( ~ ( subset @ SV184 @ SY2302 )
| ( in @ SV184 @ ( powerset @ SY2302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(946,plain,
! [SV185: $i] :
( ( ! [SY2303: $i,SY2304: $i] :
( ~ ( in @ SY2304 @ ( funcSet @ SV185 @ SY2303 ) )
| ! [SY2305: $i] :
( ~ ( in @ SY2305 @ SV185 )
| ! [SY2306: $i] :
( ~ ( in @ SY2306 @ SY2303 )
| ~ ( in @ ( kpair @ SY2305 @ SY2306 ) @ SY2304 )
| ( ( ap @ SV185 @ SY2303 @ SY2304 @ SY2305 )
= SY2306 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(947,plain,
! [SV186: $i] :
( ( ! [SY2307: $i] :
( ~ ( in @ SY2307 @ ( powerset @ SV186 ) )
| ! [SY2308: $i] :
( ~ ( in @ SY2308 @ ( powerset @ SV186 ) )
| ~ ! [SY2309: $i] :
( ~ ( in @ SY2309 @ SV186 )
| ~ ( in @ SY2309 @ SY2307 )
| ( in @ SY2309 @ SY2308 ) )
| ~ ! [SY2310: $i] :
( ~ ( in @ SY2310 @ SV186 )
| ~ ( in @ SY2310 @ SY2308 )
| ( in @ SY2310 @ SY2307 ) )
| ( SY2307 = SY2308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(948,plain,
! [SV187: $i] :
( ( ! [SY2311: $i > $o,SY2312: $i] :
( ~ ( in @ SY2312 @ SV187 )
| ~ ( SY2311 @ SY2312 )
| ( ( dsetconstr @ SV187
@ ^ [SX3: $i] : ( SY2311 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(949,plain,
! [SV188: $i > $o] :
( ( ~ ~ ! [SY2314: $i] :
~ ~ ( ~ ( SV188 @ SY2314 )
| ~ ! [SY2315: $i] :
( ~ ( SV188 @ SY2315 )
| ( SY2314 = SY2315 ) ) )
| ~ ! [SY2316: $i] :
~ ~ ( ~ ( SV188 @ SY2316 )
| ~ ! [SY2317: $i] :
( ~ ( SV188 @ SY2317 )
| ( SY2316 = SY2317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(950,plain,
! [SV189: $i] :
( ( ! [SY2318: $i,SY2319: $i] :
( ~ ( in @ SY2319 @ ( setadjoin @ SV189 @ SY2318 ) )
| ( SY2319 = SV189 )
| ( in @ SY2319 @ SY2318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(951,plain,
! [SV190: $i] :
( ( ! [SY2320: $i,SY2321: $i] :
( ~ ( in @ SY2321 @ ( funcSet @ SV190 @ SY2320 ) )
| ! [SY2322: $i] :
( ~ ( in @ SY2322 @ SV190 )
| ( ( ap @ SV190 @ SY2320 @ SY2321 @ SY2322 )
= ( ap @ SV190 @ SY2320 @ SY2321 @ SY2322 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(952,plain,
! [SV191: $i] :
( ( ! [SY2323: $i] :
( ~ ( in @ SY2323 @ ( powerset @ SV191 ) )
| ! [SY2324: $i] :
( ~ ( in @ SY2324 @ ( powerset @ SV191 ) )
| ! [SY2325: $i] :
( ~ ( in @ SY2325 @ ( powerset @ SV191 ) )
| ! [SY2326: $i] :
( ~ ( in @ SY2326 @ SV191 )
| ~ ( in @ SY2326 @ ( binintersect @ SY2323 @ SY2324 ) )
| ( in @ SY2326 @ ( binintersect @ ( binunion @ SY2323 @ SY2325 ) @ ( binunion @ SY2324 @ SY2325 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(953,plain,
! [SV192: $o] :
( ( ! [SY2327: $i] :
( ~ ( in @ SY2327 @ ( prop2set @ SV192 ) )
| SV192 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[690]) ).
thf(954,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $true ) )
| $true ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[690]) ).
thf(955,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $false ) )
| $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[690]) ).
thf(956,plain,
! [SV193: $i > $o] :
( ( ! [SY2328: $i > $o] :
( ~ ! [SY2329: $i,SY2330: $i] :
( ( SY2329 != SY2330 )
| ~ ( ~ ( ~ ( SV193 @ SY2329 )
| ( SY2328 @ SY2330 ) )
| ~ ( ~ ( SY2328 @ SY2330 )
| ( SV193 @ SY2329 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SY2328 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY2328 @ SX3 )
| ( SX2 = SX3 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY2328 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY2328 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(957,plain,
! [SV194: $i] :
( ( ~ ( singleton @ SV194 )
| ! [SY2339: $i] :
( ~ ( in @ SY2339 @ SV194 )
| ( ( setunion @ SV194 )
= SY2339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(958,plain,
! [SV195: $i] :
( ( ! [SY2340: $i,SY2341: $i] :
( ~ ( in @ SY2341 @ SV195 )
| ~ ~ ( in @ SY2341 @ SY2340 )
| ( in @ SY2341 @ ( setminus @ SV195 @ SY2340 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(959,plain,
! [SV196: $i] :
( ( ! [SY2342: $i,SY2343: $i] :
( ~ ( in @ SY2343 @ ( cartprod @ SV196 @ SY2342 ) )
| ~ ! [SY2344: $i] :
~ ~ ( ~ ( in @ SY2344 @ SV196 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SY2342 )
| ( SY2343
!= ( kpair @ SY2344 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(960,plain,
! [SV197: $i] :
( ( ! [SY2346: $o,SY2347: $i] :
( ~ ( in @ SY2347 @ SV197 )
| ! [SY2348: $i] :
( ~ ( in @ SY2348 @ SV197 )
| ~ SY2346
| ( ( if @ SV197 @ SY2346 @ SY2347 @ SY2348 )
= SY2347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(961,plain,
! [SV198: $i] :
( ( ! [SY2349: $i,SY2350: $i] :
( ~ ( subset @ SY2350 @ ( cartprod @ SV198 @ SY2349 ) )
| ! [SY2351: $i] :
( ~ ( subset @ SY2351 @ ( cartprod @ SV198 @ SY2349 ) )
| ~ ! [SY2352: $i] :
( ~ ( in @ SY2352 @ SV198 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2349 )
| ~ ( in @ ( kpair @ SY2352 @ SX5 ) @ SY2350 )
| ( in @ ( kpair @ SY2352 @ SX5 ) @ SY2351 ) ) )
| ~ ! [SY2354: $i] :
( ~ ( in @ SY2354 @ SV198 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2349 )
| ~ ( in @ ( kpair @ SY2354 @ SX5 ) @ SY2351 )
| ( in @ ( kpair @ SY2354 @ SX5 ) @ SY2350 ) ) )
| ( SY2350 = SY2351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(962,plain,
! [SV199: $i] :
( ( ! [SY2356: $i] :
( ( ( binintersect @ SV199 @ SY2356 )
!= SY2356 )
| ( subset @ SY2356 @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(963,plain,
! [SV200: $i] :
( ( ! [SY2357: $i,SY2358: $i] :
( ~ ( subset @ SY2358 @ ( cartprod @ SV200 @ SY2357 ) )
| ! [SY2359: $i > $o] :
( ~ ! [SY2360: $i] :
( ~ ( in @ SY2360 @ SV200 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2357 )
| ~ ( in @ ( kpair @ SY2360 @ SX5 ) @ SY2358 )
| ( SY2359 @ ( kpair @ SY2360 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2358 )
| ( SY2359 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(964,plain,
! [SV201: $i] :
( ( ! [SY2363: $i > $o] :
( ~ ~ ! [SY2364: $i] :
~ ~ ( ~ ( in @ SY2364 @ SV201 )
| ~ ~ ( SY2363 @ SY2364 ) )
| ~ ! [SY2365: $i] :
( ~ ( in @ SY2365 @ SV201 )
| ( SY2363 @ SY2365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(965,plain,
! [SV202: $i] :
( ( ~ ( iskpair @ SV202 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SV202 )
@ ^ [SY2366: $i] : ( in @ ( setadjoin @ SY2366 @ emptyset ) @ SV202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(966,plain,
! [SV203: $i] :
( ( ! [SY2367: $i,SY2368: $i > $i] :
( ~ ! [SY2369: $i] :
( ~ ( in @ SY2369 @ SV203 )
| ( in @ ( SY2368 @ SY2369 ) @ SY2367 ) )
| ( func @ SV203 @ SY2367
@ ( dpsetconstr @ SV203 @ SY2367
@ ^ [SX3: $i,SX4: $i] :
( ( SY2368 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(967,plain,
! [SV204: $i] :
( ( ~ ~ ! [SY2372: $i] :
~ ( in @ SY2372 @ SV204 )
| ( SV204 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(968,plain,
! [SV205: $i] :
( ( ~ ( in @ SV205 @ omega )
| ( in @ ( setadjoin @ SV205 @ SV205 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(969,plain,
! [SV206: $i] :
( ( ! [SY2373: $i,SY2374: $i] :
( ~ ~ ( in @ SY2374 @ SV206 )
| ~ ( in @ SY2374 @ SY2373 )
| ( in @ SY2374 @ ( symdiff @ SV206 @ SY2373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(970,plain,
! [SV207: $i] :
( ( ! [SY2375: $i] :
( ( SV207 != SY2375 )
| ( subset @ SY2375 @ SV207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(971,plain,
! [SV208: $i] :
( ( ~ ( in @ SV208 @ emptyset )
| ! [SX1: $o] : SX1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(972,plain,
! [SV209: $i] :
( ( ! [SY2377: $i,SY2378: $i > $i] :
( ~ ! [SY2379: $i] :
( ~ ( in @ SY2379 @ SV209 )
| ( in @ ( SY2378 @ SY2379 ) @ SY2377 ) )
| ! [SY2380: $i] :
( ~ ( in @ SY2380 @ SV209 )
| ( ( ap @ SV209 @ SY2377
@ ( lam @ SV209 @ SY2377
@ ^ [SX4: $i] : ( SY2378 @ SX4 ) )
@ SY2380 )
= ( SY2378 @ SY2380 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(973,plain,
! [SV210: $i] :
( ( ! [SY2382: $i] :
( ~ ( in @ SY2382 @ ( powerset @ SV210 ) )
| ( subset @ ( setminus @ SV210 @ ( setminus @ SV210 @ SY2382 ) ) @ SY2382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(974,plain,
! [SV211: $i] :
( ( ! [SY2383: $i] :
( ( SV211 != SY2383 )
| ! [SY2384: $i,SY2385: $i] :
( ( SY2384 != SY2385 )
| ( ( setadjoin @ SV211 @ SY2384 )
= ( setadjoin @ SY2383 @ SY2385 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(975,plain,
! [SV212: $i] :
( ( ! [SY2386: $i > $o] :
( ~ ! [SY2387: $i] :
( ~ ( in @ SY2387 @ SV212 )
| ! [SY2388: $i] :
( ~ ( in @ SY2388 @ SV212 )
| ~ ( SY2386 @ SY2387 )
| ~ ( SY2386 @ SY2388 )
| ( SY2387 = SY2388 ) ) )
| ~ ~ ! [SY2389: $i] :
~ ~ ( ~ ( in @ SY2389 @ SV212 )
| ~ ( SY2386 @ SY2389 ) )
| ( singleton
@ ( dsetconstr @ SV212
@ ^ [SX2: $i] : ( SY2386 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(976,plain,
! [SV213: $i] :
( ( ! [SY2391: $i] :
( ( ( setadjoin @ SV213 @ emptyset )
!= ( setadjoin @ SY2391 @ emptyset ) )
| ( SV213 = SY2391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(977,plain,
! [SV214: $i] :
( ( ! [SY2392: $i,SY2393: $i,SY2394: $i] :
( ( ( setadjoin @ ( setadjoin @ SV214 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV214 @ ( setadjoin @ SY2392 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY2393 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2393 @ ( setadjoin @ SY2394 @ emptyset ) ) @ emptyset ) ) )
| ( SY2393 != SY2394 )
| ( SY2392 = SY2394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(978,plain,
! [SV215: $i] :
( ( ~ ~ ( ~ ( in @ emptyset @ SV215 )
| ~ ! [SY2395: $i] :
( ~ ~ ( ~ ( in @ SY2395 @ omega )
| ~ ( in @ SY2395 @ SV215 ) )
| ( in @ ( setadjoin @ SY2395 @ SY2395 ) @ SV215 ) ) )
| ! [SY2396: $i] :
( ~ ( in @ SY2396 @ omega )
| ( in @ SY2396 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(979,plain,
! [SV216: $i] :
( ( ! [SY2397: $i,SY2398: $i] :
( ~ ( in @ SY2398 @ SV216 )
| ! [SY2399: $i] :
( ~ ( in @ SY2399 @ SY2397 )
| ( in @ ( kpair @ SY2398 @ SY2399 ) @ ( powerset @ ( powerset @ ( binunion @ SV216 @ SY2397 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(980,plain,
! [SV217: $i] :
( ( ! [SY2400: $i,SY2401: $i > $i > $o,SY2402: $i] :
( ~ ( in @ SY2402 @ SV217 )
| ! [SY2403: $i] :
( ~ ( in @ SY2403 @ SY2400 )
| ~ ( SY2401 @ SY2402 @ SY2403 )
| ( in @ ( kpair @ SY2402 @ SY2403 )
@ ( dpsetconstr @ SV217 @ SY2400
@ ^ [SX5: $i,SX6: $i] : ( SY2401 @ SX5 @ SX6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(981,plain,
! [SV218: $i] :
( ( ! [SY2406: $o,SY2407: $i] :
( ~ ( in @ SY2407 @ SV218 )
| ! [SY2408: $i] :
( ~ ( in @ SY2408 @ SV218 )
| ( in @ ( if @ SV218 @ SY2406 @ SY2407 @ SY2408 ) @ SV218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(982,plain,
! [SV219: $i] :
( ( ! [SY2409: $i,SY2410: $i] :
( ~ ( in @ SY2410 @ ( funcSet @ SV219 @ SY2409 ) )
| ! [SY2411: $i] :
( ~ ( in @ SY2411 @ ( funcSet @ SV219 @ SY2409 ) )
| ~ ! [SY2412: $i] :
( ~ ( in @ SY2412 @ SV219 )
| ( ( ap @ SV219 @ SY2409 @ SY2410 @ SY2412 )
= ( ap @ SV219 @ SY2409 @ SY2411 @ SY2412 ) ) )
| ( SY2410 = SY2411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(983,plain,
! [SV220: $i] :
( ( ! [SY2413: $i,SY2414: $i > $i > $o,SY2415: $i] :
( ~ ( in @ SY2415 @ SV220 )
| ! [SY2416: $i] :
( ~ ( in @ SY2416 @ SY2413 )
| ~ ( in @ ( kpair @ SY2415 @ SY2416 )
@ ( dpsetconstr @ SV220 @ SY2413
@ ^ [SX5: $i,SX6: $i] : ( SY2414 @ SX5 @ SX6 ) ) )
| ( SY2414 @ SY2415 @ SY2416 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(984,plain,
! [SV221: $i] :
( ( ! [SY2419: $i,SY2420: $i] :
( ~ ( func @ SV221 @ SY2419 @ SY2420 )
| ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SV221 )
| ( in @ ( ap @ SV221 @ SY2419 @ SY2420 @ SY2421 ) @ SY2419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(985,plain,
! [SV222: $i] :
( ( ! [SY2422: $i,SY2423: $i] :
( ~ ( in @ SY2423 @ SV222 )
| ( in @ ( setadjoin @ SY2423 @ emptyset ) @ ( powerset @ ( binunion @ SV222 @ SY2422 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(986,plain,
! [SV223: $i] :
( ( ! [SY2424: $i > $o] :
( ~ ( singleton
@ ( dsetconstr @ SV223
@ ^ [SX2: $i] : ( SY2424 @ SX2 ) ) )
| ~ ! [SY2426: $i] :
~ ~ ( ~ ( in @ SY2426 @ SV223 )
| ~ ( SY2424 @ SY2426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(987,plain,
! [SV224: $i] :
( ( ! [SY2427: $i] :
( ~ ( ( SV224 != SY2427 ) )
| ~ ( in @ SY2427 @ ( setadjoin @ SV224 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(988,plain,
! [SV225: $i] :
( ( ! [SY2428: $i] :
( ~ ! [SY2429: $i] :
~ ( ~ ( ~ ( in @ SY2429 @ SV225 )
| ( in @ SY2429 @ SY2428 ) )
| ~ ( ~ ( in @ SY2429 @ SY2428 )
| ( in @ SY2429 @ SV225 ) ) )
| ( SV225 = SY2428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(989,plain,
! [SV226: $i] :
( ( ! [SY2430: $i,SY2431: $i] :
( ~ ( in @ SY2431 @ SV226 )
| ~ ( in @ SY2431 @ SY2430 )
| ~ ( in @ SY2431 @ ( symdiff @ SV226 @ SY2430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(990,plain,
! [SV227: $i] :
( ( ! [SY2432: $i] :
( ~ ( in @ SY2432 @ ( powerset @ SV227 ) )
| ! [SY2433: $i] :
( ~ ( in @ SY2433 @ SV227 )
| ~ ( in @ SY2433 @ ( setminus @ SV227 @ ( setminus @ SV227 @ SY2432 ) ) )
| ( in @ SY2433 @ SY2432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(991,plain,
! [SV228: $i] :
( ( ! [SY2434: $i,SY2435: $i,SY2436: $i] :
( ( ( setadjoin @ ( setadjoin @ SV228 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV228 @ ( setadjoin @ SY2434 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY2435 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2435 @ ( setadjoin @ SY2436 @ emptyset ) ) @ emptyset ) ) )
| ( SV228 = SY2435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(992,plain,
! [SV229: $i] :
( ( ! [SY2437: $i] :
( ~ ( in @ SY2437 @ ( powerset @ SV229 ) )
| ! [SY2438: $i] :
( ~ ( in @ SY2438 @ ( powerset @ SV229 ) )
| ! [SY2439: $i] :
( ~ ( in @ SY2439 @ ( powerset @ SV229 ) )
| ( in @ ( binintersect @ SY2437 @ SY2438 ) @ ( powerset @ ( binintersect @ ( binunion @ SY2437 @ SY2439 ) @ ( binunion @ SY2438 @ SY2439 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(993,plain,
! [SV230: $i] :
( ( ~ ( ( SV230 != emptyset ) )
| ~ ! [SY2440: $i] :
~ ~ ( ~ ( in @ SY2440 @ SV230 )
| ~ $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(994,plain,
! [SV231: $i] :
( ( ! [SY2441: $o,SY2442: $i] :
( ~ ( in @ SY2442 @ SV231 )
| ! [SY2443: $i] :
( ~ ( in @ SY2443 @ SV231 )
| ~ SY2441
| ( ( dsetconstr @ SV231
@ ^ [SX4: $i] :
( ~ ( ~ SY2441
| ( SX4 != SY2442 ) )
| ~ ( ~ ~ SY2441
| ( SX4 != SY2443 ) ) ) )
= ( setadjoin @ SY2442 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(995,plain,
! [SV232: $i] :
( ( ! [SY2445: $i,SY2446: $i] :
( ~ ( in @ SY2445 @ ( powerset @ SV232 ) )
| ~ ( in @ SY2446 @ SY2445 )
| ( in @ SY2446 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(996,plain,
! [SV233: $i] :
( ( ! [SY2447: $i] :
( ~ ( in @ SY2447 @ ( powerset @ SV233 ) )
| ! [SY2448: $i] :
( ~ ( in @ SY2448 @ SV233 )
| ~ ( in @ SY2448 @ SY2447 )
| ~ ( in @ SY2448 @ ( setminus @ SV233 @ SY2447 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(997,plain,
! [SV234: $i] :
( ( ! [SY2449: $i,SY2450: $i > $i] :
( ~ ! [SY2451: $i] :
( ~ ( in @ SY2451 @ SV234 )
| ( in @ ( SY2450 @ SY2451 ) @ SY2449 ) )
| ! [SY2452: $i] :
( ~ ( in @ SY2452 @ SV234 )
| ( ( ap @ SV234 @ SY2449
@ ( lam @ SV234 @ SY2449
@ ^ [SX4: $i] : ( SY2450 @ SX4 ) )
@ SY2452 )
= ( SY2450 @ SY2452 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(998,plain,
! [SV235: $i] :
( ( ! [SY2454: $i] :
( ~ ~ ~ ! [SY2455: $i] :
~ ~ ( ~ ( in @ SY2455 @ SV235 )
| ~ ( in @ SY2455 @ SY2454 ) )
| ( ( binintersect @ SV235 @ SY2454 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(999,plain,
! [SV236: $i] :
( ( ! [SY2456: $i,SY2457: $i,SY2458: $i] :
( ( ( kpair @ SV236 @ SY2456 )
!= ( kpair @ SY2457 @ SY2458 ) )
| ( SV236 = SY2457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(1000,plain,
! [SV237: $i] :
( ( ! [SY2459: $i,SY2460: $i] :
( ~ ( subset @ SV237 @ SY2460 )
| ( subset @ SV237 @ ( setadjoin @ SY2459 @ SY2460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(1001,plain,
! [SV238: $i] :
( ( ! [SY2461: $i,SY2462: $i] :
( ~ ( in @ SY2462 @ ( setadjoin @ SV238 @ ( setadjoin @ SY2461 @ emptyset ) ) )
| ( SY2462 = SV238 )
| ( SY2462 = SY2461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(1002,plain,
! [SV239: $i] :
( ( ! [SY2463: $i,SY2464: $i,SY2465: $i] :
( ( ( kpair @ SV239 @ SY2463 )
!= ( kpair @ SY2464 @ SY2465 ) )
| ( SY2463 = SY2465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(1003,plain,
! [SV240: $i] :
( ( ! [SY2466: $i] :
( ( SV240 != SY2466 )
| ( ( setadjoin @ SV240 @ ( setadjoin @ SY2466 @ emptyset ) )
= ( setadjoin @ SV240 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(1004,plain,
! [SV241: $i] :
( ( ! [SY2467: $i] :
( ( SV241 != SY2467 )
| ( ( powerset @ SV241 )
= ( powerset @ SY2467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(1005,plain,
! [SV242: $i] :
( ( ! [SY2468: $i,SY2469: $i > $i] :
( ~ ! [SY2470: $i] :
( ~ ( in @ SY2470 @ SV242 )
| ( in @ ( SY2469 @ SY2470 ) @ SY2468 ) )
| ( func @ SV242 @ SY2468
@ ( lam @ SV242 @ SY2468
@ ^ [SX3: $i] : ( SY2469 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(1006,plain,
! [SV243: $i] :
( ( ! [SY2472: $i] :
( ~ ( in @ SY2472 @ ( powerset @ SV243 ) )
| ! [SY2473: $i] :
( ~ ( in @ SY2473 @ ( powerset @ SV243 ) )
| ! [SY2474: $i] :
( ~ ( in @ SY2474 @ SV243 )
| ~ ( in @ SY2472 @ ( powerset @ SY2473 ) )
| ~ ( in @ SY2474 @ SY2472 )
| ( in @ SY2474 @ SY2473 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(1007,plain,
! [SV244: $i] :
( ( ! [SY2475: $o,SY2476: $i] :
( ~ ( in @ SY2476 @ SV244 )
| ! [SY2477: $i] :
( ~ ( in @ SY2477 @ SV244 )
| ~ ~ SY2475
| ( in @ SY2477
@ ( dsetconstr @ SV244
@ ^ [SX4: $i] :
( ~ ( ~ SY2475
| ( SX4 != SY2476 ) )
| ~ ( ~ ~ SY2475
| ( SX4 != SY2477 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(1008,plain,
! [SV245: $i] :
( ( ! [SY2479: $i] :
( ~ ( in @ SY2479 @ SV245 )
| ( in @ ( setadjoin @ SY2479 @ emptyset ) @ ( powerset @ SV245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(1009,plain,
! [SV246: $i] :
( ( ! [SY2480: $i] :
( ~ ( in @ SY2480 @ SV246 )
| ( subset @ ( setadjoin @ SY2480 @ emptyset ) @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(1010,plain,
! [SV247: $i] :
( ( ! [SY2481: $i,SY2482: $i] :
( ~ ( func @ SV247 @ SY2481 @ SY2482 )
| ! [SY2483: $i] :
( ~ ( func @ SV247 @ SY2481 @ SY2483 )
| ~ ! [SY2484: $i] :
( ~ ( in @ SY2484 @ SV247 )
| ( ( ap @ SV247 @ SY2481 @ SY2482 @ SY2484 )
= ( ap @ SV247 @ SY2481 @ SY2483 @ SY2484 ) ) )
| ! [SY2485: $i] :
( ~ ( in @ SY2485 @ SV247 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2481 )
| ~ ( in @ ( kpair @ SY2485 @ SX5 ) @ SY2483 )
| ( in @ ( kpair @ SY2485 @ SX5 ) @ SY2482 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(1011,plain,
! [SV248: $i] :
( ( ! [SY2487: $i] :
( ~ ( in @ SY2487 @ ( powerset @ SV248 ) )
| ! [SY2488: $i] :
( ~ ( in @ SY2488 @ ( powerset @ SV248 ) )
| ( subset @ ( setminus @ SV248 @ SY2487 ) @ ( setminus @ SV248 @ ( binintersect @ SY2487 @ SY2488 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(1012,plain,
! [SV249: $i > $i > $o] :
( ( ! [SY2489: $i] :
( ~ ! [SY2490: $i] :
( ~ ( in @ SY2490 @ SY2489 )
| ~ ! [SY2491: $i] :
~ ~ ( ~ ( SV249 @ SY2490 @ SY2491 )
| ~ ! [SY2492: $i] :
( ~ ( SV249 @ SY2490 @ SY2492 )
| ( SY2491 = SY2492 ) ) ) )
| ~ ! [SY2493: $i] :
~ ! [SY2494: $i] :
~ ( ~ ( ~ ( in @ SY2494 @ SY2493 )
| ~ ! [SY2495: $i] :
~ ~ ( ~ ( in @ SY2495 @ SY2489 )
| ~ ( SV249 @ SY2495 @ SY2494 ) ) )
| ~ ( ~ ~ ! [SY2496: $i] :
~ ~ ( ~ ( in @ SY2496 @ SY2489 )
| ~ ( SV249 @ SY2496 @ SY2494 ) )
| ( in @ SY2494 @ SY2493 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(1013,plain,
! [SV250: $i] :
( ( ! [SY2497: $i] :
( ( SV250 != SY2497 )
| ( in @ SV250 @ ( setadjoin @ SY2497 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(1014,plain,
! [SV251: $i] :
( ( ! [SY2498: $i] :
( ( ( setminus @ SV251 @ SY2498 )
!= emptyset )
| ( subset @ SV251 @ SY2498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(1015,plain,
! [SV252: $i] :
( ( ! [SY2499: $o,SY2500: $i] :
( ~ ( in @ SY2500 @ SV252 )
| ! [SY2501: $i] :
( ~ ( in @ SY2501 @ SV252 )
| ~ ~ SY2499
| ( ( if @ SV252 @ SY2499 @ SY2500 @ SY2501 )
= SY2501 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(1016,plain,
! [SV253: $i] :
( ( ! [SY2502: $i,SY2503: $i] :
( ~ ( in @ SY2503 @ SV253 )
| ! [SY2504: $i] :
( ~ ( in @ SY2504 @ SY2502 )
| ( in @ ( setadjoin @ ( setadjoin @ SY2503 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2503 @ ( setadjoin @ SY2504 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV253 @ SY2502 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(1017,plain,
! [SV254: $i] :
( ( ! [SY2505: $i] :
( ( SV254 != SY2505 )
| ! [SY2506: $i,SY2507: $i] :
( ( SY2506 != SY2507 )
| ~ ( ~ ( ~ ( in @ SY2506 @ SV254 )
| ( in @ SY2507 @ SY2505 ) )
| ~ ( ~ ( in @ SY2507 @ SY2505 )
| ( in @ SY2506 @ SV254 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(1018,plain,
! [SV255: $i] :
( ( ! [SY2508: $i] :
( ~ ( subset @ SV255 @ SY2508 )
| ~ ( subset @ SY2508 @ SV255 )
| ( SV255 = SY2508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(1019,plain,
! [SV256: $i > $o] :
( ( ~ ~ ! [SY2509: $i] :
~ ~ ( ~ ( SV256 @ SY2509 )
| ~ ! [SY2510: $i] :
( ~ ( SV256 @ SY2510 )
| ( SY2509 = SY2510 ) ) )
| ~ ! [SY2511: $i] :
~ ! [SY2512: $i] :
~ ( ~ ( ~ ( SV256 @ SY2512 )
| ( SY2512 = SY2511 ) )
| ~ ( ( SY2512 != SY2511 )
| ( SV256 @ SY2512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(1020,plain,
! [SV257: $i] :
( ( ! [SY2513: $i] :
( ~ ( in @ SY2513 @ ( powerset @ SV257 ) )
| ! [SY2514: $i] :
( ~ ( in @ SY2514 @ ( powerset @ SV257 ) )
| ( in @ ( binunion @ SY2513 @ SY2514 ) @ ( powerset @ SV257 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(1021,plain,
! [SV258: $i] :
( ( ! [SY2515: $i,SY2516: $i] :
( ~ ( in @ SY2516 @ SV258 )
| ! [SY2517: $i] :
( ~ ( in @ SY2517 @ SY2515 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY2516 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2516 @ ( setadjoin @ SY2517 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV258 @ SY2515 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(1022,plain,
! [SV259: $i,SV1: $i] :
( ( ! [SY2518: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV1 @ SV259
@ ^ [Xx: $i,Xy: $i] : ( SY2518 @ Xx @ Xy ) )
@ ( cartprod @ SV1 @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(1023,plain,
! [SV260: $i,SV2: $i] :
( ( ! [SY2521: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV2 @ SV260
@ ^ [Xx: $i,Xy: $i] : ( SY2521 @ Xx @ Xy ) )
@ ( cartprod @ SV2 @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(1024,plain,
! [SV261: $i,SV3: $i] :
( ( ( ksnd @ ( kpair @ SV3 @ SV261 ) )
= SV261 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(1025,plain,
! [SV262: $i,SV4: $i] :
( ( ( kfst @ ( kpair @ SV4 @ SV262 ) )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(1026,plain,
! [SV263: $i,SV8: $i] :
( ( iskpair @ ( kpair @ SV8 @ SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(1027,plain,
! [SV264: $i,SV9: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ SV9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV9 @ ( setadjoin @ SV264 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(1028,plain,
! [SV10: $i,SV265: $i] :
( ( in @ SV265 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV10 @ ( setadjoin @ SV265 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(1029,plain,
! [SV266: $i,SV11: $i] :
( ( in @ SV11 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV11 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV11 @ ( setadjoin @ SV266 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(1030,plain,
! [SV12: $i,SV267: $i] :
( ( in @ SV267 @ ( setadjoin @ SV12 @ ( setadjoin @ SV267 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(1031,plain,
! [SV268: $i,SV13: $i] :
( ( subset @ ( setminus @ SV13 @ SV268 ) @ SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(1032,plain,
! [SV269: $i,SV14: $i] :
( ( ! [SY2524: $i] :
( ( binintersect @ SV14 @ ( binunion @ SV269 @ SY2524 ) )
= ( binunion @ ( binintersect @ SV14 @ SV269 ) @ ( binintersect @ SV14 @ SY2524 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(1033,plain,
! [SV270: $i,SV15: $i] :
( ( subset @ ( binintersect @ SV15 @ SV270 ) @ SV270 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(1034,plain,
! [SV271: $i,SV16: $i] :
( ( subset @ ( binintersect @ SV16 @ SV271 ) @ SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(1035,plain,
! [SV17: $i,SV272: $i] :
( ( subset @ SV272 @ ( binunion @ SV17 @ SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(1036,plain,
! [SV273: $i,SV18: $i] :
( ( subset @ SV18 @ ( binunion @ SV18 @ SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(1037,plain,
! [SV19: $i,SV274: $i] :
( ( in @ SV274 @ ( setadjoin @ SV19 @ ( setadjoin @ SV274 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(1038,plain,
! [SV275: $i > $o,SV20: $i] :
( ( subset
@ ( dsetconstr @ SV20
@ ^ [SY2525: $i] : ( SV275 @ SY2525 ) )
@ SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(1039,plain,
! [SV276: $i > $o,SV21: $i] :
( ( in
@ ( dsetconstr @ SV21
@ ^ [SY2526: $i] : ( SV276 @ SY2526 ) )
@ ( powerset @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(1040,plain,
! [SV23: $i,SV277: $i] :
( ( subset @ SV277 @ ( setadjoin @ SV23 @ SV277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(1041,plain,
! [SV26: $i,SV278: $i] :
( ( in @ SV278 @ ( setadjoin @ SV26 @ ( setadjoin @ SV278 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(1042,plain,
! [SV279: $i,SV27: $i] :
( ( in @ SV27 @ ( setadjoin @ SV27 @ ( setadjoin @ SV279 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(1043,plain,
! [SV280: $i,SV31: $i] :
( ( in @ SV31 @ ( setadjoin @ SV31 @ SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(1044,plain,
! [SV32: $i] :
( ( in @ SV32 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(1045,plain,
! [SV33: $i] :
( ( in @ SV33 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(1046,plain,
! [SV281: $i,SV34: $i] :
( ( ! [SY2527: $i] :
( ~ ( func @ SV34 @ SV281 @ SY2527 )
| ( in @ SY2527 @ ( funcSet @ SV34 @ SV281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(1047,plain,
! [SV35: $i > $o] :
( ( ( ~ ~ ! [SY1900: $i] :
~ ~ ( ~ ( SV35 @ SY1900 )
| ~ ! [SY1901: $i] :
( ~ ( SV35 @ SY1901 )
| ( SY1900 = SY1901 ) ) ) )
= $true )
| ( ( ~ ! [SY1902: $i] :
~ ~ ( ~ ( SV35 @ SY1902 )
| ~ ! [SY1903: $i] :
( ~ ( SV35 @ SY1903 )
| ( SY1902 = SY1903 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[791]) ).
thf(1048,plain,
! [SV36: $i,SV282: $i] :
( ( ~ ( in @ SV282 @ ( powerset @ SV36 ) )
| ! [SY2528: $i] :
( ~ ( in @ SY2528 @ ( powerset @ SV36 ) )
| ~ ( subset @ ( setminus @ SV36 @ SY2528 ) @ ( setminus @ SV36 @ SV282 ) )
| ( subset @ SV282 @ SY2528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(1049,plain,
! [SV283: $i,SV37: $i] :
( ( ~ ( in @ SV37 @ ( setadjoin @ SV283 @ emptyset ) )
| ( SV37 = SV283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(1050,plain,
! [SV284: $i,SV38: $i] :
( ( ! [SY2529: $i] :
( ~ ( func @ SV38 @ SV284 @ SY2529 )
| ! [SY2530: $i] :
( ~ ( in @ SY2530 @ SV38 )
| ! [SY2531: $i] :
( ~ ( in @ SY2531 @ SV284 )
| ~ ( in @ ( kpair @ SY2530 @ SY2531 ) @ SY2529 )
| ( ( ap @ SV38 @ SV284 @ SY2529 @ SY2530 )
= SY2531 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(1051,plain,
! [SV285: $o,SV39: $i] :
( ( ! [SY2532: $i] :
( ~ ( in @ SY2532 @ SV39 )
| ! [SY2533: $i] :
( ~ ( in @ SY2533 @ SV39 )
| ~ SV285
| ( in @ SY2532
@ ( dsetconstr @ SV39
@ ^ [SY2534: $i] :
( ~ ( ~ SV285
| ( SY2534 != SY2532 ) )
| ~ ( ~ ~ SV285
| ( SY2534 != SY2533 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[795]) ).
thf(1052,plain,
! [SV39: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV39 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV39 )
| ~ $true
| ( in @ SX0
@ ( dsetconstr @ SV39
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[795]) ).
thf(1053,plain,
! [SV39: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV39 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV39 )
| ~ $false
| ( in @ SX0
@ ( dsetconstr @ SV39
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[795]) ).
thf(1054,plain,
! [SV286: $i,SV40: $i] :
( ( ( SV40 != SV286 )
| ! [SY2535: $i > $o,SY2536: $i > $o] :
( ~ ! [SY2537: $i] :
( ~ ( in @ SY2537 @ SV40 )
| ! [SY2538: $i] :
( ~ ( in @ SY2538 @ SV286 )
| ( SY2537 != SY2538 )
| ~ ( ~ ( ~ ( SY2535 @ SY2537 )
| ( SY2536 @ SY2538 ) )
| ~ ( ~ ( SY2536 @ SY2538 )
| ( SY2535 @ SY2537 ) ) ) ) )
| ( ( dsetconstr @ SV40
@ ^ [SX4: $i] : ( SY2535 @ SX4 ) )
= ( dsetconstr @ SV286
@ ^ [SX4: $i] : ( SY2536 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(1055,plain,
! [SV287: $i > $o,SV41: $i] :
( ( ~ ~ ~ ! [SY2541: $i] :
~ ~ ( ~ ( in @ SY2541 @ SV41 )
| ~ ( SV287 @ SY2541 ) )
| ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV41 )
| ~ ( SV287 @ SY2542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(1056,plain,
! [SV42: $o] :
( ( ( ~ SV42 ) = $true )
| ( ( set2prop @ ( prop2set @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(1057,plain,
( ( ( ~ $true ) = $true )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(1058,plain,
( ( ( ~ $false ) = $true )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[800]) ).
thf(1059,plain,
! [SV288: $i,SV43: $i] :
( ( ! [SY2543: $i] :
( ~ ~ ( in @ SY2543 @ SV43 )
| ~ ( in @ SY2543 @ ( setminus @ SV43 @ SV288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(1060,plain,
! [SV44: $i > $o] :
( ( ( ~ ~ ! [SY1927: $i] :
~ ! [SY1928: $i] :
~ ( ~ ( ~ ( SV44 @ SY1928 )
| ( SY1928 = SY1927 ) )
| ~ ( ( SY1928 != SY1927 )
| ( SV44 @ SY1928 ) ) ) )
= $true )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[802]) ).
thf(1061,plain,
! [SV289: $i,SV45: $i] :
( ( ! [SY2544: $i] :
( ~ ( in @ SY2544 @ ( setminus @ SV45 @ SV289 ) )
| ~ ( in @ SY2544 @ SV289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(1062,plain,
! [SV290: $i,SV46: $i] :
( ( ! [SY2545: $i] :
( ~ ( in @ SY2545 @ SV46 )
| ! [SY2546: $i] :
( ~ ( in @ SY2546 @ SV290 )
| ( in @ ( kpair @ SY2545 @ SY2546 ) @ ( cartprod @ SV46 @ SV290 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(1063,plain,
! [SV291: $i,SV47: $i] :
( ( ! [SY2547: $i] :
~ ( ~ ( ~ ( in @ SY2547 @ ( setadjoin @ SV47 @ SV291 ) )
| ( SY2547 = SV47 )
| ( in @ SY2547 @ SV291 ) )
| ~ ( ~ ( ( SY2547 = SV47 )
| ( in @ SY2547 @ SV291 ) )
| ( in @ SY2547 @ ( setadjoin @ SV47 @ SV291 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1064,plain,
! [SV48: $o] :
( ( ( ~ SV48 ) = $true )
| ( ( in @ emptyset @ ( prop2set @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[806]) ).
thf(1065,plain,
( ( ( ~ $true ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[807]) ).
thf(1066,plain,
( ( ( ~ $false ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[808]) ).
thf(1067,plain,
! [SV49: $i,SV292: $i] :
( ( ~ ( in @ SV292 @ ( powerset @ SV49 ) )
| ( in @ ( setminus @ SV49 @ SV292 ) @ ( powerset @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1068,plain,
! [SV293: $i,SV50: $i] :
( ( ! [SY2548: $i] :
( ~ ( in @ SY2548 @ ( setminus @ SV50 @ SV293 ) )
| ( in @ SY2548 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1069,plain,
! [SV294: $i,SV51: $i] :
( ( ! [SY2549: $i] :
( ~ ( func @ SV51 @ SV294 @ SY2549 )
| ! [SY2550: $i] :
( ~ ( in @ SY2550 @ SV51 )
| ( singleton
@ ( dsetconstr @ SV294
@ ^ [SX4: $i] : ( in @ ( kpair @ SY2550 @ SX4 ) @ SY2549 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(1070,plain,
! [SV52: $i,SV295: $i] :
( ( ~ ( in @ SV295 @ ( powerset @ SV52 ) )
| ( subset @ SV295 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(1071,plain,
! [SV53: $i] :
( ( ( ~ ( singleton @ SV53 ) )
= $true )
| ( ( in @ ( setunion @ SV53 ) @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[813]) ).
thf(1072,plain,
! [SV54: $i] :
( ( ( ~ ( iskpair @ SV54 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV54 )
@ ^ [SY1946: $i] :
( SV54
= ( kpair @ ( kfst @ SV54 ) @ SY1946 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[814]) ).
thf(1073,plain,
! [SV296: $i,SV55: $i] :
( ( ! [SY2552: $i] :
( ~ ( in @ SY2552 @ SV55 )
| ! [SY2553: $i] :
( ~ ( in @ SY2553 @ SV296 )
| ( ( kpair @ SY2552 @ SY2553 )
= ( kpair @ SY2552 @ SY2553 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1074,plain,
! [SV297: $i,SV56: $i] :
( ( ! [SY2554: $i] :
( ~ ( in @ SY2554 @ SV56 )
| ! [SY2555: $i] :
( ~ ( in @ SY2555 @ SV297 )
| ( ( ksnd @ ( kpair @ SY2554 @ SY2555 ) )
= SY2555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(1075,plain,
! [SV298: $i,SV57: $i] :
( ( ! [SY2556: $i] :
( ~ ( func @ SV57 @ SV298 @ SY2556 )
| ! [SY2557: $i] :
( ~ ( in @ SY2557 @ SV57 )
| ( in @ ( kpair @ SY2557 @ ( ap @ SV57 @ SV298 @ SY2556 @ SY2557 ) ) @ SY2556 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(1076,plain,
! [SV299: $i,SV58: $i] :
( ( ! [SY2558: $i] :
( ~ ( in @ SY2558 @ ( cartprod @ SV58 @ SV299 ) )
| ( in @ ( kfst @ SY2558 ) @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1077,plain,
! [SV300: $i,SV59: $i] :
( ( ! [SY2559: $i] :
( ( ( setadjoin @ SV59 @ ( setadjoin @ SV300 @ emptyset ) )
!= ( setadjoin @ SY2559 @ emptyset ) )
| ( SV59 = SV300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1078,plain,
! [SV301: $o,SV60: $i] :
( ( ! [SY2560: $i] :
( ~ ( in @ SY2560 @ SV60 )
| ! [SY2561: $i] :
( ~ ( in @ SY2561 @ SV60 )
| ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY2562: $i] :
( ~ ( ~ SV301
| ( SY2562 != SY2560 ) )
| ~ ( ~ ~ SV301
| ( SY2562 != SY2561 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[820]) ).
thf(1079,plain,
! [SV60: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV60 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV60 )
| ( singleton
@ ( dsetconstr @ SV60
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[820]) ).
thf(1080,plain,
! [SV60: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV60 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV60 )
| ( singleton
@ ( dsetconstr @ SV60
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[820]) ).
thf(1081,plain,
! [SV302: $i,SV61: $i] :
( ( ! [SY2563: $i] :
( ~ ( in @ SY2563 @ ( funcSet @ SV61 @ SV302 ) )
| ( func @ SV61 @ SV302 @ SY2563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1082,plain,
! [SV303: $i,SV62: $i] :
( ( ! [SY2564: $i] :
( ~ ( in @ SY2564 @ SV62 )
| ~ ( in @ SY2564 @ SV303 )
| ( in @ SY2564 @ ( binintersect @ SV62 @ SV303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1083,plain,
! [SV304: $i,SV63: $i] :
( ( ! [SY2565: $i] :
( ~ ( subset @ SY2565 @ SV63 )
| ~ ( subset @ SY2565 @ SV304 )
| ( subset @ SY2565 @ ( binintersect @ SV63 @ SV304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1084,plain,
! [SV64: $i,SV305: $i] :
( ( ~ ( in @ SV305 @ ( powerset @ SV64 ) )
| ! [SY2566: $i] :
( ~ ( in @ SY2566 @ ( powerset @ SV64 ) )
| ! [SY2567: $i] :
( ~ ( in @ SY2567 @ SV64 )
| ~ ( in @ SY2567 @ ( setminus @ SV64 @ SV305 ) )
| ~ ( in @ SY2567 @ ( binintersect @ SV305 @ SY2566 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1085,plain,
! [SV306: $i,SV65: $i] :
( ( ! [SY2568: $i] :
( ~ ( in @ SY2568 @ ( binintersect @ SV65 @ SV306 ) )
| ( in @ SY2568 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1086,plain,
! [SV66: $i,SV307: $i] :
( ( ~ ( in @ SV307 @ ( powerset @ SV66 ) )
| ! [SY2569: $i] :
( ~ ( in @ SY2569 @ ( powerset @ SV66 ) )
| ! [SY2570: $i] :
( ~ ( in @ SY2570 @ SV66 )
| ~ ~ ( in @ SY2570 @ ( binunion @ SV307 @ SY2569 ) )
| ~ ( in @ SY2570 @ SY2569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1087,plain,
! [SV308: $i,SV67: $i] :
( ( ! [SY2571: $i] :
( ~ ( func @ SV67 @ SV308 @ SY2571 )
| ! [SY2572: $i] :
( ~ ( in @ SY2572 @ SV67 )
| ( ( ap @ SV67 @ SV308 @ SY2571 @ SY2572 )
= ( ap @ SV67 @ SV308 @ SY2571 @ SY2572 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1088,plain,
! [SV68: $i,SV309: $i] :
( ( ! [SY2573: $i] :
( ~ ( in @ SY2573 @ SV309 )
| ~ ( in @ SY2573 @ ( setminus @ SV68 @ SV309 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(1089,plain,
! [SV69: $i,SV310: $i] :
( ( ~ ( ~ ( ~ ( in @ SV310 @ ( setunion @ SV69 ) )
| ~ ! [SY2574: $i] :
~ ~ ( ~ ( in @ SV310 @ SY2574 )
| ~ ( in @ SY2574 @ SV69 ) ) )
| ~ ( ~ ~ ! [SY2575: $i] :
~ ~ ( ~ ( in @ SV310 @ SY2575 )
| ~ ( in @ SY2575 @ SV69 ) )
| ( in @ SV310 @ ( setunion @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(1090,plain,
! [SV70: $i,SV311: $i] :
( ( ~ ( in @ SV311 @ ( powerset @ SV70 ) )
| ! [SY2576: $i] :
( ~ ( in @ SY2576 @ ( powerset @ SV70 ) )
| ! [SY2577: $i] :
( ~ ( in @ SY2577 @ SV70 )
| ~ ( in @ SY2577 @ ( setminus @ SV70 @ ( binunion @ SV311 @ SY2576 ) ) )
| ~ ( in @ SY2577 @ SV311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1091,plain,
! [SV312: $i,SV71: $i] :
( ( ~ ! [SY2578: $i] :
( ~ ( in @ SY2578 @ SV71 )
| ( in @ SY2578 @ SV312 ) )
| ( subset @ SV71 @ SV312 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(1092,plain,
! [SV313: $i > $o,SV72: $i] :
( ( ! [SY2579: $i] :
( ~ ( in @ SY2579
@ ( dsetconstr @ SV72
@ ^ [SY2580: $i] : ( SV313 @ SY2580 ) ) )
| ( SV313 @ SY2579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1093,plain,
! [SV73: $i,SV314: $i] :
( ( ~ ( in @ SV314 @ ( powerset @ SV73 ) )
| ! [SY2581: $i] :
( ~ ( in @ SY2581 @ ( powerset @ SV73 ) )
| ~ ! [SY2582: $i] :
( ~ ( in @ SY2582 @ SV73 )
| ~ ( in @ SY2582 @ SV314 )
| ( in @ SY2582 @ SY2581 ) )
| ( in @ SV314 @ ( powerset @ SY2581 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1094,plain,
! [SV315: $i,SV74: $i] :
( ( ! [SY2583: $i] :
( ~ ( in @ SY2583 @ ( symdiff @ SV74 @ SV315 ) )
| ! [SY2584: $o] :
( ~ ( ~ ( in @ SY2583 @ SV74 )
| ~ ~ ( in @ SY2583 @ SV315 )
| SY2584 )
| ~ ( ~ ~ ( in @ SY2583 @ SV74 )
| ~ ( in @ SY2583 @ SV315 )
| SY2584 )
| SY2584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1095,plain,
! [SV75: $i] :
( ( ( ~ ! [SY2000: $i] :
~ ( in @ SY2000 @ SV75 ) )
= $true )
| ( ( SV75 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(1096,plain,
! [SV316: $i,SV76: $i] :
( ( ! [SY2585: $i] :
( ~ ( subset @ SV76 @ SV316 )
| ~ ~ ( in @ SY2585 @ SV316 )
| ~ ( in @ SY2585 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1097,plain,
! [SV317: $i,SV77: $i] :
( ( ! [SY2586: $i > $i > $o,SY2587: $i,SY2588: $i] :
( ~ ( in @ ( kpair @ SY2587 @ SY2588 )
@ ( dpsetconstr @ SV77 @ SV317
@ ^ [SX5: $i,SX6: $i] : ( SY2586 @ SX5 @ SX6 ) ) )
| ( in @ SY2588 @ SV317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1098,plain,
! [SV78: $i] :
( ( ( ~ ( ( SV78 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY2009: $i] :
~ ( in @ SY2009 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[838]) ).
thf(1099,plain,
! [SV318: $i > $o,SV79: $i] :
( ( ~ ~ ~ ! [SY2591: $i] :
~ ~ ( ~ ( in @ SY2591 @ SV79 )
| ~ ( SV318 @ SY2591 ) )
| ! [SY2592: $i] :
( ~ ( in @ SY2592 @ SV79 )
| ~ ( SV318 @ SY2592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1100,plain,
! [SV319: $i,SV80: $i] :
( ( ! [SY2593: $i] :
( ~ ( in @ SY2593 @ SV80 )
| ( in @ SY2593 @ ( binunion @ SV80 @ SV319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1101,plain,
! [SV81: $i,SV320: $i] :
( ( ~ ( in @ SV320 @ SV81 )
| ( in @ SV320 @ ( powerset @ ( setunion @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1102,plain,
! [SV82: $i] :
( ( ( ~ ~ ! [SY2016: $i] :
~ ( in @ SY2016 @ SV82 ) )
= $true )
| ( ( ~ ! [SY2017: $i] :
~ ~ ( ~ ( in @ SY2017 @ SV82 )
| ~ ~ ~ ! [SY2018: $i] :
~ ~ ( ~ ( in @ SY2018 @ SY2017 )
| ~ ( in @ SY2018 @ SV82 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(1103,plain,
! [SV321: $i,SV83: $i] :
( ( ( ( binintersect @ SV83 @ SV321 )
!= SV83 )
| ( subset @ SV83 @ SV321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1104,plain,
! [SV322: $i,SV84: $i] :
( ( ! [SY2594: $i,SY2595: $o] :
( ~ ( in @ SY2594 @ ( binunion @ SV84 @ SV322 ) )
| ~ ( ~ ( in @ SY2594 @ SV84 )
| SY2595 )
| ~ ( ~ ( in @ SY2594 @ SV322 )
| SY2595 )
| SY2595 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1105,plain,
! [SV85: $i,SV323: $i] :
( ( ~ ( in @ SV323 @ ( powerset @ SV85 ) )
| ! [SY2596: $i] :
( ~ ( in @ SY2596 @ ( powerset @ SV85 ) )
| ! [SY2597: $i] :
( ~ ( in @ SY2597 @ SV85 )
| ~ ~ ( in @ SY2597 @ ( binunion @ SV323 @ SY2596 ) )
| ~ ( in @ SY2597 @ SV323 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1106,plain,
! [SV86: $i > $o,SV324: $i] :
( ( ~ ( in @ SV324 @ emptyset )
| ( SV86 @ SV324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1107,plain,
! [SV325: $i > $o,SV87: $i] :
( ( ~ ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ SV87 )
| ( SV325 @ SY2598 ) )
| ~ ! [SY2599: $i] :
~ ~ ( ~ ( in @ SY2599 @ SV87 )
| ~ ~ ( SV325 @ SY2599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1108,plain,
! [SV326: $i,SV88: $i] :
( ( ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ SV88 )
| ( in @ SY2600 @ SV326 ) )
| ~ ! [SY2601: $i] :
( ~ ( in @ SY2601 @ SV326 )
| ( in @ SY2601 @ SV88 ) )
| ( SV88 = SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1109,plain,
! [SV327: $i,SV89: $i] :
( ( ( SV89 != SV327 )
| ( subset @ SV89 @ SV327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1110,plain,
! [SV90: $i,SV328: $i] :
( ( ~ ( in @ SV328 @ ( powerset @ SV90 ) )
| ( in @ ( powerset @ SV328 ) @ ( powerset @ ( powerset @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1111,plain,
! [SV91: $i > $o] :
( ( ( ~ ~ ! [SY2035: $i] :
~ ~ ( ~ ( SV91 @ SY2035 )
| ~ ! [SY2036: $i] :
( ~ ( SV91 @ SY2036 )
| ( SY2035 = SY2036 ) ) ) )
= $true )
| ( ( ! [SY2037: $i,SY2038: $i] :
( ~ ( SV91 @ SY2037 )
| ~ ( SV91 @ SY2038 )
| ( SY2037 = SY2038 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(1112,plain,
! [SV329: $i,SV92: $i] :
( ( ! [SY2602: $i] :
( ~ ( func @ SV92 @ SV329 @ SY2602 )
| ! [SY2603: $i] :
( ~ ( in @ SY2603 @ SV92 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV329
@ ^ [SX4: $i] : ( in @ ( kpair @ SY2603 @ SX4 ) @ SY2602 ) ) )
@ SV329 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1113,plain,
! [SV330: $i,SV93: $i] :
( ( ( SV93 != SV330 )
| ( ( setadjoin @ ( setadjoin @ SV93 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV93 @ ( setadjoin @ SV330 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV93 @ emptyset ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1114,plain,
! [SV331: $i,SV94: $i] :
( ( ! [SY2605: $i] :
( ~ ( in @ SY2605 @ SV94 )
| ~ ~ ( in @ SY2605 @ SV331 )
| ~ ( subset @ SV94 @ SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1115,plain,
! [SV332: $i,SV95: $i] :
( ( ! [SY2606: $i] :
( ~ ( subset @ SY2606 @ ( cartprod @ SV95 @ SV332 ) )
| ! [SY2607: $i] :
( ~ ( subset @ SY2607 @ ( cartprod @ SV95 @ SV332 ) )
| ~ ! [SY2608: $i] :
( ~ ( in @ SY2608 @ SV95 )
| ! [SY2609: $i] :
( ~ ( in @ SY2609 @ SV332 )
| ~ ( in @ ( kpair @ SY2608 @ SY2609 ) @ SY2606 )
| ( in @ ( kpair @ SY2608 @ SY2609 ) @ SY2607 ) ) )
| ( subset @ SY2606 @ SY2607 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1116,plain,
! [SV96: $i,SV333: $i] :
( ( ~ ( in @ SV333 @ ( setunion @ SV96 ) )
| ~ ! [SY2610: $i] :
~ ~ ( ~ ( in @ SY2610 @ SV96 )
| ~ ( in @ SV333 @ SY2610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1117,plain,
! [SV97: $i,SV334: $i] :
( ( ~ ( in @ SV334 @ ( powerset @ SV97 ) )
| ! [SY2611: $i] :
( ~ ( in @ SY2611 @ SV97 )
| ~ ~ ( in @ SY2611 @ ( setminus @ SV97 @ SV334 ) )
| ( in @ SY2611 @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1118,plain,
! [SV335: $i > $o,SV98: $i] :
( ( ! [SY2612: $i] :
( ~ ( in @ SY2612 @ SV98 )
| ~ ( ~ ( ~ ( in @ SY2612
@ ( dsetconstr @ SV98
@ ^ [SY2613: $i] : ( SV335 @ SY2613 ) ) )
| ( SV335 @ SY2612 ) )
| ~ ( ~ ( SV335 @ SY2612 )
| ( in @ SY2612
@ ( dsetconstr @ SV98
@ ^ [SY2614: $i] : ( SV335 @ SY2614 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1119,plain,
! [SV99: $i,SV336: $i] :
( ( ~ ! [SY2615: $i] :
( ~ ( in @ SY2615 @ SV336 )
| ( in @ SY2615 @ SV99 ) )
| ( in @ SV336 @ ( powerset @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1120,plain,
! [SV337: $i > $o,SV100: $i] :
( ( ! [SY2616: $i] :
( ~ ( in @ SY2616 @ SV100 )
| ~ ( SV337 @ SY2616 )
| ~ ! [SY2617: $i] :
( ~ ( in @ SY2617 @ SV100 )
| ~ ( SV337 @ SY2617 )
| ( SY2617 = SY2616 ) )
| ( singleton
@ ( dsetconstr @ SV100
@ ^ [SY2618: $i] : ( SV337 @ SY2618 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1121,plain,
! [SV338: $i,SV101: $i] :
( ( ! [SY2619: $i > $i > $o,SY2620: $i,SY2621: $i] :
( ~ ( in @ ( kpair @ SY2620 @ SY2621 )
@ ( dpsetconstr @ SV101 @ SV338
@ ^ [SX5: $i,SX6: $i] : ( SY2619 @ SX5 @ SX6 ) ) )
| ( SY2619 @ SY2620 @ SY2621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1122,plain,
( ( ! [SY2624: $i] :
( ~ ( in @ SY2624 @ ( powerset @ sK1_SX0 ) )
| ! [SY2625: $i] :
( ~ ( in @ SY2625 @ ( powerset @ sK1_SX0 ) )
| ! [SY2626: $o,SY2627: $i] :
( ~ ( in @ SY2627 @ sK1_SX0 )
| ~ ( in @ SY2627 @ ( binunion @ SY2624 @ SY2625 ) )
| ~ ( ~ ( in @ SY2627 @ SY2624 )
| SY2626 )
| ~ ( ~ ( in @ SY2627 @ SY2625 )
| SY2626 )
| SY2626 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[862]) ).
thf(1123,plain,
! [SV339: $i,SV102: $i] :
( ( ~ ( in @ SV102 @ ( setadjoin @ SV339 @ emptyset ) )
| ( in @ SV339 @ ( setadjoin @ SV102 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1124,plain,
! [SV340: $i,SV103: $i] :
( ( ! [SY2628: $i] :
( ~ ( in @ SY2628 @ ( funcSet @ SV103 @ SV340 ) )
| ( ( lam @ SV103 @ SV340
@ ^ [SY2629: $i] : ( ap @ SV103 @ SV340 @ SY2628 @ SY2629 ) )
= SY2628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1125,plain,
! [SV341: $i,SV104: $i] :
( ( ! [SY2630: $i] :
( ~ ( in @ SY2630 @ SV104 )
| ! [SY2631: $i] :
( ~ ( in @ SY2631 @ SV341 )
| ( subset @ ( setadjoin @ SY2630 @ ( setadjoin @ SY2631 @ emptyset ) ) @ ( binunion @ SV104 @ SV341 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1126,plain,
! [SV342: $i,SV105: $i] :
( ( ! [SY2632: $i] :
( ~ ( subset @ SY2632 @ ( cartprod @ SV105 @ SV342 ) )
| ! [SY2633: $i > $o] :
( ~ ! [SY2634: $i] :
( ~ ( in @ SY2634 @ SV105 )
| ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV342 )
| ~ ( in @ ( kpair @ SY2634 @ SY2635 ) @ SY2632 )
| ( SY2633 @ ( kpair @ SY2634 @ SY2635 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2632 )
| ( SY2633 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1127,plain,
! [SV106: $i > $o] :
( ( ( ~ ~ ! [SY2084: $i] :
~ ~ ( ~ ( SV106 @ SY2084 )
| ~ ! [SY2085: $i] :
( ~ ( SV106 @ SY2085 )
| ( SY2084 = SY2085 ) ) ) )
= $true )
| ( ( ! [SY2086: $i,SY2087: $i] :
( ~ ( SV106 @ SY2086 )
| ~ ( SV106 @ SY2087 )
| ( SY2086 = SY2087 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(1128,plain,
! [SV343: $i > $o,SV107: $i] :
( ( ! [SY2637: $i] :
( ~ ( in @ SY2637 @ SV107 )
| ~ ( SV343 @ SY2637 )
| ( in @ SY2637
@ ( dsetconstr @ SV107
@ ^ [SY2638: $i] : ( SV343 @ SY2638 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1129,plain,
! [SV108: $i > $o] :
( ( ( ~ ~ ! [SY2091: $i] :
~ ~ ( ~ ( SV108 @ SY2091 )
| ~ ! [SY2092: $i] :
( ~ ( SV108 @ SY2092 )
| ( SY2091 = SY2092 ) ) ) )
= $true )
| ( ( SV108
@ ( descr
@ ^ [SY2093: $i] : ( SV108 @ SY2093 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[869]) ).
thf(1130,plain,
! [SV344: $i,SV109: $i] :
( ( ! [SY2639: $i > $i > $o,SY2640: $i,SY2641: $i] :
( ~ ( in @ ( kpair @ SY2640 @ SY2641 )
@ ( dpsetconstr @ SV109 @ SV344
@ ^ [SX5: $i,SX6: $i] : ( SY2639 @ SX5 @ SX6 ) ) )
| ( in @ SY2640 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1131,plain,
! [SV345: $i,SV110: $i] :
( ( ~ ( subset @ SV110 @ SV345 )
| ( ( binintersect @ SV110 @ SV345 )
= SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1132,plain,
! [SV111: $i] :
( ( ( ~ ! [SY2101: $i] :
~ ( in @ SY2101 @ SV111 ) )
= $true )
| ( ( SV111 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(1133,plain,
! [SV112: $i,SV346: $i] :
( ( ~ ( subset @ SV346 @ SV112 )
| ( ( binintersect @ SV112 @ SV346 )
= SV346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1134,plain,
! [SV347: $i,SV113: $i] :
( ( ! [SY2644: $i] :
( ~ ~ ( in @ SY2644 @ ( setminus @ SV113 @ SV347 ) )
| ~ ~ ( in @ SY2644 @ SV347 )
| ~ ( in @ SY2644 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1135,plain,
! [SV114: $i > $o] :
( ( ( ~ ~ ! [SY2105: $i] :
~ ~ ( ~ ( SV114 @ SY2105 )
| ~ ! [SY2106: $i] :
( ~ ( SV114 @ SY2106 )
| ( SY2105 = SY2106 ) ) ) )
= $true )
| ( ( ~ ! [SY2107: $i] :
~ ( SV114 @ SY2107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(1136,plain,
! [SV115: $i,SV348: $i] :
( ( ~ ( in @ SV348 @ ( powerset @ SV115 ) )
| ! [SY2645: $i] :
( ~ ( in @ SY2645 @ ( powerset @ SV115 ) )
| ! [SY2646: $i] :
( ~ ( in @ SY2646 @ ( powerset @ SV115 ) )
| ! [SY2647: $i] :
( ~ ( in @ SY2647 @ SV115 )
| ~ ( in @ SY2647 @ ( binintersect @ SV348 @ SY2645 ) )
| ( in @ SY2647 @ ( binunion @ SV348 @ SY2646 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1137,plain,
! [SV116: $i] :
( ( ( ~ ( iskpair @ SV116 ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV116 ) @ ( ksnd @ SV116 ) )
= SV116 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(1138,plain,
! [SV117: $i,SV349: $i] :
( ( ~ ( in @ SV349 @ ( powerset @ SV117 ) )
| ! [SY2648: $i] :
( ~ ( in @ SY2648 @ ( powerset @ SV117 ) )
| ( in @ ( binintersect @ SV349 @ SY2648 ) @ ( powerset @ SV117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1139,plain,
! [SV350: $i > $o,SV118: $i] :
( ( ~ ! [SY2649: $i] :
( ~ ( in @ SY2649 @ SV118 )
| ~ ( SV350 @ SY2649 ) )
| ~ ~ ! [SY2650: $i] :
~ ~ ( ~ ( in @ SY2650 @ SV118 )
| ~ ( SV350 @ SY2650 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1140,plain,
! [SV351: $i > $o,SV119: $i] :
( ( ~ ~ ! [SY2651: $i] :
( ~ ( in @ SY2651 @ SV119 )
| ( SV351 @ SY2651 ) )
| ~ ! [SY2652: $i] :
~ ~ ( ~ ( in @ SY2652 @ SV119 )
| ~ ~ ( SV351 @ SY2652 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1141,plain,
! [SV120: $i,SV352: $i] :
( ( ~ ( in @ SV352 @ ( powerset @ SV120 ) )
| ! [SY2653: $i] :
( ~ ( in @ SY2653 @ ( powerset @ SV120 ) )
| ! [SY2654: $i] :
( ~ ( in @ SY2654 @ SV120 )
| ~ ~ ( in @ SY2654 @ SY2653 )
| ~ ( in @ SY2654 @ ( binintersect @ SV352 @ SY2653 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1142,plain,
! [SV121: $i,SV353: $i] :
( ( ~ ( in @ SV353 @ ( powerset @ SV121 ) )
| ! [SY2655: $i] :
( ~ ( in @ SY2655 @ ( powerset @ SV121 ) )
| ~ ( subset @ SV353 @ ( setminus @ SV121 @ SY2655 ) )
| ! [SY2656: $i] :
( ~ ( in @ SY2656 @ SV121 )
| ~ ( in @ SY2656 @ SY2655 )
| ( in @ SY2656 @ ( setminus @ SV121 @ SV353 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1143,plain,
! [SV354: $i,SV122: $i] :
( ( ~ ~ ( subset @ SV122 @ SV354 )
| ( SV122 != SV354 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1144,plain,
! [SV355: $i,SV123: $i] :
( ( ! [SY2657: $i > $i] :
( ~ ! [SY2658: $i] :
( ~ ( in @ SY2658 @ SV123 )
| ( in @ ( SY2657 @ SY2658 ) @ SV355 ) )
| ( in
@ ( lam @ SV123 @ SV355
@ ^ [SX3: $i] : ( SY2657 @ SX3 ) )
@ ( funcSet @ SV123 @ SV355 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1145,plain,
! [SV124: $i,SV356: $i] :
( ( ! [SY2660: $i] :
( ~ ( in @ SV356 @ SY2660 )
| ~ ( in @ SY2660 @ SV124 )
| ( in @ SV356 @ ( setunion @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1146,plain,
! [SV357: $i,SV125: $i] :
( ( ! [SY2661: $i] :
( ~ ( in @ ( setadjoin @ SY2661 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV125 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV125 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) ) )
| ( SV125 = SY2661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1147,plain,
! [SV358: $i,SV126: $i] :
( ( ! [SY2662: $i] :
( ~ ( in @ SY2662 @ ( setadjoin @ SV126 @ SV358 ) )
| ! [SY2663: $o] :
( ~ ( ( SY2662 != SV126 )
| SY2663 )
| ~ ( ~ ( in @ SY2662 @ SV358 )
| SY2663 )
| SY2663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1148,plain,
! [SV359: $i,SV127: $i] :
( ( ! [SY2664: $i] :
( ~ ~ ( in @ SY2664 @ SV127 )
| ~ ~ ( in @ SY2664 @ SV359 )
| ~ ( in @ SY2664 @ ( symdiff @ SV127 @ SV359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1149,plain,
! [SV360: $i,SV128: $i] :
( ( ! [SY2665: $i] :
( ~ ( in @ SY2665 @ SV128 )
| ! [SY2666: $i] :
( ~ ( in @ SY2666 @ SV360 )
| ( in @ ( setadjoin @ SY2665 @ ( setadjoin @ SY2666 @ emptyset ) ) @ ( powerset @ ( binunion @ SV128 @ SV360 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1150,plain,
! [SV129: $i,SV361: $i] :
( ( ~ ( in @ SV361 @ ( powerset @ SV129 ) )
| ! [SY2667: $i] :
( ~ ( in @ SY2667 @ ( powerset @ SV129 ) )
| ~ ( subset @ SV361 @ ( setminus @ SV129 @ SY2667 ) )
| ( subset @ SY2667 @ ( setminus @ SV129 @ SV361 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1151,plain,
! [SV130: $i,SV362: $i] :
( ( ~ ( in @ SV362 @ ( powerset @ SV130 ) )
| ! [SY2668: $i] :
( ~ ( in @ SY2668 @ ( powerset @ SV130 ) )
| ! [SY2669: $i] :
( ~ ( in @ SY2669 @ SV130 )
| ~ ~ ( in @ SY2669 @ SV362 )
| ~ ( in @ SY2669 @ ( binintersect @ SV362 @ SY2668 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1152,plain,
! [SV131: $i,SV363: $i] :
( ( ~ ( in @ SV363 @ ( powerset @ SV131 ) )
| ! [SY2670: $i] :
( ~ ( in @ SY2670 @ ( powerset @ SV131 ) )
| ! [SY2671: $i] :
( ~ ( in @ SY2671 @ SV131 )
| ~ ( in @ SY2671 @ ( setminus @ SV131 @ SV363 ) )
| ( in @ SY2671 @ ( setminus @ SV131 @ ( binintersect @ SV363 @ SY2670 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1153,plain,
! [SV364: $i,SV132: $i] :
( ( ! [SY2672: $i] :
( ~ ( in @ SY2672 @ ( cartprod @ SV132 @ SV364 ) )
| ( in @ ( ksnd @ SY2672 ) @ SV364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1154,plain,
! [SV133: $i,SV365: $i] :
( ( ~ ( in @ SV365 @ ( powerset @ SV133 ) )
| ! [SY2673: $i] :
( ~ ( in @ SY2673 @ SV133 )
| ~ ( in @ SY2673 @ SV365 )
| ( in @ SY2673 @ ( setminus @ SV133 @ ( setminus @ SV133 @ SV365 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1155,plain,
! [SV366: $i,SV134: $i] :
( ( ! [SY2674: $i] :
( ~ ( func @ SV134 @ SV366 @ SY2674 )
| ( ( lam @ SV134 @ SV366
@ ^ [SY2675: $i] : ( ap @ SV134 @ SV366 @ SY2674 @ SY2675 ) )
= SY2674 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1156,plain,
! [SV367: $i > $o,SV135: $i] :
( ( ~ ( singleton
@ ( dsetconstr @ SV135
@ ^ [SY2676: $i] : ( SV367 @ SY2676 ) ) )
| ! [SY2677: $i] :
( ~ ( in @ SY2677 @ SV135 )
| ! [SY2678: $i] :
( ~ ( in @ SY2678 @ SV135 )
| ~ ( SV367 @ SY2677 )
| ~ ( SV367 @ SY2678 )
| ( SY2677 = SY2678 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1157,plain,
! [SV136: $i,SV368: $i] :
( ( ~ ( in @ SV368 @ ( setunion @ SV136 ) )
| ! [SY2679: $o] :
( ~ ! [SY2680: $i] :
( ~ ( in @ SV368 @ SY2680 )
| ~ ( in @ SY2680 @ SV136 )
| SY2679 )
| SY2679 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1158,plain,
! [SV137: $i,SV369: $i] :
( ( ~ ( in @ SV369 @ ( powerset @ SV137 ) )
| ! [SY2681: $i] :
( ~ ( in @ SY2681 @ ( powerset @ SV137 ) )
| ! [SY2682: $i] :
( ~ ( in @ SY2682 @ SV137 )
| ~ ( subset @ SV369 @ SY2681 )
| ~ ~ ( in @ SY2682 @ SY2681 )
| ~ ( in @ SY2682 @ SV369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1159,plain,
! [SV370: $i,SV138: $i] :
( ( ! [SY2683: $i] :
( ~ ( in @ SY2683 @ ( setadjoin @ SV138 @ ( setadjoin @ SV370 @ emptyset ) ) )
| ( SY2683 = SV138 )
| ( SY2683 = SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1160,plain,
! [SV139: $i] :
( ( ( ~ ( in @ SV139 @ emptyset ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[900]) ).
thf(1161,plain,
! [SV371: $i,SV140: $i] :
( ( ! [SY2684: $i] :
( ~ ( in @ SY2684 @ ( cartprod @ SV140 @ SV371 ) )
| ( iskpair @ SY2684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1162,plain,
! [SV141: $i,SV372: $i] :
( ( ! [SY2685: $i] :
( ~ ( in @ SY2685 @ SV372 )
| ( in @ SY2685 @ ( setadjoin @ SV141 @ SV372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1163,plain,
! [SV373: $i,SV142: $i] :
( ( ! [SY2686: $i,SY2687: $i] :
( ~ ( in @ ( kpair @ SY2686 @ SY2687 ) @ ( cartprod @ SV142 @ SV373 ) )
| ( in @ SY2687 @ SV373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1164,plain,
! [SV374: $i,SV143: $i] :
( ( ! [SY2688: $i] :
( ~ ( in @ SY2688 @ ( funcSet @ SV143 @ SV374 ) )
| ! [SY2689: $i] :
( ~ ( in @ SY2689 @ SV143 )
| ( in @ ( kpair @ SY2689 @ ( ap @ SV143 @ SV374 @ SY2688 @ SY2689 ) ) @ SY2688 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1165,plain,
! [SV375: $i,SV144: $i] :
( ( ~ ( subset @ SV144 @ SV375 )
| ( subset @ ( powerset @ SV144 ) @ ( powerset @ SV375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1166,plain,
! [SV376: $i,SV145: $i] :
( ( ! [SY2690: $i] :
( ~ ( in @ SY2690 @ ( cartprod @ SV145 @ SV376 ) )
| ( ( kpair @ ( kfst @ SY2690 ) @ ( ksnd @ SY2690 ) )
= SY2690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1167,plain,
! [SV146: $i,SV377: $i] :
( ( ~ ( in @ SV377 @ ( powerset @ SV146 ) )
| ! [SY2691: $i] :
( ~ ( in @ SY2691 @ ( powerset @ SV146 ) )
| ~ ! [SY2692: $i] :
( ~ ( in @ SY2692 @ SV146 )
| ~ ( in @ SY2692 @ SV377 )
| ( in @ SY2692 @ SY2691 ) )
| ( subset @ SV377 @ SY2691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1168,plain,
! [SV147: $i] :
( ( ! [SY2186: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY2187: $i] :
( ~ ( in @ SY2187 @ SY2186 )
| ! [SY2188: $i] :
( ~ ( in @ SY2188 @ SY2187 )
| ( in @ SY2188 @ SV147 ) ) )
| ~ ! [SY2189: $i,SY2190: $i] :
( ~ ~ ( ~ ( in @ SY2189 @ SV147 )
| ~ ( in @ SY2190 @ SV147 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2186 )
| ~ ( ~ ( ~ ( in @ SY2189 @ SX4 )
| ( in @ SY2190 @ SX4 ) )
| ~ ( ~ ( in @ SY2190 @ SX4 )
| ( in @ SY2189 @ SX4 ) ) ) )
| ( SY2189 = SY2190 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY2186 )
| ~ ( in @ SX3 @ SY2186 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY2196: $i] :
( ~ ~ ( ~ ! [SY2197: $i] :
( ~ ( in @ SY2197 @ SY2196 )
| ( in @ SY2197 @ SV147 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY2196 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY2186 )
| ~ ( in @ SX4 @ SY2196 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY2196 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2186 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(1169,plain,
! [SV378: $i,SV148: $i] :
( ( ! [SY2693: $i] :
( ~ ( subset @ SV148 @ SV378 )
| ~ ( in @ SY2693 @ SV148 )
| ( in @ SY2693 @ SV378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1170,plain,
! [SV149: $i,SV379: $i] :
( ( ~ ( subset @ SV379 @ SV149 )
| ( in @ SV379 @ ( powerset @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1171,plain,
! [SV150: $i,SV380: $i] :
( ( ! [SY2694: $i] :
( ~ ( in @ SY2694 @ SV380 )
| ( in @ SY2694 @ ( binunion @ SV150 @ SV380 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1172,plain,
! [SV151: $i,SV381: $i] :
( ( ~ ( in @ SV381 @ ( powerset @ SV151 ) )
| ! [SY2695: $i] :
( ~ ( in @ SY2695 @ ( powerset @ SV151 ) )
| ! [SY2696: $i] :
( ~ ( in @ SY2696 @ ( powerset @ SV151 ) )
| ! [SY2697: $i] :
( ~ ( in @ SY2697 @ SV151 )
| ~ ( in @ SY2697 @ ( binintersect @ SV381 @ SY2695 ) )
| ( in @ SY2697 @ ( binunion @ SY2695 @ SY2696 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1173,plain,
! [SV382: $i,SV152: $i] :
( ( ( SV152 != SV382 )
| ( ( setunion @ SV152 )
= ( setunion @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1174,plain,
! [SV383: $i,SV153: $i] :
( ( ! [SY2698: $i,SY2699: $i] :
( ~ ( in @ ( kpair @ SY2698 @ SY2699 ) @ ( cartprod @ SV153 @ SV383 ) )
| ( in @ SY2698 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1175,plain,
! [SV384: $i,SV154: $i] :
( ( ! [SY2700: $i] :
( ~ ( in @ SY2700 @ ( binunion @ SV154 @ SV384 ) )
| ( in @ SY2700 @ SV154 )
| ( in @ SY2700 @ SV384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1176,plain,
! [SV385: $i,SV155: $i] :
( ( ~ ! [SY2701: $i] :
( ~ ( in @ SY2701 @ SV155 )
| ( in @ SY2701 @ SV385 ) )
| ( subset @ SV155 @ SV385 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1177,plain,
! [SV156: $i,SV386: $i] :
( ( ~ ( in @ SV386 @ ( powerset @ SV156 ) )
| ! [SY2702: $i] :
( ~ ( in @ SY2702 @ ( powerset @ SV156 ) )
| ! [SY2703: $i] :
( ~ ( in @ SY2703 @ SV156 )
| ~ ( subset @ SV386 @ ( setminus @ SV156 @ SY2702 ) )
| ~ ( in @ SY2703 @ SY2702 )
| ~ ( in @ SY2703 @ SV386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1178,plain,
! [SV387: $i > $o,SV157: $i] :
( ( ! [SY2704: $i] :
( ~ ( in @ SY2704
@ ( dsetconstr @ SV157
@ ^ [SY2705: $i] : ( SV387 @ SY2705 ) ) )
| ( in @ SY2704 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1179,plain,
! [SV388: $i,SV158: $i] :
( ( ! [SY2706: $i] :
( ~ ~ ( in @ SY2706 @ ( setminus @ SV158 @ SV388 ) )
| ~ ( in @ SY2706 @ SV158 )
| ( in @ SY2706 @ SV388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1180,plain,
! [SV159: $i,SV389: $i] :
( ( ~ ( in @ SV389 @ ( powerset @ SV159 ) )
| ( SV389
= ( setminus @ SV159 @ ( setminus @ SV159 @ SV389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1181,plain,
! [SV160: $i > $o] :
( ( ( ~ ~ ! [SY2230: $i] :
~ ( SV160 @ SY2230 ) )
= $true )
| ( ( ~ ! [SY2231: $i,SY2232: $i] :
( ~ ( SV160 @ SY2231 )
| ~ ( SV160 @ SY2232 )
| ( SY2231 = SY2232 ) )
| ~ ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(1182,plain,
! [SV161: $i,SV390: $i] :
( ( ~ ( in @ SV390 @ ( powerset @ SV161 ) )
| ! [SY2707: $i] :
( ~ ( in @ SY2707 @ ( powerset @ SV161 ) )
| ( in @ ( setminus @ SV161 @ SV390 ) @ ( powerset @ ( setminus @ SV161 @ ( binintersect @ SV390 @ SY2707 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1183,plain,
! [SV162: $i,SV391: $i] :
( ( ~ ( in @ SV391 @ ( powerset @ SV162 ) )
| ! [SY2708: $i] :
( ~ ( in @ SY2708 @ ( powerset @ SV162 ) )
| ( in @ ( setminus @ SV391 @ SY2708 ) @ ( powerset @ SV162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1184,plain,
! [SV163: $i] :
( ( ( ~ ( subset @ SV163 @ emptyset ) )
= $true )
| ( ( SV163 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(1185,plain,
! [SV392: $i,SV164: $i] :
( ( ! [SY2709: $i] :
( ~ ( in @ SY2709 @ SV164 )
| ~ ~ ( in @ SY2709 @ SV392 )
| ( in @ SY2709 @ ( symdiff @ SV164 @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1186,plain,
! [SV393: $i,SV165: $i] :
( ( ( SV165 != SV393 )
| ! [SY2710: $i,SY2711: $i] :
( ( SY2710 != SY2711 )
| ~ ( in @ SY2710 @ SV165 )
| ( in @ SY2711 @ SV393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1187,plain,
! [SV394: $i,SV166: $i] :
( ( ! [SY2712: $i] :
( ~ ( in @ SY2712 @ SV166 )
| ~ ~ ( in @ SY2712 @ SV394 )
| ( SV166 != SV394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1188,plain,
! [SV167: $i,SV395: $i] :
( ( ~ ( in @ SV395 @ ( powerset @ SV167 ) )
| ! [SY2713: $i] :
( ~ ( in @ SY2713 @ ( powerset @ SV167 ) )
| ! [SY2714: $i] :
( ~ ( in @ SY2714 @ SV167 )
| ~ ( in @ SY2714 @ ( setminus @ SV167 @ ( binunion @ SV395 @ SY2713 ) ) )
| ( in @ SY2714 @ ( setminus @ SV167 @ SV395 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1189,plain,
! [SV396: $i,SV168: $i] :
( ( ! [SY2715: $i] :
( ~ ( func @ SV168 @ SV396 @ SY2715 )
| ! [SY2716: $i] :
( ~ ( func @ SV168 @ SV396 @ SY2716 )
| ~ ! [SY2717: $i] :
( ~ ( in @ SY2717 @ SV168 )
| ( ( ap @ SV168 @ SV396 @ SY2715 @ SY2717 )
= ( ap @ SV168 @ SV396 @ SY2716 @ SY2717 ) ) )
| ( SY2715 = SY2716 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1190,plain,
! [SV397: $o,SV169: $i] :
( ( ! [SY2718: $i] :
( ~ ( in @ SY2718 @ SV169 )
| ! [SY2719: $i] :
( ~ ( in @ SY2719 @ SV169 )
| ( in @ ( if @ SV169 @ SV397 @ SY2718 @ SY2719 ) @ ( setadjoin @ SY2718 @ ( setadjoin @ SY2719 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[930]) ).
thf(1191,plain,
! [SV169: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV169 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV169 )
| ( in @ ( if @ SV169 @ $true @ SX0 @ SX1 ) @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[930]) ).
thf(1192,plain,
! [SV169: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV169 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV169 )
| ( in @ ( if @ SV169 @ $false @ SX0 @ SX1 ) @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[930]) ).
thf(1193,plain,
! [SV398: $i,SV170: $i] :
( ( ! [SY2720: $i > $i] :
( ~ ! [SY2721: $i] :
( ~ ( in @ SY2721 @ SV170 )
| ( in @ ( SY2720 @ SY2721 ) @ SV398 ) )
| ( ( lam @ SV170 @ SV398
@ ^ [SX3: $i] : ( SY2720 @ SX3 ) )
= ( lam @ SV170 @ SV398
@ ^ [SX3: $i] : ( SY2720 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1194,plain,
! [SV399: $o,SV171: $i] :
( ( ! [SY2724: $i] :
( ~ ( in @ SY2724 @ SV171 )
| ! [SY2725: $i] :
( ~ ( in @ SY2725 @ SV171 )
| ~ ~ SV399
| ( ( dsetconstr @ SV171
@ ^ [SY2726: $i] :
( ~ ( ~ SV399
| ( SY2726 != SY2724 ) )
| ~ ( ~ ~ SV399
| ( SY2726 != SY2725 ) ) ) )
= ( setadjoin @ SY2725 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[932]) ).
thf(1195,plain,
! [SV171: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV171 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV171 )
| ~ ~ $true
| ( ( dsetconstr @ SV171
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX1 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[932]) ).
thf(1196,plain,
! [SV171: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV171 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV171 )
| ~ ~ $false
| ( ( dsetconstr @ SV171
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX1 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[932]) ).
thf(1197,plain,
! [SV172: $i,SV400: $i] :
( ( ~ ( ~ ( ~ ( in @ SV400 @ ( powerset @ SV172 ) )
| ! [SY2727: $i] :
( ~ ( in @ SY2727 @ SV400 )
| ( in @ SY2727 @ SV172 ) ) )
| ~ ( ~ ! [SY2728: $i] :
( ~ ( in @ SY2728 @ SV400 )
| ( in @ SY2728 @ SV172 ) )
| ( in @ SV400 @ ( powerset @ SV172 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1198,plain,
! [SV401: $i,SV173: $i] :
( ( ! [SY2729: $i,SY2730: $i] :
( ( ( setadjoin @ ( setadjoin @ SV173 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV173 @ ( setadjoin @ SV401 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY2729 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2729 @ ( setadjoin @ SY2730 @ emptyset ) ) @ emptyset ) ) )
| ( SV401 = SY2730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1199,plain,
! [SV402: $i,SV174: $i] :
( ( ! [SY2731: $i] :
( ~ ( in @ SY2731 @ SV174 )
| ! [SY2732: $i] :
( ~ ( in @ SY2732 @ SV402 )
| ( ( kfst @ ( kpair @ SY2731 @ SY2732 ) )
= SY2731 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1200,plain,
! [SV403: $i,SV175: $i] :
( ( ! [SY2733: $i] :
( ~ ( in @ SY2733 @ ( funcSet @ SV175 @ SV403 ) )
| ! [SY2734: $i] :
( ~ ( in @ SY2734 @ SV175 )
| ( in @ ( ap @ SV175 @ SV403 @ SY2733 @ SY2734 ) @ SV403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1201,plain,
! [SV176: $i,SV404: $i] :
( ( ~ ( in @ SV404 @ ( powerset @ SV176 ) )
| ! [SY2735: $i] :
( ~ ( in @ SY2735 @ ( powerset @ SV176 ) )
| ~ ( subset @ SV404 @ SY2735 )
| ( subset @ ( setminus @ SV176 @ SY2735 ) @ ( setminus @ SV176 @ SV404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1202,plain,
! [SV405: $i,SV177: $i] :
( ( ! [SY2736: $i] :
( ~ ( subset @ SV177 @ SV405 )
| ~ ( subset @ SV405 @ SY2736 )
| ( subset @ SV177 @ SY2736 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1203,plain,
! [SV406: $i,SV178: $i] :
( ( ! [SY2737: $i] :
( ~ ( in @ SY2737 @ ( binintersect @ SV178 @ SV406 ) )
| ( in @ SY2737 @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1204,plain,
! [SV179: $i,SV407: $i] :
( ( ~ ( in @ SV407 @ ( powerset @ SV179 ) )
| ( subset @ SV407 @ ( setminus @ SV179 @ ( setminus @ SV179 @ SV407 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1205,plain,
! [SV408: $i > $o,SV180: $i] :
( ( ~ ~ ! [SY2738: $i] :
~ ~ ( ~ ( in @ SY2738 @ SV180 )
| ~ ( SV408 @ SY2738 ) )
| ( ( dsetconstr @ SV180
@ ^ [SY2739: $i] : ( SV408 @ SY2739 ) )
!= emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1206,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ~ ! [SY2740: $i] :
( ~ ( in @ SY2740 @ SV181 )
| ! [SY2741: $i] :
( ~ ( in @ SY2741 @ SV181 )
| ~ ( SV409 @ SY2740 )
| ~ ( SV409 @ SY2741 )
| ( SY2740 = SY2741 ) ) )
| ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) )
| ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1207,plain,
! [SV410: $i,SV182: $i] :
( ( ~ ( subset @ SV182 @ SV410 )
| ( ( setminus @ SV182 @ SV410 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1208,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ~ ! [SY2744: $i,SY2745: $i] :
( ( SY2744 != SY2745 )
| ~ ( ~ ( ~ ( SV183 @ SY2744 )
| ( SV411 @ SY2745 ) )
| ~ ( ~ ( SV411 @ SY2745 )
| ( SV183 @ SY2744 ) ) ) )
| ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1209,plain,
! [SV412: $i,SV184: $i] :
( ( ~ ( subset @ SV184 @ SV412 )
| ( in @ SV184 @ ( powerset @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1210,plain,
! [SV413: $i,SV185: $i] :
( ( ! [SY2752: $i] :
( ~ ( in @ SY2752 @ ( funcSet @ SV185 @ SV413 ) )
| ! [SY2753: $i] :
( ~ ( in @ SY2753 @ SV185 )
| ! [SY2754: $i] :
( ~ ( in @ SY2754 @ SV413 )
| ~ ( in @ ( kpair @ SY2753 @ SY2754 ) @ SY2752 )
| ( ( ap @ SV185 @ SV413 @ SY2752 @ SY2753 )
= SY2754 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1211,plain,
! [SV186: $i,SV414: $i] :
( ( ~ ( in @ SV414 @ ( powerset @ SV186 ) )
| ! [SY2755: $i] :
( ~ ( in @ SY2755 @ ( powerset @ SV186 ) )
| ~ ! [SY2756: $i] :
( ~ ( in @ SY2756 @ SV186 )
| ~ ( in @ SY2756 @ SV414 )
| ( in @ SY2756 @ SY2755 ) )
| ~ ! [SY2757: $i] :
( ~ ( in @ SY2757 @ SV186 )
| ~ ( in @ SY2757 @ SY2755 )
| ( in @ SY2757 @ SV414 ) )
| ( SV414 = SY2755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1212,plain,
! [SV415: $i > $o,SV187: $i] :
( ( ! [SY2758: $i] :
( ~ ( in @ SY2758 @ SV187 )
| ~ ( SV415 @ SY2758 )
| ( ( dsetconstr @ SV187
@ ^ [SY2759: $i] : ( SV415 @ SY2759 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1213,plain,
! [SV188: $i > $o] :
( ( ( ~ ~ ! [SY2314: $i] :
~ ~ ( ~ ( SV188 @ SY2314 )
| ~ ! [SY2315: $i] :
( ~ ( SV188 @ SY2315 )
| ( SY2314 = SY2315 ) ) ) )
= $true )
| ( ( ~ ! [SY2316: $i] :
~ ~ ( ~ ( SV188 @ SY2316 )
| ~ ! [SY2317: $i] :
( ~ ( SV188 @ SY2317 )
| ( SY2316 = SY2317 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(1214,plain,
! [SV416: $i,SV189: $i] :
( ( ! [SY2760: $i] :
( ~ ( in @ SY2760 @ ( setadjoin @ SV189 @ SV416 ) )
| ( SY2760 = SV189 )
| ( in @ SY2760 @ SV416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1215,plain,
! [SV417: $i,SV190: $i] :
( ( ! [SY2761: $i] :
( ~ ( in @ SY2761 @ ( funcSet @ SV190 @ SV417 ) )
| ! [SY2762: $i] :
( ~ ( in @ SY2762 @ SV190 )
| ( ( ap @ SV190 @ SV417 @ SY2761 @ SY2762 )
= ( ap @ SV190 @ SV417 @ SY2761 @ SY2762 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1216,plain,
! [SV191: $i,SV418: $i] :
( ( ~ ( in @ SV418 @ ( powerset @ SV191 ) )
| ! [SY2763: $i] :
( ~ ( in @ SY2763 @ ( powerset @ SV191 ) )
| ! [SY2764: $i] :
( ~ ( in @ SY2764 @ ( powerset @ SV191 ) )
| ! [SY2765: $i] :
( ~ ( in @ SY2765 @ SV191 )
| ~ ( in @ SY2765 @ ( binintersect @ SV418 @ SY2763 ) )
| ( in @ SY2765 @ ( binintersect @ ( binunion @ SV418 @ SY2764 ) @ ( binunion @ SY2763 @ SY2764 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1217,plain,
! [SV192: $o,SV419: $i] :
( ( ~ ( in @ SV419 @ ( prop2set @ SV192 ) )
| SV192 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1218,plain,
! [SV420: $i] :
( ( ~ ( in @ SV420 @ ( prop2set @ $true ) )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1219,plain,
! [SV421: $i] :
( ( ~ ( in @ SV421 @ ( prop2set @ $false ) )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1220,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ~ ! [SY2766: $i,SY2767: $i] :
( ( SY2766 != SY2767 )
| ~ ( ~ ( ~ ( SV193 @ SY2766 )
| ( SV422 @ SY2767 ) )
| ~ ( ~ ( SV422 @ SY2767 )
| ( SV193 @ SY2766 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1221,plain,
! [SV194: $i] :
( ( ( ~ ( singleton @ SV194 ) )
= $true )
| ( ( ! [SY2339: $i] :
( ~ ( in @ SY2339 @ SV194 )
| ( ( setunion @ SV194 )
= SY2339 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[957]) ).
thf(1222,plain,
! [SV423: $i,SV195: $i] :
( ( ! [SY2776: $i] :
( ~ ( in @ SY2776 @ SV195 )
| ~ ~ ( in @ SY2776 @ SV423 )
| ( in @ SY2776 @ ( setminus @ SV195 @ SV423 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1223,plain,
! [SV424: $i,SV196: $i] :
( ( ! [SY2777: $i] :
( ~ ( in @ SY2777 @ ( cartprod @ SV196 @ SV424 ) )
| ~ ! [SY2778: $i] :
~ ~ ( ~ ( in @ SY2778 @ SV196 )
| ~ ~ ! [SY2779: $i] :
~ ~ ( ~ ( in @ SY2779 @ SV424 )
| ( SY2777
!= ( kpair @ SY2778 @ SY2779 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1224,plain,
! [SV425: $o,SV197: $i] :
( ( ! [SY2780: $i] :
( ~ ( in @ SY2780 @ SV197 )
| ! [SY2781: $i] :
( ~ ( in @ SY2781 @ SV197 )
| ~ SV425
| ( ( if @ SV197 @ SV425 @ SY2780 @ SY2781 )
= SY2780 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[960]) ).
thf(1225,plain,
! [SV197: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV197 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV197 )
| ~ $true
| ( ( if @ SV197 @ $true @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[960]) ).
thf(1226,plain,
! [SV197: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV197 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV197 )
| ~ $false
| ( ( if @ SV197 @ $false @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[960]) ).
thf(1227,plain,
! [SV426: $i,SV198: $i] :
( ( ! [SY2782: $i] :
( ~ ( subset @ SY2782 @ ( cartprod @ SV198 @ SV426 ) )
| ! [SY2783: $i] :
( ~ ( subset @ SY2783 @ ( cartprod @ SV198 @ SV426 ) )
| ~ ! [SY2784: $i] :
( ~ ( in @ SY2784 @ SV198 )
| ! [SY2785: $i] :
( ~ ( in @ SY2785 @ SV426 )
| ~ ( in @ ( kpair @ SY2784 @ SY2785 ) @ SY2782 )
| ( in @ ( kpair @ SY2784 @ SY2785 ) @ SY2783 ) ) )
| ~ ! [SY2786: $i] :
( ~ ( in @ SY2786 @ SV198 )
| ! [SY2787: $i] :
( ~ ( in @ SY2787 @ SV426 )
| ~ ( in @ ( kpair @ SY2786 @ SY2787 ) @ SY2783 )
| ( in @ ( kpair @ SY2786 @ SY2787 ) @ SY2782 ) ) )
| ( SY2782 = SY2783 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1228,plain,
! [SV427: $i,SV199: $i] :
( ( ( ( binintersect @ SV199 @ SV427 )
!= SV427 )
| ( subset @ SV427 @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1229,plain,
! [SV428: $i,SV200: $i] :
( ( ! [SY2788: $i] :
( ~ ( subset @ SY2788 @ ( cartprod @ SV200 @ SV428 ) )
| ! [SY2789: $i > $o] :
( ~ ! [SY2790: $i] :
( ~ ( in @ SY2790 @ SV200 )
| ! [SY2791: $i] :
( ~ ( in @ SY2791 @ SV428 )
| ~ ( in @ ( kpair @ SY2790 @ SY2791 ) @ SY2788 )
| ( SY2789 @ ( kpair @ SY2790 @ SY2791 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2788 )
| ( SY2789 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1230,plain,
! [SV429: $i > $o,SV201: $i] :
( ( ~ ~ ! [SY2793: $i] :
~ ~ ( ~ ( in @ SY2793 @ SV201 )
| ~ ~ ( SV429 @ SY2793 ) )
| ~ ! [SY2794: $i] :
( ~ ( in @ SY2794 @ SV201 )
| ( SV429 @ SY2794 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1231,plain,
! [SV202: $i] :
( ( ( ~ ( iskpair @ SV202 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV202 )
@ ^ [SY2366: $i] : ( in @ ( setadjoin @ SY2366 @ emptyset ) @ SV202 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1232,plain,
! [SV430: $i,SV203: $i] :
( ( ! [SY2795: $i > $i] :
( ~ ! [SY2796: $i] :
( ~ ( in @ SY2796 @ SV203 )
| ( in @ ( SY2795 @ SY2796 ) @ SV430 ) )
| ( func @ SV203 @ SV430
@ ( dpsetconstr @ SV203 @ SV430
@ ^ [SX3: $i,SX4: $i] :
( ( SY2795 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1233,plain,
! [SV204: $i] :
( ( ( ~ ~ ! [SY2372: $i] :
~ ( in @ SY2372 @ SV204 ) )
= $true )
| ( ( SV204 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1234,plain,
! [SV205: $i] :
( ( ( ~ ( in @ SV205 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV205 @ SV205 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[968]) ).
thf(1235,plain,
! [SV431: $i,SV206: $i] :
( ( ! [SY2799: $i] :
( ~ ~ ( in @ SY2799 @ SV206 )
| ~ ( in @ SY2799 @ SV431 )
| ( in @ SY2799 @ ( symdiff @ SV206 @ SV431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1236,plain,
! [SV432: $i,SV207: $i] :
( ( ( SV207 != SV432 )
| ( subset @ SV432 @ SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1237,plain,
! [SV208: $i] :
( ( ( ~ ( in @ SV208 @ emptyset ) )
= $true )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1238,plain,
! [SV433: $i,SV209: $i] :
( ( ! [SY2800: $i > $i] :
( ~ ! [SY2801: $i] :
( ~ ( in @ SY2801 @ SV209 )
| ( in @ ( SY2800 @ SY2801 ) @ SV433 ) )
| ! [SY2802: $i] :
( ~ ( in @ SY2802 @ SV209 )
| ( ( ap @ SV209 @ SV433
@ ( lam @ SV209 @ SV433
@ ^ [SX4: $i] : ( SY2800 @ SX4 ) )
@ SY2802 )
= ( SY2800 @ SY2802 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1239,plain,
! [SV210: $i,SV434: $i] :
( ( ~ ( in @ SV434 @ ( powerset @ SV210 ) )
| ( subset @ ( setminus @ SV210 @ ( setminus @ SV210 @ SV434 ) ) @ SV434 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1240,plain,
! [SV435: $i,SV211: $i] :
( ( ( SV211 != SV435 )
| ! [SY2804: $i,SY2805: $i] :
( ( SY2804 != SY2805 )
| ( ( setadjoin @ SV211 @ SY2804 )
= ( setadjoin @ SV435 @ SY2805 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1241,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ~ ! [SY2806: $i] :
( ~ ( in @ SY2806 @ SV212 )
| ! [SY2807: $i] :
( ~ ( in @ SY2807 @ SV212 )
| ~ ( SV436 @ SY2806 )
| ~ ( SV436 @ SY2807 )
| ( SY2806 = SY2807 ) ) )
| ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) )
| ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1242,plain,
! [SV437: $i,SV213: $i] :
( ( ( ( setadjoin @ SV213 @ emptyset )
!= ( setadjoin @ SV437 @ emptyset ) )
| ( SV213 = SV437 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1243,plain,
! [SV438: $i,SV214: $i] :
( ( ! [SY2810: $i,SY2811: $i] :
( ( ( setadjoin @ ( setadjoin @ SV214 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV214 @ ( setadjoin @ SV438 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY2810 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2810 @ ( setadjoin @ SY2811 @ emptyset ) ) @ emptyset ) ) )
| ( SY2810 != SY2811 )
| ( SV438 = SY2811 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1244,plain,
! [SV215: $i] :
( ( ( ~ ~ ( ~ ( in @ emptyset @ SV215 )
| ~ ! [SY2395: $i] :
( ~ ~ ( ~ ( in @ SY2395 @ omega )
| ~ ( in @ SY2395 @ SV215 ) )
| ( in @ ( setadjoin @ SY2395 @ SY2395 ) @ SV215 ) ) ) )
= $true )
| ( ( ! [SY2396: $i] :
( ~ ( in @ SY2396 @ omega )
| ( in @ SY2396 @ SV215 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1245,plain,
! [SV439: $i,SV216: $i] :
( ( ! [SY2812: $i] :
( ~ ( in @ SY2812 @ SV216 )
| ! [SY2813: $i] :
( ~ ( in @ SY2813 @ SV439 )
| ( in @ ( kpair @ SY2812 @ SY2813 ) @ ( powerset @ ( powerset @ ( binunion @ SV216 @ SV439 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1246,plain,
! [SV440: $i,SV217: $i] :
( ( ! [SY2814: $i > $i > $o,SY2815: $i] :
( ~ ( in @ SY2815 @ SV217 )
| ! [SY2816: $i] :
( ~ ( in @ SY2816 @ SV440 )
| ~ ( SY2814 @ SY2815 @ SY2816 )
| ( in @ ( kpair @ SY2815 @ SY2816 )
@ ( dpsetconstr @ SV217 @ SV440
@ ^ [SX5: $i,SX6: $i] : ( SY2814 @ SX5 @ SX6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1247,plain,
! [SV441: $o,SV218: $i] :
( ( ! [SY2819: $i] :
( ~ ( in @ SY2819 @ SV218 )
| ! [SY2820: $i] :
( ~ ( in @ SY2820 @ SV218 )
| ( in @ ( if @ SV218 @ SV441 @ SY2819 @ SY2820 ) @ SV218 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[981]) ).
thf(1248,plain,
! [SV218: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV218 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV218 )
| ( in @ ( if @ SV218 @ $true @ SX0 @ SX1 ) @ SV218 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[981]) ).
thf(1249,plain,
! [SV218: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV218 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV218 )
| ( in @ ( if @ SV218 @ $false @ SX0 @ SX1 ) @ SV218 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[981]) ).
thf(1250,plain,
! [SV442: $i,SV219: $i] :
( ( ! [SY2821: $i] :
( ~ ( in @ SY2821 @ ( funcSet @ SV219 @ SV442 ) )
| ! [SY2822: $i] :
( ~ ( in @ SY2822 @ ( funcSet @ SV219 @ SV442 ) )
| ~ ! [SY2823: $i] :
( ~ ( in @ SY2823 @ SV219 )
| ( ( ap @ SV219 @ SV442 @ SY2821 @ SY2823 )
= ( ap @ SV219 @ SV442 @ SY2822 @ SY2823 ) ) )
| ( SY2821 = SY2822 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1251,plain,
! [SV443: $i,SV220: $i] :
( ( ! [SY2824: $i > $i > $o,SY2825: $i] :
( ~ ( in @ SY2825 @ SV220 )
| ! [SY2826: $i] :
( ~ ( in @ SY2826 @ SV443 )
| ~ ( in @ ( kpair @ SY2825 @ SY2826 )
@ ( dpsetconstr @ SV220 @ SV443
@ ^ [SX5: $i,SX6: $i] : ( SY2824 @ SX5 @ SX6 ) ) )
| ( SY2824 @ SY2825 @ SY2826 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1252,plain,
! [SV444: $i,SV221: $i] :
( ( ! [SY2829: $i] :
( ~ ( func @ SV221 @ SV444 @ SY2829 )
| ! [SY2830: $i] :
( ~ ( in @ SY2830 @ SV221 )
| ( in @ ( ap @ SV221 @ SV444 @ SY2829 @ SY2830 ) @ SV444 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1253,plain,
! [SV445: $i,SV222: $i] :
( ( ! [SY2831: $i] :
( ~ ( in @ SY2831 @ SV222 )
| ( in @ ( setadjoin @ SY2831 @ emptyset ) @ ( powerset @ ( binunion @ SV222 @ SV445 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1254,plain,
! [SV446: $i > $o,SV223: $i] :
( ( ~ ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY2832: $i] : ( SV446 @ SY2832 ) ) )
| ~ ! [SY2833: $i] :
~ ~ ( ~ ( in @ SY2833 @ SV223 )
| ~ ( SV446 @ SY2833 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1255,plain,
! [SV447: $i,SV224: $i] :
( ( ~ ( ( SV224 != SV447 ) )
| ~ ( in @ SV447 @ ( setadjoin @ SV224 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1256,plain,
! [SV448: $i,SV225: $i] :
( ( ~ ! [SY2834: $i] :
~ ( ~ ( ~ ( in @ SY2834 @ SV225 )
| ( in @ SY2834 @ SV448 ) )
| ~ ( ~ ( in @ SY2834 @ SV448 )
| ( in @ SY2834 @ SV225 ) ) )
| ( SV225 = SV448 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1257,plain,
! [SV449: $i,SV226: $i] :
( ( ! [SY2835: $i] :
( ~ ( in @ SY2835 @ SV226 )
| ~ ( in @ SY2835 @ SV449 )
| ~ ( in @ SY2835 @ ( symdiff @ SV226 @ SV449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1258,plain,
! [SV227: $i,SV450: $i] :
( ( ~ ( in @ SV450 @ ( powerset @ SV227 ) )
| ! [SY2836: $i] :
( ~ ( in @ SY2836 @ SV227 )
| ~ ( in @ SY2836 @ ( setminus @ SV227 @ ( setminus @ SV227 @ SV450 ) ) )
| ( in @ SY2836 @ SV450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1259,plain,
! [SV451: $i,SV228: $i] :
( ( ! [SY2837: $i,SY2838: $i] :
( ( ( setadjoin @ ( setadjoin @ SV228 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV228 @ ( setadjoin @ SV451 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY2837 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2837 @ ( setadjoin @ SY2838 @ emptyset ) ) @ emptyset ) ) )
| ( SV228 = SY2837 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1260,plain,
! [SV229: $i,SV452: $i] :
( ( ~ ( in @ SV452 @ ( powerset @ SV229 ) )
| ! [SY2839: $i] :
( ~ ( in @ SY2839 @ ( powerset @ SV229 ) )
| ! [SY2840: $i] :
( ~ ( in @ SY2840 @ ( powerset @ SV229 ) )
| ( in @ ( binintersect @ SV452 @ SY2839 ) @ ( powerset @ ( binintersect @ ( binunion @ SV452 @ SY2840 ) @ ( binunion @ SY2839 @ SY2840 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1261,plain,
! [SV230: $i] :
( ( ( ~ ( ( SV230 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY2440: $i] :
~ ~ ( ~ ( in @ SY2440 @ SV230 )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1262,plain,
! [SV453: $o,SV231: $i] :
( ( ! [SY2841: $i] :
( ~ ( in @ SY2841 @ SV231 )
| ! [SY2842: $i] :
( ~ ( in @ SY2842 @ SV231 )
| ~ SV453
| ( ( dsetconstr @ SV231
@ ^ [SY2843: $i] :
( ~ ( ~ SV453
| ( SY2843 != SY2841 ) )
| ~ ( ~ ~ SV453
| ( SY2843 != SY2842 ) ) ) )
= ( setadjoin @ SY2841 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[994]) ).
thf(1263,plain,
! [SV231: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV231 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV231 )
| ~ $true
| ( ( dsetconstr @ SV231
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[994]) ).
thf(1264,plain,
! [SV231: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV231 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV231 )
| ~ $false
| ( ( dsetconstr @ SV231
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[994]) ).
thf(1265,plain,
! [SV232: $i,SV454: $i] :
( ( ! [SY2844: $i] :
( ~ ( in @ SV454 @ ( powerset @ SV232 ) )
| ~ ( in @ SY2844 @ SV454 )
| ( in @ SY2844 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1266,plain,
! [SV233: $i,SV455: $i] :
( ( ~ ( in @ SV455 @ ( powerset @ SV233 ) )
| ! [SY2845: $i] :
( ~ ( in @ SY2845 @ SV233 )
| ~ ( in @ SY2845 @ SV455 )
| ~ ( in @ SY2845 @ ( setminus @ SV233 @ SV455 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1267,plain,
! [SV456: $i,SV234: $i] :
( ( ! [SY2846: $i > $i] :
( ~ ! [SY2847: $i] :
( ~ ( in @ SY2847 @ SV234 )
| ( in @ ( SY2846 @ SY2847 ) @ SV456 ) )
| ! [SY2848: $i] :
( ~ ( in @ SY2848 @ SV234 )
| ( ( ap @ SV234 @ SV456
@ ( lam @ SV234 @ SV456
@ ^ [SX4: $i] : ( SY2846 @ SX4 ) )
@ SY2848 )
= ( SY2846 @ SY2848 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1268,plain,
! [SV457: $i,SV235: $i] :
( ( ~ ~ ~ ! [SY2850: $i] :
~ ~ ( ~ ( in @ SY2850 @ SV235 )
| ~ ( in @ SY2850 @ SV457 ) )
| ( ( binintersect @ SV235 @ SV457 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1269,plain,
! [SV458: $i,SV236: $i] :
( ( ! [SY2851: $i,SY2852: $i] :
( ( ( kpair @ SV236 @ SV458 )
!= ( kpair @ SY2851 @ SY2852 ) )
| ( SV236 = SY2851 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1270,plain,
! [SV459: $i,SV237: $i] :
( ( ! [SY2853: $i] :
( ~ ( subset @ SV237 @ SY2853 )
| ( subset @ SV237 @ ( setadjoin @ SV459 @ SY2853 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1271,plain,
! [SV460: $i,SV238: $i] :
( ( ! [SY2854: $i] :
( ~ ( in @ SY2854 @ ( setadjoin @ SV238 @ ( setadjoin @ SV460 @ emptyset ) ) )
| ( SY2854 = SV238 )
| ( SY2854 = SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1272,plain,
! [SV461: $i,SV239: $i] :
( ( ! [SY2855: $i,SY2856: $i] :
( ( ( kpair @ SV239 @ SV461 )
!= ( kpair @ SY2855 @ SY2856 ) )
| ( SV461 = SY2856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1273,plain,
! [SV462: $i,SV240: $i] :
( ( ( SV240 != SV462 )
| ( ( setadjoin @ SV240 @ ( setadjoin @ SV462 @ emptyset ) )
= ( setadjoin @ SV240 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1274,plain,
! [SV463: $i,SV241: $i] :
( ( ( SV241 != SV463 )
| ( ( powerset @ SV241 )
= ( powerset @ SV463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1275,plain,
! [SV464: $i,SV242: $i] :
( ( ! [SY2857: $i > $i] :
( ~ ! [SY2858: $i] :
( ~ ( in @ SY2858 @ SV242 )
| ( in @ ( SY2857 @ SY2858 ) @ SV464 ) )
| ( func @ SV242 @ SV464
@ ( lam @ SV242 @ SV464
@ ^ [SX3: $i] : ( SY2857 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1276,plain,
! [SV243: $i,SV465: $i] :
( ( ~ ( in @ SV465 @ ( powerset @ SV243 ) )
| ! [SY2860: $i] :
( ~ ( in @ SY2860 @ ( powerset @ SV243 ) )
| ! [SY2861: $i] :
( ~ ( in @ SY2861 @ SV243 )
| ~ ( in @ SV465 @ ( powerset @ SY2860 ) )
| ~ ( in @ SY2861 @ SV465 )
| ( in @ SY2861 @ SY2860 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1277,plain,
! [SV466: $o,SV244: $i] :
( ( ! [SY2862: $i] :
( ~ ( in @ SY2862 @ SV244 )
| ! [SY2863: $i] :
( ~ ( in @ SY2863 @ SV244 )
| ~ ~ SV466
| ( in @ SY2863
@ ( dsetconstr @ SV244
@ ^ [SY2864: $i] :
( ~ ( ~ SV466
| ( SY2864 != SY2862 ) )
| ~ ( ~ ~ SV466
| ( SY2864 != SY2863 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1007]) ).
thf(1278,plain,
! [SV244: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV244 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV244 )
| ~ ~ $true
| ( in @ SX1
@ ( dsetconstr @ SV244
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1007]) ).
thf(1279,plain,
! [SV244: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV244 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV244 )
| ~ ~ $false
| ( in @ SX1
@ ( dsetconstr @ SV244
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1007]) ).
thf(1280,plain,
! [SV245: $i,SV467: $i] :
( ( ~ ( in @ SV467 @ SV245 )
| ( in @ ( setadjoin @ SV467 @ emptyset ) @ ( powerset @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1281,plain,
! [SV246: $i,SV468: $i] :
( ( ~ ( in @ SV468 @ SV246 )
| ( subset @ ( setadjoin @ SV468 @ emptyset ) @ SV246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1282,plain,
! [SV469: $i,SV247: $i] :
( ( ! [SY2865: $i] :
( ~ ( func @ SV247 @ SV469 @ SY2865 )
| ! [SY2866: $i] :
( ~ ( func @ SV247 @ SV469 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( in @ SY2867 @ SV247 )
| ( ( ap @ SV247 @ SV469 @ SY2865 @ SY2867 )
= ( ap @ SV247 @ SV469 @ SY2866 @ SY2867 ) ) )
| ! [SY2868: $i] :
( ~ ( in @ SY2868 @ SV247 )
| ! [SY2869: $i] :
( ~ ( in @ SY2869 @ SV469 )
| ~ ( in @ ( kpair @ SY2868 @ SY2869 ) @ SY2866 )
| ( in @ ( kpair @ SY2868 @ SY2869 ) @ SY2865 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1283,plain,
! [SV248: $i,SV470: $i] :
( ( ~ ( in @ SV470 @ ( powerset @ SV248 ) )
| ! [SY2870: $i] :
( ~ ( in @ SY2870 @ ( powerset @ SV248 ) )
| ( subset @ ( setminus @ SV248 @ SV470 ) @ ( setminus @ SV248 @ ( binintersect @ SV470 @ SY2870 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1284,plain,
! [SV249: $i > $i > $o,SV471: $i] :
( ( ~ ! [SY2871: $i] :
( ~ ( in @ SY2871 @ SV471 )
| ~ ! [SY2491: $i] :
~ ~ ( ~ ( SV249 @ SY2871 @ SY2491 )
| ~ ! [SY2492: $i] :
( ~ ( SV249 @ SY2871 @ SY2492 )
| ( SY2491 = SY2492 ) ) ) )
| ~ ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1285,plain,
! [SV472: $i,SV250: $i] :
( ( ( SV250 != SV472 )
| ( in @ SV250 @ ( setadjoin @ SV472 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1286,plain,
! [SV473: $i,SV251: $i] :
( ( ( ( setminus @ SV251 @ SV473 )
!= emptyset )
| ( subset @ SV251 @ SV473 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1287,plain,
! [SV474: $o,SV252: $i] :
( ( ! [SY2878: $i] :
( ~ ( in @ SY2878 @ SV252 )
| ! [SY2879: $i] :
( ~ ( in @ SY2879 @ SV252 )
| ~ ~ SV474
| ( ( if @ SV252 @ SV474 @ SY2878 @ SY2879 )
= SY2879 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1015]) ).
thf(1288,plain,
! [SV252: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV252 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV252 )
| ~ ~ $true
| ( ( if @ SV252 @ $true @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1015]) ).
thf(1289,plain,
! [SV252: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV252 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV252 )
| ~ ~ $false
| ( ( if @ SV252 @ $false @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1015]) ).
thf(1290,plain,
! [SV475: $i,SV253: $i] :
( ( ! [SY2880: $i] :
( ~ ( in @ SY2880 @ SV253 )
| ! [SY2881: $i] :
( ~ ( in @ SY2881 @ SV475 )
| ( in @ ( setadjoin @ ( setadjoin @ SY2880 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2880 @ ( setadjoin @ SY2881 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV253 @ SV475 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1291,plain,
! [SV476: $i,SV254: $i] :
( ( ( SV254 != SV476 )
| ! [SY2882: $i,SY2883: $i] :
( ( SY2882 != SY2883 )
| ~ ( ~ ( ~ ( in @ SY2882 @ SV254 )
| ( in @ SY2883 @ SV476 ) )
| ~ ( ~ ( in @ SY2883 @ SV476 )
| ( in @ SY2882 @ SV254 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1292,plain,
! [SV477: $i,SV255: $i] :
( ( ~ ( subset @ SV255 @ SV477 )
| ~ ( subset @ SV477 @ SV255 )
| ( SV255 = SV477 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1293,plain,
! [SV256: $i > $o] :
( ( ( ~ ~ ! [SY2509: $i] :
~ ~ ( ~ ( SV256 @ SY2509 )
| ~ ! [SY2510: $i] :
( ~ ( SV256 @ SY2510 )
| ( SY2509 = SY2510 ) ) ) )
= $true )
| ( ( ~ ! [SY2511: $i] :
~ ! [SY2512: $i] :
~ ( ~ ( ~ ( SV256 @ SY2512 )
| ( SY2512 = SY2511 ) )
| ~ ( ( SY2512 != SY2511 )
| ( SV256 @ SY2512 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1019]) ).
thf(1294,plain,
! [SV257: $i,SV478: $i] :
( ( ~ ( in @ SV478 @ ( powerset @ SV257 ) )
| ! [SY2884: $i] :
( ~ ( in @ SY2884 @ ( powerset @ SV257 ) )
| ( in @ ( binunion @ SV478 @ SY2884 ) @ ( powerset @ SV257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1295,plain,
! [SV479: $i,SV258: $i] :
( ( ! [SY2885: $i] :
( ~ ( in @ SY2885 @ SV258 )
| ! [SY2886: $i] :
( ~ ( in @ SY2886 @ SV479 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY2885 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2885 @ ( setadjoin @ SY2886 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV258 @ SV479 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1296,plain,
! [SV480: $i > $i > $o,SV259: $i,SV1: $i] :
( ( subset
@ ( dpsetconstr @ SV1 @ SV259
@ ^ [SY2887: $i,SY2888: $i] : ( SV480 @ SY2887 @ SY2888 ) )
@ ( cartprod @ SV1 @ SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1297,plain,
! [SV481: $i > $i > $o,SV260: $i,SV2: $i] :
( ( subset
@ ( dpsetconstr @ SV2 @ SV260
@ ^ [SY2889: $i,SY2890: $i] : ( SV481 @ SY2889 @ SY2890 ) )
@ ( cartprod @ SV2 @ SV260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1298,plain,
! [SV482: $i,SV269: $i,SV14: $i] :
( ( ( binintersect @ SV14 @ ( binunion @ SV269 @ SV482 ) )
= ( binunion @ ( binintersect @ SV14 @ SV269 ) @ ( binintersect @ SV14 @ SV482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1299,plain,
! [SV483: $i,SV281: $i,SV34: $i] :
( ( ~ ( func @ SV34 @ SV281 @ SV483 )
| ( in @ SV483 @ ( funcSet @ SV34 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1300,plain,
! [SV35: $i > $o] :
( ( ( ~ ! [SY1900: $i] :
~ ~ ( ~ ( SV35 @ SY1900 )
| ~ ! [SY1901: $i] :
( ~ ( SV35 @ SY1901 )
| ( SY1900 = SY1901 ) ) ) )
= $false )
| ( ( ~ ! [SY1902: $i] :
~ ~ ( ~ ( SV35 @ SY1902 )
| ~ ! [SY1903: $i] :
( ~ ( SV35 @ SY1903 )
| ( SY1902 = SY1903 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1301,plain,
! [SV36: $i,SV282: $i] :
( ( ( ~ ( in @ SV282 @ ( powerset @ SV36 ) ) )
= $true )
| ( ( ! [SY2528: $i] :
( ~ ( in @ SY2528 @ ( powerset @ SV36 ) )
| ~ ( subset @ ( setminus @ SV36 @ SY2528 ) @ ( setminus @ SV36 @ SV282 ) )
| ( subset @ SV282 @ SY2528 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1302,plain,
! [SV283: $i,SV37: $i] :
( ( ( ~ ( in @ SV37 @ ( setadjoin @ SV283 @ emptyset ) ) )
= $true )
| ( ( SV37 = SV283 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1303,plain,
! [SV484: $i,SV284: $i,SV38: $i] :
( ( ~ ( func @ SV38 @ SV284 @ SV484 )
| ! [SY2891: $i] :
( ~ ( in @ SY2891 @ SV38 )
| ! [SY2892: $i] :
( ~ ( in @ SY2892 @ SV284 )
| ~ ( in @ ( kpair @ SY2891 @ SY2892 ) @ SV484 )
| ( ( ap @ SV38 @ SV284 @ SV484 @ SY2891 )
= SY2892 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1304,plain,
! [SV285: $o,SV39: $i,SV485: $i] :
( ( ~ ( in @ SV485 @ SV39 )
| ! [SY2893: $i] :
( ~ ( in @ SY2893 @ SV39 )
| ~ SV285
| ( in @ SV485
@ ( dsetconstr @ SV39
@ ^ [SY2894: $i] :
( ~ ( ~ SV285
| ( SY2894 != SV485 ) )
| ~ ( ~ ~ SV285
| ( SY2894 != SY2893 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1305,plain,
! [SV39: $i,SV486: $i] :
( ( ~ ( in @ SV486 @ SV39 )
| ! [SY2895: $i] :
( ~ ( in @ SY2895 @ SV39 )
| ~ $true
| ( in @ SV486
@ ( dsetconstr @ SV39
@ ^ [SY2896: $i] :
( ~ ( ~ $true
| ( SY2896 != SV486 ) )
| ~ ( ~ ~ $true
| ( SY2896 != SY2895 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1306,plain,
! [SV39: $i,SV487: $i] :
( ( ~ ( in @ SV487 @ SV39 )
| ! [SY2897: $i] :
( ~ ( in @ SY2897 @ SV39 )
| ~ $false
| ( in @ SV487
@ ( dsetconstr @ SV39
@ ^ [SY2898: $i] :
( ~ ( ~ $false
| ( SY2898 != SV487 ) )
| ~ ( ~ ~ $false
| ( SY2898 != SY2897 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1307,plain,
! [SV286: $i,SV40: $i] :
( ( ( SV40 != SV286 )
= $true )
| ( ( ! [SY2535: $i > $o,SY2536: $i > $o] :
( ~ ! [SY2537: $i] :
( ~ ( in @ SY2537 @ SV40 )
| ! [SY2538: $i] :
( ~ ( in @ SY2538 @ SV286 )
| ( SY2537 != SY2538 )
| ~ ( ~ ( ~ ( SY2535 @ SY2537 )
| ( SY2536 @ SY2538 ) )
| ~ ( ~ ( SY2536 @ SY2538 )
| ( SY2535 @ SY2537 ) ) ) ) )
| ( ( dsetconstr @ SV40
@ ^ [SX4: $i] : ( SY2535 @ SX4 ) )
= ( dsetconstr @ SV286
@ ^ [SX4: $i] : ( SY2536 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1054]) ).
thf(1308,plain,
! [SV287: $i > $o,SV41: $i] :
( ( ( ~ ~ ~ ! [SY2541: $i] :
~ ~ ( ~ ( in @ SY2541 @ SV41 )
| ~ ( SV287 @ SY2541 ) ) )
= $true )
| ( ( ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV41 )
| ~ ( SV287 @ SY2542 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1309,plain,
! [SV42: $o] :
( ( SV42 = $false )
| ( ( set2prop @ ( prop2set @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1056]) ).
thf(1310,plain,
( ( $true = $false )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1311,plain,
( ( $false = $false )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1312,plain,
! [SV288: $i,SV43: $i,SV488: $i] :
( ( ~ ~ ( in @ SV488 @ SV43 )
| ~ ( in @ SV488 @ ( setminus @ SV43 @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1313,plain,
! [SV44: $i > $o] :
( ( ( ~ ! [SY1927: $i] :
~ ! [SY1928: $i] :
~ ( ~ ( ~ ( SV44 @ SY1928 )
| ( SY1928 = SY1927 ) )
| ~ ( ( SY1928 != SY1927 )
| ( SV44 @ SY1928 ) ) ) )
= $false )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1314,plain,
! [SV289: $i,SV45: $i,SV489: $i] :
( ( ~ ( in @ SV489 @ ( setminus @ SV45 @ SV289 ) )
| ~ ( in @ SV489 @ SV289 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1315,plain,
! [SV290: $i,SV46: $i,SV490: $i] :
( ( ~ ( in @ SV490 @ SV46 )
| ! [SY2899: $i] :
( ~ ( in @ SY2899 @ SV290 )
| ( in @ ( kpair @ SV490 @ SY2899 ) @ ( cartprod @ SV46 @ SV290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1316,plain,
! [SV291: $i,SV47: $i,SV491: $i] :
( ( ~ ( ~ ( ~ ( in @ SV491 @ ( setadjoin @ SV47 @ SV291 ) )
| ( SV491 = SV47 )
| ( in @ SV491 @ SV291 ) )
| ~ ( ~ ( ( SV491 = SV47 )
| ( in @ SV491 @ SV291 ) )
| ( in @ SV491 @ ( setadjoin @ SV47 @ SV291 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1317,plain,
! [SV48: $o] :
( ( SV48 = $false )
| ( ( in @ emptyset @ ( prop2set @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1064]) ).
thf(1318,plain,
( ( $true = $false )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1319,plain,
( ( $false = $false )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1320,plain,
! [SV49: $i,SV292: $i] :
( ( ( ~ ( in @ SV292 @ ( powerset @ SV49 ) ) )
= $true )
| ( ( in @ ( setminus @ SV49 @ SV292 ) @ ( powerset @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1067]) ).
thf(1321,plain,
! [SV293: $i,SV50: $i,SV492: $i] :
( ( ~ ( in @ SV492 @ ( setminus @ SV50 @ SV293 ) )
| ( in @ SV492 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1322,plain,
! [SV493: $i,SV294: $i,SV51: $i] :
( ( ~ ( func @ SV51 @ SV294 @ SV493 )
| ! [SY2900: $i] :
( ~ ( in @ SY2900 @ SV51 )
| ( singleton
@ ( dsetconstr @ SV294
@ ^ [SY2901: $i] : ( in @ ( kpair @ SY2900 @ SY2901 ) @ SV493 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1323,plain,
! [SV52: $i,SV295: $i] :
( ( ( ~ ( in @ SV295 @ ( powerset @ SV52 ) ) )
= $true )
| ( ( subset @ SV295 @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1324,plain,
! [SV53: $i] :
( ( ( singleton @ SV53 )
= $false )
| ( ( in @ ( setunion @ SV53 ) @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1325,plain,
! [SV54: $i] :
( ( ( iskpair @ SV54 )
= $false )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV54 )
@ ^ [SY1946: $i] :
( SV54
= ( kpair @ ( kfst @ SV54 ) @ SY1946 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1326,plain,
! [SV296: $i,SV55: $i,SV494: $i] :
( ( ~ ( in @ SV494 @ SV55 )
| ! [SY2902: $i] :
( ~ ( in @ SY2902 @ SV296 )
| ( ( kpair @ SV494 @ SY2902 )
= ( kpair @ SV494 @ SY2902 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1327,plain,
! [SV297: $i,SV56: $i,SV495: $i] :
( ( ~ ( in @ SV495 @ SV56 )
| ! [SY2903: $i] :
( ~ ( in @ SY2903 @ SV297 )
| ( ( ksnd @ ( kpair @ SV495 @ SY2903 ) )
= SY2903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1328,plain,
! [SV496: $i,SV298: $i,SV57: $i] :
( ( ~ ( func @ SV57 @ SV298 @ SV496 )
| ! [SY2904: $i] :
( ~ ( in @ SY2904 @ SV57 )
| ( in @ ( kpair @ SY2904 @ ( ap @ SV57 @ SV298 @ SV496 @ SY2904 ) ) @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1329,plain,
! [SV299: $i,SV58: $i,SV497: $i] :
( ( ~ ( in @ SV497 @ ( cartprod @ SV58 @ SV299 ) )
| ( in @ ( kfst @ SV497 ) @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1330,plain,
! [SV498: $i,SV300: $i,SV59: $i] :
( ( ( ( setadjoin @ SV59 @ ( setadjoin @ SV300 @ emptyset ) )
!= ( setadjoin @ SV498 @ emptyset ) )
| ( SV59 = SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1331,plain,
! [SV301: $o,SV60: $i,SV499: $i] :
( ( ~ ( in @ SV499 @ SV60 )
| ! [SY2905: $i] :
( ~ ( in @ SY2905 @ SV60 )
| ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY2906: $i] :
( ~ ( ~ SV301
| ( SY2906 != SV499 ) )
| ~ ( ~ ~ SV301
| ( SY2906 != SY2905 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1332,plain,
! [SV60: $i,SV500: $i] :
( ( ~ ( in @ SV500 @ SV60 )
| ! [SY2907: $i] :
( ~ ( in @ SY2907 @ SV60 )
| ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY2908: $i] :
( ~ ( ~ $true
| ( SY2908 != SV500 ) )
| ~ ( ~ ~ $true
| ( SY2908 != SY2907 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1333,plain,
! [SV60: $i,SV501: $i] :
( ( ~ ( in @ SV501 @ SV60 )
| ! [SY2909: $i] :
( ~ ( in @ SY2909 @ SV60 )
| ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY2910: $i] :
( ~ ( ~ $false
| ( SY2910 != SV501 ) )
| ~ ( ~ ~ $false
| ( SY2910 != SY2909 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1334,plain,
! [SV302: $i,SV61: $i,SV502: $i] :
( ( ~ ( in @ SV502 @ ( funcSet @ SV61 @ SV302 ) )
| ( func @ SV61 @ SV302 @ SV502 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1335,plain,
! [SV303: $i,SV62: $i,SV503: $i] :
( ( ~ ( in @ SV503 @ SV62 )
| ~ ( in @ SV503 @ SV303 )
| ( in @ SV503 @ ( binintersect @ SV62 @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1336,plain,
! [SV304: $i,SV63: $i,SV504: $i] :
( ( ~ ( subset @ SV504 @ SV63 )
| ~ ( subset @ SV504 @ SV304 )
| ( subset @ SV504 @ ( binintersect @ SV63 @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1337,plain,
! [SV64: $i,SV305: $i] :
( ( ( ~ ( in @ SV305 @ ( powerset @ SV64 ) ) )
= $true )
| ( ( ! [SY2566: $i] :
( ~ ( in @ SY2566 @ ( powerset @ SV64 ) )
| ! [SY2567: $i] :
( ~ ( in @ SY2567 @ SV64 )
| ~ ( in @ SY2567 @ ( setminus @ SV64 @ SV305 ) )
| ~ ( in @ SY2567 @ ( binintersect @ SV305 @ SY2566 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1338,plain,
! [SV306: $i,SV65: $i,SV505: $i] :
( ( ~ ( in @ SV505 @ ( binintersect @ SV65 @ SV306 ) )
| ( in @ SV505 @ SV306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1339,plain,
! [SV66: $i,SV307: $i] :
( ( ( ~ ( in @ SV307 @ ( powerset @ SV66 ) ) )
= $true )
| ( ( ! [SY2569: $i] :
( ~ ( in @ SY2569 @ ( powerset @ SV66 ) )
| ! [SY2570: $i] :
( ~ ( in @ SY2570 @ SV66 )
| ~ ~ ( in @ SY2570 @ ( binunion @ SV307 @ SY2569 ) )
| ~ ( in @ SY2570 @ SY2569 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1086]) ).
thf(1340,plain,
! [SV506: $i,SV308: $i,SV67: $i] :
( ( ~ ( func @ SV67 @ SV308 @ SV506 )
| ! [SY2911: $i] :
( ~ ( in @ SY2911 @ SV67 )
| ( ( ap @ SV67 @ SV308 @ SV506 @ SY2911 )
= ( ap @ SV67 @ SV308 @ SV506 @ SY2911 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1341,plain,
! [SV68: $i,SV309: $i,SV507: $i] :
( ( ~ ( in @ SV507 @ SV309 )
| ~ ( in @ SV507 @ ( setminus @ SV68 @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1342,plain,
! [SV69: $i,SV310: $i] :
( ( ~ ( ~ ( in @ SV310 @ ( setunion @ SV69 ) )
| ~ ! [SY2574: $i] :
~ ~ ( ~ ( in @ SV310 @ SY2574 )
| ~ ( in @ SY2574 @ SV69 ) ) )
| ~ ( ~ ~ ! [SY2575: $i] :
~ ~ ( ~ ( in @ SV310 @ SY2575 )
| ~ ( in @ SY2575 @ SV69 ) )
| ( in @ SV310 @ ( setunion @ SV69 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1343,plain,
! [SV70: $i,SV311: $i] :
( ( ( ~ ( in @ SV311 @ ( powerset @ SV70 ) ) )
= $true )
| ( ( ! [SY2576: $i] :
( ~ ( in @ SY2576 @ ( powerset @ SV70 ) )
| ! [SY2577: $i] :
( ~ ( in @ SY2577 @ SV70 )
| ~ ( in @ SY2577 @ ( setminus @ SV70 @ ( binunion @ SV311 @ SY2576 ) ) )
| ~ ( in @ SY2577 @ SV311 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1344,plain,
! [SV312: $i,SV71: $i] :
( ( ( ~ ! [SY2578: $i] :
( ~ ( in @ SY2578 @ SV71 )
| ( in @ SY2578 @ SV312 ) ) )
= $true )
| ( ( subset @ SV71 @ SV312 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1091]) ).
thf(1345,plain,
! [SV313: $i > $o,SV72: $i,SV508: $i] :
( ( ~ ( in @ SV508
@ ( dsetconstr @ SV72
@ ^ [SY2580: $i] : ( SV313 @ SY2580 ) ) )
| ( SV313 @ SV508 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1346,plain,
! [SV73: $i,SV314: $i] :
( ( ( ~ ( in @ SV314 @ ( powerset @ SV73 ) ) )
= $true )
| ( ( ! [SY2581: $i] :
( ~ ( in @ SY2581 @ ( powerset @ SV73 ) )
| ~ ! [SY2582: $i] :
( ~ ( in @ SY2582 @ SV73 )
| ~ ( in @ SY2582 @ SV314 )
| ( in @ SY2582 @ SY2581 ) )
| ( in @ SV314 @ ( powerset @ SY2581 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1093]) ).
thf(1347,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ~ ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
| ! [SY2913: $o] :
( ~ ( ~ ( in @ SV509 @ SV74 )
| ~ ~ ( in @ SV509 @ SV315 )
| SY2913 )
| ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SY2913 )
| SY2913 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1348,plain,
! [SV75: $i] :
( ( ( ! [SY2000: $i] :
~ ( in @ SY2000 @ SV75 ) )
= $false )
| ( ( SV75 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1349,plain,
! [SV510: $i,SV316: $i,SV76: $i] :
( ( ~ ( subset @ SV76 @ SV316 )
| ~ ~ ( in @ SV510 @ SV316 )
| ~ ( in @ SV510 @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1350,plain,
! [SV511: $i > $i > $o,SV317: $i,SV77: $i] :
( ( ! [SY2914: $i,SY2915: $i] :
( ~ ( in @ ( kpair @ SY2914 @ SY2915 )
@ ( dpsetconstr @ SV77 @ SV317
@ ^ [SY2916: $i,SY2917: $i] : ( SV511 @ SY2916 @ SY2917 ) ) )
| ( in @ SY2915 @ SV317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1351,plain,
! [SV78: $i] :
( ( ( SV78 != emptyset )
= $false )
| ( ( ~ ! [SY2009: $i] :
~ ( in @ SY2009 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1098]) ).
thf(1352,plain,
! [SV318: $i > $o,SV79: $i] :
( ( ( ~ ~ ~ ! [SY2591: $i] :
~ ~ ( ~ ( in @ SY2591 @ SV79 )
| ~ ( SV318 @ SY2591 ) ) )
= $true )
| ( ( ! [SY2592: $i] :
( ~ ( in @ SY2592 @ SV79 )
| ~ ( SV318 @ SY2592 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1099]) ).
thf(1353,plain,
! [SV319: $i,SV80: $i,SV512: $i] :
( ( ~ ( in @ SV512 @ SV80 )
| ( in @ SV512 @ ( binunion @ SV80 @ SV319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1354,plain,
! [SV81: $i,SV320: $i] :
( ( ( ~ ( in @ SV320 @ SV81 ) )
= $true )
| ( ( in @ SV320 @ ( powerset @ ( setunion @ SV81 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1101]) ).
thf(1355,plain,
! [SV82: $i] :
( ( ( ~ ! [SY2016: $i] :
~ ( in @ SY2016 @ SV82 ) )
= $false )
| ( ( ~ ! [SY2017: $i] :
~ ~ ( ~ ( in @ SY2017 @ SV82 )
| ~ ~ ~ ! [SY2018: $i] :
~ ~ ( ~ ( in @ SY2018 @ SY2017 )
| ~ ( in @ SY2018 @ SV82 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1356,plain,
! [SV321: $i,SV83: $i] :
( ( ( ( binintersect @ SV83 @ SV321 )
!= SV83 )
= $true )
| ( ( subset @ SV83 @ SV321 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1103]) ).
thf(1357,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( ! [SY2918: $o] :
( ~ ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
| ~ ( ~ ( in @ SV513 @ SV84 )
| SY2918 )
| ~ ( ~ ( in @ SV513 @ SV322 )
| SY2918 )
| SY2918 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1358,plain,
! [SV85: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ ( powerset @ SV85 ) ) )
= $true )
| ( ( ! [SY2596: $i] :
( ~ ( in @ SY2596 @ ( powerset @ SV85 ) )
| ! [SY2597: $i] :
( ~ ( in @ SY2597 @ SV85 )
| ~ ~ ( in @ SY2597 @ ( binunion @ SV323 @ SY2596 ) )
| ~ ( in @ SY2597 @ SV323 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1359,plain,
! [SV86: $i > $o,SV324: $i] :
( ( ( ~ ( in @ SV324 @ emptyset ) )
= $true )
| ( ( SV86 @ SV324 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1106]) ).
thf(1360,plain,
! [SV325: $i > $o,SV87: $i] :
( ( ( ~ ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ SV87 )
| ( SV325 @ SY2598 ) ) )
= $true )
| ( ( ~ ! [SY2599: $i] :
~ ~ ( ~ ( in @ SY2599 @ SV87 )
| ~ ~ ( SV325 @ SY2599 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1361,plain,
! [SV326: $i,SV88: $i] :
( ( ( ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ SV88 )
| ( in @ SY2600 @ SV326 ) ) )
= $true )
| ( ( ~ ! [SY2601: $i] :
( ~ ( in @ SY2601 @ SV326 )
| ( in @ SY2601 @ SV88 ) )
| ( SV88 = SV326 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1362,plain,
! [SV327: $i,SV89: $i] :
( ( ( SV89 != SV327 )
= $true )
| ( ( subset @ SV89 @ SV327 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1363,plain,
! [SV90: $i,SV328: $i] :
( ( ( ~ ( in @ SV328 @ ( powerset @ SV90 ) ) )
= $true )
| ( ( in @ ( powerset @ SV328 ) @ ( powerset @ ( powerset @ SV90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1110]) ).
thf(1364,plain,
! [SV91: $i > $o] :
( ( ( ~ ! [SY2035: $i] :
~ ~ ( ~ ( SV91 @ SY2035 )
| ~ ! [SY2036: $i] :
( ~ ( SV91 @ SY2036 )
| ( SY2035 = SY2036 ) ) ) )
= $false )
| ( ( ! [SY2037: $i,SY2038: $i] :
( ~ ( SV91 @ SY2037 )
| ~ ( SV91 @ SY2038 )
| ( SY2037 = SY2038 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1365,plain,
! [SV514: $i,SV329: $i,SV92: $i] :
( ( ~ ( func @ SV92 @ SV329 @ SV514 )
| ! [SY2919: $i] :
( ~ ( in @ SY2919 @ SV92 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV329
@ ^ [SY2920: $i] : ( in @ ( kpair @ SY2919 @ SY2920 ) @ SV514 ) ) )
@ SV329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1366,plain,
! [SV330: $i,SV93: $i] :
( ( ( SV93 != SV330 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV93 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV93 @ ( setadjoin @ SV330 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV93 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1113]) ).
thf(1367,plain,
! [SV331: $i,SV94: $i,SV515: $i] :
( ( ~ ( in @ SV515 @ SV94 )
| ~ ~ ( in @ SV515 @ SV331 )
| ~ ( subset @ SV94 @ SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1368,plain,
! [SV332: $i,SV95: $i,SV516: $i] :
( ( ~ ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) )
| ! [SY2921: $i] :
( ~ ( subset @ SY2921 @ ( cartprod @ SV95 @ SV332 ) )
| ~ ! [SY2922: $i] :
( ~ ( in @ SY2922 @ SV95 )
| ! [SY2923: $i] :
( ~ ( in @ SY2923 @ SV332 )
| ~ ( in @ ( kpair @ SY2922 @ SY2923 ) @ SV516 )
| ( in @ ( kpair @ SY2922 @ SY2923 ) @ SY2921 ) ) )
| ( subset @ SV516 @ SY2921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1369,plain,
! [SV96: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ ( setunion @ SV96 ) ) )
= $true )
| ( ( ~ ! [SY2610: $i] :
~ ~ ( ~ ( in @ SY2610 @ SV96 )
| ~ ( in @ SV333 @ SY2610 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1116]) ).
thf(1370,plain,
! [SV97: $i,SV334: $i] :
( ( ( ~ ( in @ SV334 @ ( powerset @ SV97 ) ) )
= $true )
| ( ( ! [SY2611: $i] :
( ~ ( in @ SY2611 @ SV97 )
| ~ ~ ( in @ SY2611 @ ( setminus @ SV97 @ SV334 ) )
| ( in @ SY2611 @ SV334 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1117]) ).
thf(1371,plain,
! [SV335: $i > $o,SV98: $i,SV517: $i] :
( ( ~ ( in @ SV517 @ SV98 )
| ~ ( ~ ( ~ ( in @ SV517
@ ( dsetconstr @ SV98
@ ^ [SY2613: $i] : ( SV335 @ SY2613 ) ) )
| ( SV335 @ SV517 ) )
| ~ ( ~ ( SV335 @ SV517 )
| ( in @ SV517
@ ( dsetconstr @ SV98
@ ^ [SY2614: $i] : ( SV335 @ SY2614 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1372,plain,
! [SV99: $i,SV336: $i] :
( ( ( ~ ! [SY2615: $i] :
( ~ ( in @ SY2615 @ SV336 )
| ( in @ SY2615 @ SV99 ) ) )
= $true )
| ( ( in @ SV336 @ ( powerset @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1373,plain,
! [SV337: $i > $o,SV100: $i,SV518: $i] :
( ( ~ ( in @ SV518 @ SV100 )
| ~ ( SV337 @ SV518 )
| ~ ! [SY2926: $i] :
( ~ ( in @ SY2926 @ SV100 )
| ~ ( SV337 @ SY2926 )
| ( SY2926 = SV518 ) )
| ( singleton
@ ( dsetconstr @ SV100
@ ^ [SY2618: $i] : ( SV337 @ SY2618 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1374,plain,
! [SV519: $i > $i > $o,SV338: $i,SV101: $i] :
( ( ! [SY2928: $i,SY2929: $i] :
( ~ ( in @ ( kpair @ SY2928 @ SY2929 )
@ ( dpsetconstr @ SV101 @ SV338
@ ^ [SY2930: $i,SY2931: $i] : ( SV519 @ SY2930 @ SY2931 ) ) )
| ( SV519 @ SY2928 @ SY2929 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1375,plain,
( ( ~ ( in @ sK2_SY2624 @ ( powerset @ sK1_SX0 ) )
| ! [SY2932: $i] :
( ~ ( in @ SY2932 @ ( powerset @ sK1_SX0 ) )
| ! [SY2933: $o,SY2934: $i] :
( ~ ( in @ SY2934 @ sK1_SX0 )
| ~ ( in @ SY2934 @ ( binunion @ sK2_SY2624 @ SY2932 ) )
| ~ ( ~ ( in @ SY2934 @ sK2_SY2624 )
| SY2933 )
| ~ ( ~ ( in @ SY2934 @ SY2932 )
| SY2933 )
| SY2933 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1122]) ).
thf(1376,plain,
! [SV339: $i,SV102: $i] :
( ( ( ~ ( in @ SV102 @ ( setadjoin @ SV339 @ emptyset ) ) )
= $true )
| ( ( in @ SV339 @ ( setadjoin @ SV102 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1377,plain,
! [SV340: $i,SV103: $i,SV520: $i] :
( ( ~ ( in @ SV520 @ ( funcSet @ SV103 @ SV340 ) )
| ( ( lam @ SV103 @ SV340
@ ^ [SY2935: $i] : ( ap @ SV103 @ SV340 @ SV520 @ SY2935 ) )
= SV520 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1378,plain,
! [SV341: $i,SV104: $i,SV521: $i] :
( ( ~ ( in @ SV521 @ SV104 )
| ! [SY2936: $i] :
( ~ ( in @ SY2936 @ SV341 )
| ( subset @ ( setadjoin @ SV521 @ ( setadjoin @ SY2936 @ emptyset ) ) @ ( binunion @ SV104 @ SV341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1379,plain,
! [SV342: $i,SV105: $i,SV522: $i] :
( ( ~ ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
| ! [SY2937: $i > $o] :
( ~ ! [SY2938: $i] :
( ~ ( in @ SY2938 @ SV105 )
| ! [SY2939: $i] :
( ~ ( in @ SY2939 @ SV342 )
| ~ ( in @ ( kpair @ SY2938 @ SY2939 ) @ SV522 )
| ( SY2937 @ ( kpair @ SY2938 @ SY2939 ) ) ) )
| ! [SY2940: $i] :
( ~ ( in @ SY2940 @ SV522 )
| ( SY2937 @ SY2940 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1380,plain,
! [SV106: $i > $o] :
( ( ( ~ ! [SY2084: $i] :
~ ~ ( ~ ( SV106 @ SY2084 )
| ~ ! [SY2085: $i] :
( ~ ( SV106 @ SY2085 )
| ( SY2084 = SY2085 ) ) ) )
= $false )
| ( ( ! [SY2086: $i,SY2087: $i] :
( ~ ( SV106 @ SY2086 )
| ~ ( SV106 @ SY2087 )
| ( SY2086 = SY2087 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1381,plain,
! [SV343: $i > $o,SV107: $i,SV523: $i] :
( ( ~ ( in @ SV523 @ SV107 )
| ~ ( SV343 @ SV523 )
| ( in @ SV523
@ ( dsetconstr @ SV107
@ ^ [SY2638: $i] : ( SV343 @ SY2638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1382,plain,
! [SV108: $i > $o] :
( ( ( ~ ! [SY2091: $i] :
~ ~ ( ~ ( SV108 @ SY2091 )
| ~ ! [SY2092: $i] :
( ~ ( SV108 @ SY2092 )
| ( SY2091 = SY2092 ) ) ) )
= $false )
| ( ( SV108
@ ( descr
@ ^ [SY2093: $i] : ( SV108 @ SY2093 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1383,plain,
! [SV524: $i > $i > $o,SV344: $i,SV109: $i] :
( ( ! [SY2942: $i,SY2943: $i] :
( ~ ( in @ ( kpair @ SY2942 @ SY2943 )
@ ( dpsetconstr @ SV109 @ SV344
@ ^ [SY2944: $i,SY2945: $i] : ( SV524 @ SY2944 @ SY2945 ) ) )
| ( in @ SY2942 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1384,plain,
! [SV345: $i,SV110: $i] :
( ( ( ~ ( subset @ SV110 @ SV345 ) )
= $true )
| ( ( ( binintersect @ SV110 @ SV345 )
= SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1131]) ).
thf(1385,plain,
! [SV111: $i] :
( ( ( ! [SY2101: $i] :
~ ( in @ SY2101 @ SV111 ) )
= $false )
| ( ( SV111 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1386,plain,
! [SV112: $i,SV346: $i] :
( ( ( ~ ( subset @ SV346 @ SV112 ) )
= $true )
| ( ( ( binintersect @ SV112 @ SV346 )
= SV346 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1387,plain,
! [SV347: $i,SV113: $i,SV525: $i] :
( ( ~ ~ ( in @ SV525 @ ( setminus @ SV113 @ SV347 ) )
| ~ ~ ( in @ SV525 @ SV347 )
| ~ ( in @ SV525 @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1388,plain,
! [SV114: $i > $o] :
( ( ( ~ ! [SY2105: $i] :
~ ~ ( ~ ( SV114 @ SY2105 )
| ~ ! [SY2106: $i] :
( ~ ( SV114 @ SY2106 )
| ( SY2105 = SY2106 ) ) ) )
= $false )
| ( ( ~ ! [SY2107: $i] :
~ ( SV114 @ SY2107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1389,plain,
! [SV115: $i,SV348: $i] :
( ( ( ~ ( in @ SV348 @ ( powerset @ SV115 ) ) )
= $true )
| ( ( ! [SY2645: $i] :
( ~ ( in @ SY2645 @ ( powerset @ SV115 ) )
| ! [SY2646: $i] :
( ~ ( in @ SY2646 @ ( powerset @ SV115 ) )
| ! [SY2647: $i] :
( ~ ( in @ SY2647 @ SV115 )
| ~ ( in @ SY2647 @ ( binintersect @ SV348 @ SY2645 ) )
| ( in @ SY2647 @ ( binunion @ SV348 @ SY2646 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1390,plain,
! [SV116: $i] :
( ( ( iskpair @ SV116 )
= $false )
| ( ( ( kpair @ ( kfst @ SV116 ) @ ( ksnd @ SV116 ) )
= SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1391,plain,
! [SV117: $i,SV349: $i] :
( ( ( ~ ( in @ SV349 @ ( powerset @ SV117 ) ) )
= $true )
| ( ( ! [SY2648: $i] :
( ~ ( in @ SY2648 @ ( powerset @ SV117 ) )
| ( in @ ( binintersect @ SV349 @ SY2648 ) @ ( powerset @ SV117 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1392,plain,
! [SV350: $i > $o,SV118: $i] :
( ( ( ~ ! [SY2649: $i] :
( ~ ( in @ SY2649 @ SV118 )
| ~ ( SV350 @ SY2649 ) ) )
= $true )
| ( ( ~ ~ ! [SY2650: $i] :
~ ~ ( ~ ( in @ SY2650 @ SV118 )
| ~ ( SV350 @ SY2650 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1393,plain,
! [SV351: $i > $o,SV119: $i] :
( ( ( ~ ~ ! [SY2651: $i] :
( ~ ( in @ SY2651 @ SV119 )
| ( SV351 @ SY2651 ) ) )
= $true )
| ( ( ~ ! [SY2652: $i] :
~ ~ ( ~ ( in @ SY2652 @ SV119 )
| ~ ~ ( SV351 @ SY2652 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1140]) ).
thf(1394,plain,
! [SV120: $i,SV352: $i] :
( ( ( ~ ( in @ SV352 @ ( powerset @ SV120 ) ) )
= $true )
| ( ( ! [SY2653: $i] :
( ~ ( in @ SY2653 @ ( powerset @ SV120 ) )
| ! [SY2654: $i] :
( ~ ( in @ SY2654 @ SV120 )
| ~ ~ ( in @ SY2654 @ SY2653 )
| ~ ( in @ SY2654 @ ( binintersect @ SV352 @ SY2653 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1395,plain,
! [SV121: $i,SV353: $i] :
( ( ( ~ ( in @ SV353 @ ( powerset @ SV121 ) ) )
= $true )
| ( ( ! [SY2655: $i] :
( ~ ( in @ SY2655 @ ( powerset @ SV121 ) )
| ~ ( subset @ SV353 @ ( setminus @ SV121 @ SY2655 ) )
| ! [SY2656: $i] :
( ~ ( in @ SY2656 @ SV121 )
| ~ ( in @ SY2656 @ SY2655 )
| ( in @ SY2656 @ ( setminus @ SV121 @ SV353 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1396,plain,
! [SV354: $i,SV122: $i] :
( ( ( ~ ~ ( subset @ SV122 @ SV354 ) )
= $true )
| ( ( SV122 != SV354 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1397,plain,
! [SV355: $i,SV526: $i > $i,SV123: $i] :
( ( ~ ! [SY2946: $i] :
( ~ ( in @ SY2946 @ SV123 )
| ( in @ ( SV526 @ SY2946 ) @ SV355 ) )
| ( in
@ ( lam @ SV123 @ SV355
@ ^ [SY2947: $i] : ( SV526 @ SY2947 ) )
@ ( funcSet @ SV123 @ SV355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1398,plain,
! [SV124: $i,SV527: $i,SV356: $i] :
( ( ~ ( in @ SV356 @ SV527 )
| ~ ( in @ SV527 @ SV124 )
| ( in @ SV356 @ ( setunion @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1399,plain,
! [SV357: $i,SV125: $i,SV528: $i] :
( ( ~ ( in @ ( setadjoin @ SV528 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV125 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV125 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) ) )
| ( SV125 = SV528 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1400,plain,
! [SV358: $i,SV126: $i,SV529: $i] :
( ( ~ ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
| ! [SY2948: $o] :
( ~ ( ( SV529 != SV126 )
| SY2948 )
| ~ ( ~ ( in @ SV529 @ SV358 )
| SY2948 )
| SY2948 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1401,plain,
! [SV359: $i,SV127: $i,SV530: $i] :
( ( ~ ~ ( in @ SV530 @ SV127 )
| ~ ~ ( in @ SV530 @ SV359 )
| ~ ( in @ SV530 @ ( symdiff @ SV127 @ SV359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1402,plain,
! [SV360: $i,SV128: $i,SV531: $i] :
( ( ~ ( in @ SV531 @ SV128 )
| ! [SY2949: $i] :
( ~ ( in @ SY2949 @ SV360 )
| ( in @ ( setadjoin @ SV531 @ ( setadjoin @ SY2949 @ emptyset ) ) @ ( powerset @ ( binunion @ SV128 @ SV360 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1403,plain,
! [SV129: $i,SV361: $i] :
( ( ( ~ ( in @ SV361 @ ( powerset @ SV129 ) ) )
= $true )
| ( ( ! [SY2667: $i] :
( ~ ( in @ SY2667 @ ( powerset @ SV129 ) )
| ~ ( subset @ SV361 @ ( setminus @ SV129 @ SY2667 ) )
| ( subset @ SY2667 @ ( setminus @ SV129 @ SV361 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1404,plain,
! [SV130: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ ( powerset @ SV130 ) ) )
= $true )
| ( ( ! [SY2668: $i] :
( ~ ( in @ SY2668 @ ( powerset @ SV130 ) )
| ! [SY2669: $i] :
( ~ ( in @ SY2669 @ SV130 )
| ~ ~ ( in @ SY2669 @ SV362 )
| ~ ( in @ SY2669 @ ( binintersect @ SV362 @ SY2668 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1405,plain,
! [SV131: $i,SV363: $i] :
( ( ( ~ ( in @ SV363 @ ( powerset @ SV131 ) ) )
= $true )
| ( ( ! [SY2670: $i] :
( ~ ( in @ SY2670 @ ( powerset @ SV131 ) )
| ! [SY2671: $i] :
( ~ ( in @ SY2671 @ SV131 )
| ~ ( in @ SY2671 @ ( setminus @ SV131 @ SV363 ) )
| ( in @ SY2671 @ ( setminus @ SV131 @ ( binintersect @ SV363 @ SY2670 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1406,plain,
! [SV364: $i,SV132: $i,SV532: $i] :
( ( ~ ( in @ SV532 @ ( cartprod @ SV132 @ SV364 ) )
| ( in @ ( ksnd @ SV532 ) @ SV364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1407,plain,
! [SV133: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ ( powerset @ SV133 ) ) )
= $true )
| ( ( ! [SY2673: $i] :
( ~ ( in @ SY2673 @ SV133 )
| ~ ( in @ SY2673 @ SV365 )
| ( in @ SY2673 @ ( setminus @ SV133 @ ( setminus @ SV133 @ SV365 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1408,plain,
! [SV533: $i,SV366: $i,SV134: $i] :
( ( ~ ( func @ SV134 @ SV366 @ SV533 )
| ( ( lam @ SV134 @ SV366
@ ^ [SY2950: $i] : ( ap @ SV134 @ SV366 @ SV533 @ SY2950 ) )
= SV533 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1409,plain,
! [SV367: $i > $o,SV135: $i] :
( ( ( ~ ( singleton
@ ( dsetconstr @ SV135
@ ^ [SY2676: $i] : ( SV367 @ SY2676 ) ) ) )
= $true )
| ( ( ! [SY2677: $i] :
( ~ ( in @ SY2677 @ SV135 )
| ! [SY2678: $i] :
( ~ ( in @ SY2678 @ SV135 )
| ~ ( SV367 @ SY2677 )
| ~ ( SV367 @ SY2678 )
| ( SY2677 = SY2678 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1156]) ).
thf(1410,plain,
! [SV136: $i,SV368: $i] :
( ( ( ~ ( in @ SV368 @ ( setunion @ SV136 ) ) )
= $true )
| ( ( ! [SY2679: $o] :
( ~ ! [SY2680: $i] :
( ~ ( in @ SV368 @ SY2680 )
| ~ ( in @ SY2680 @ SV136 )
| SY2679 )
| SY2679 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1411,plain,
! [SV137: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ ( powerset @ SV137 ) ) )
= $true )
| ( ( ! [SY2681: $i] :
( ~ ( in @ SY2681 @ ( powerset @ SV137 ) )
| ! [SY2682: $i] :
( ~ ( in @ SY2682 @ SV137 )
| ~ ( subset @ SV369 @ SY2681 )
| ~ ~ ( in @ SY2682 @ SY2681 )
| ~ ( in @ SY2682 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1412,plain,
! [SV370: $i,SV138: $i,SV534: $i] :
( ( ~ ( in @ SV534 @ ( setadjoin @ SV138 @ ( setadjoin @ SV370 @ emptyset ) ) )
| ( SV534 = SV138 )
| ( SV534 = SV370 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1413,plain,
! [SV139: $i] :
( ( ( in @ SV139 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1414,plain,
! [SV371: $i,SV140: $i,SV535: $i] :
( ( ~ ( in @ SV535 @ ( cartprod @ SV140 @ SV371 ) )
| ( iskpair @ SV535 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1415,plain,
! [SV141: $i,SV372: $i,SV536: $i] :
( ( ~ ( in @ SV536 @ SV372 )
| ( in @ SV536 @ ( setadjoin @ SV141 @ SV372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1416,plain,
! [SV373: $i,SV142: $i,SV537: $i] :
( ( ! [SY2951: $i] :
( ~ ( in @ ( kpair @ SV537 @ SY2951 ) @ ( cartprod @ SV142 @ SV373 ) )
| ( in @ SY2951 @ SV373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1417,plain,
! [SV374: $i,SV143: $i,SV538: $i] :
( ( ~ ( in @ SV538 @ ( funcSet @ SV143 @ SV374 ) )
| ! [SY2952: $i] :
( ~ ( in @ SY2952 @ SV143 )
| ( in @ ( kpair @ SY2952 @ ( ap @ SV143 @ SV374 @ SV538 @ SY2952 ) ) @ SV538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1418,plain,
! [SV375: $i,SV144: $i] :
( ( ( ~ ( subset @ SV144 @ SV375 ) )
= $true )
| ( ( subset @ ( powerset @ SV144 ) @ ( powerset @ SV375 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1165]) ).
thf(1419,plain,
! [SV376: $i,SV145: $i,SV539: $i] :
( ( ~ ( in @ SV539 @ ( cartprod @ SV145 @ SV376 ) )
| ( ( kpair @ ( kfst @ SV539 ) @ ( ksnd @ SV539 ) )
= SV539 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1420,plain,
! [SV146: $i,SV377: $i] :
( ( ( ~ ( in @ SV377 @ ( powerset @ SV146 ) ) )
= $true )
| ( ( ! [SY2691: $i] :
( ~ ( in @ SY2691 @ ( powerset @ SV146 ) )
| ~ ! [SY2692: $i] :
( ~ ( in @ SY2692 @ SV146 )
| ~ ( in @ SY2692 @ SV377 )
| ( in @ SY2692 @ SY2691 ) )
| ( subset @ SV377 @ SY2691 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1421,plain,
! [SV147: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY2953: $i] :
( ~ ( in @ SY2953 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY2188: $i] :
( ~ ( in @ SY2188 @ SY2953 )
| ( in @ SY2188 @ SV147 ) ) )
| ~ ! [SY2955: $i,SY2956: $i] :
( ~ ~ ( ~ ( in @ SY2955 @ SV147 )
| ~ ( in @ SY2956 @ SV147 ) )
| ~ ! [SY2957: $i] :
( ~ ( in @ SY2957 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SY2955 @ SY2957 )
| ( in @ SY2956 @ SY2957 ) )
| ~ ( ~ ( in @ SY2956 @ SY2957 )
| ( in @ SY2955 @ SY2957 ) ) ) )
| ( SY2955 = SY2956 ) ) )
| ~ ! [SY2958: $i,SY2959: $i] :
( ~ ~ ( ~ ( in @ SY2958 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY2959 @ ( sK3_SY2186 @ SV147 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2958 )
| ( in @ SX4 @ SY2959 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2959 )
| ( in @ SX4 @ SY2958 ) ) ) )
| ~ ! [SY2962: $i] :
( ~ ~ ( ~ ! [SY2197: $i] :
( ~ ( in @ SY2197 @ SY2962 )
| ( in @ SY2197 @ SV147 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY2962 ) )
| ~ ! [SY2965: $i] :
~ ~ ! [SY2966: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY2965 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY2966 @ SY2962 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY2965 )
| ~ ( in @ SX5 @ SY2962 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY2965 ) )
| ( in @ SY2966 @ SY2968 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1168]) ).
thf(1422,plain,
! [SV540: $i,SV378: $i,SV148: $i] :
( ( ~ ( subset @ SV148 @ SV378 )
| ~ ( in @ SV540 @ SV148 )
| ( in @ SV540 @ SV378 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1423,plain,
! [SV149: $i,SV379: $i] :
( ( ( ~ ( subset @ SV379 @ SV149 ) )
= $true )
| ( ( in @ SV379 @ ( powerset @ SV149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1424,plain,
! [SV150: $i,SV380: $i,SV541: $i] :
( ( ~ ( in @ SV541 @ SV380 )
| ( in @ SV541 @ ( binunion @ SV150 @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1425,plain,
! [SV151: $i,SV381: $i] :
( ( ( ~ ( in @ SV381 @ ( powerset @ SV151 ) ) )
= $true )
| ( ( ! [SY2695: $i] :
( ~ ( in @ SY2695 @ ( powerset @ SV151 ) )
| ! [SY2696: $i] :
( ~ ( in @ SY2696 @ ( powerset @ SV151 ) )
| ! [SY2697: $i] :
( ~ ( in @ SY2697 @ SV151 )
| ~ ( in @ SY2697 @ ( binintersect @ SV381 @ SY2695 ) )
| ( in @ SY2697 @ ( binunion @ SY2695 @ SY2696 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1426,plain,
! [SV382: $i,SV152: $i] :
( ( ( SV152 != SV382 )
= $true )
| ( ( ( setunion @ SV152 )
= ( setunion @ SV382 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1427,plain,
! [SV383: $i,SV153: $i,SV542: $i] :
( ( ! [SY2970: $i] :
( ~ ( in @ ( kpair @ SV542 @ SY2970 ) @ ( cartprod @ SV153 @ SV383 ) )
| ( in @ SV542 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1428,plain,
! [SV384: $i,SV154: $i,SV543: $i] :
( ( ~ ( in @ SV543 @ ( binunion @ SV154 @ SV384 ) )
| ( in @ SV543 @ SV154 )
| ( in @ SV543 @ SV384 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1429,plain,
! [SV385: $i,SV155: $i] :
( ( ( ~ ! [SY2701: $i] :
( ~ ( in @ SY2701 @ SV155 )
| ( in @ SY2701 @ SV385 ) ) )
= $true )
| ( ( subset @ SV155 @ SV385 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1176]) ).
thf(1430,plain,
! [SV156: $i,SV386: $i] :
( ( ( ~ ( in @ SV386 @ ( powerset @ SV156 ) ) )
= $true )
| ( ( ! [SY2702: $i] :
( ~ ( in @ SY2702 @ ( powerset @ SV156 ) )
| ! [SY2703: $i] :
( ~ ( in @ SY2703 @ SV156 )
| ~ ( subset @ SV386 @ ( setminus @ SV156 @ SY2702 ) )
| ~ ( in @ SY2703 @ SY2702 )
| ~ ( in @ SY2703 @ SV386 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1177]) ).
thf(1431,plain,
! [SV387: $i > $o,SV157: $i,SV544: $i] :
( ( ~ ( in @ SV544
@ ( dsetconstr @ SV157
@ ^ [SY2705: $i] : ( SV387 @ SY2705 ) ) )
| ( in @ SV544 @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1432,plain,
! [SV388: $i,SV158: $i,SV545: $i] :
( ( ~ ~ ( in @ SV545 @ ( setminus @ SV158 @ SV388 ) )
| ~ ( in @ SV545 @ SV158 )
| ( in @ SV545 @ SV388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1433,plain,
! [SV159: $i,SV389: $i] :
( ( ( ~ ( in @ SV389 @ ( powerset @ SV159 ) ) )
= $true )
| ( ( SV389
= ( setminus @ SV159 @ ( setminus @ SV159 @ SV389 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1434,plain,
! [SV160: $i > $o] :
( ( ( ~ ! [SY2230: $i] :
~ ( SV160 @ SY2230 ) )
= $false )
| ( ( ~ ! [SY2231: $i,SY2232: $i] :
( ~ ( SV160 @ SY2231 )
| ~ ( SV160 @ SY2232 )
| ( SY2231 = SY2232 ) )
| ~ ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1435,plain,
! [SV161: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ ( powerset @ SV161 ) ) )
= $true )
| ( ( ! [SY2707: $i] :
( ~ ( in @ SY2707 @ ( powerset @ SV161 ) )
| ( in @ ( setminus @ SV161 @ SV390 ) @ ( powerset @ ( setminus @ SV161 @ ( binintersect @ SV390 @ SY2707 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1182]) ).
thf(1436,plain,
! [SV162: $i,SV391: $i] :
( ( ( ~ ( in @ SV391 @ ( powerset @ SV162 ) ) )
= $true )
| ( ( ! [SY2708: $i] :
( ~ ( in @ SY2708 @ ( powerset @ SV162 ) )
| ( in @ ( setminus @ SV391 @ SY2708 ) @ ( powerset @ SV162 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1183]) ).
thf(1437,plain,
! [SV163: $i] :
( ( ( subset @ SV163 @ emptyset )
= $false )
| ( ( SV163 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1438,plain,
! [SV392: $i,SV164: $i,SV546: $i] :
( ( ~ ( in @ SV546 @ SV164 )
| ~ ~ ( in @ SV546 @ SV392 )
| ( in @ SV546 @ ( symdiff @ SV164 @ SV392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1439,plain,
! [SV393: $i,SV165: $i] :
( ( ( SV165 != SV393 )
= $true )
| ( ( ! [SY2710: $i,SY2711: $i] :
( ( SY2710 != SY2711 )
| ~ ( in @ SY2710 @ SV165 )
| ( in @ SY2711 @ SV393 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1186]) ).
thf(1440,plain,
! [SV394: $i,SV166: $i,SV547: $i] :
( ( ~ ( in @ SV547 @ SV166 )
| ~ ~ ( in @ SV547 @ SV394 )
| ( SV166 != SV394 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1441,plain,
! [SV167: $i,SV395: $i] :
( ( ( ~ ( in @ SV395 @ ( powerset @ SV167 ) ) )
= $true )
| ( ( ! [SY2713: $i] :
( ~ ( in @ SY2713 @ ( powerset @ SV167 ) )
| ! [SY2714: $i] :
( ~ ( in @ SY2714 @ SV167 )
| ~ ( in @ SY2714 @ ( setminus @ SV167 @ ( binunion @ SV395 @ SY2713 ) ) )
| ( in @ SY2714 @ ( setminus @ SV167 @ SV395 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1188]) ).
thf(1442,plain,
! [SV548: $i,SV396: $i,SV168: $i] :
( ( ~ ( func @ SV168 @ SV396 @ SV548 )
| ! [SY2972: $i] :
( ~ ( func @ SV168 @ SV396 @ SY2972 )
| ~ ! [SY2973: $i] :
( ~ ( in @ SY2973 @ SV168 )
| ( ( ap @ SV168 @ SV396 @ SV548 @ SY2973 )
= ( ap @ SV168 @ SV396 @ SY2972 @ SY2973 ) ) )
| ( SV548 = SY2972 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1443,plain,
! [SV397: $o,SV169: $i,SV549: $i] :
( ( ~ ( in @ SV549 @ SV169 )
| ! [SY2974: $i] :
( ~ ( in @ SY2974 @ SV169 )
| ( in @ ( if @ SV169 @ SV397 @ SV549 @ SY2974 ) @ ( setadjoin @ SV549 @ ( setadjoin @ SY2974 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1444,plain,
! [SV169: $i,SV550: $i] :
( ( ~ ( in @ SV550 @ SV169 )
| ! [SY2975: $i] :
( ~ ( in @ SY2975 @ SV169 )
| ( in @ ( if @ SV169 @ $true @ SV550 @ SY2975 ) @ ( setadjoin @ SV550 @ ( setadjoin @ SY2975 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1445,plain,
! [SV169: $i,SV551: $i] :
( ( ~ ( in @ SV551 @ SV169 )
| ! [SY2976: $i] :
( ~ ( in @ SY2976 @ SV169 )
| ( in @ ( if @ SV169 @ $false @ SV551 @ SY2976 ) @ ( setadjoin @ SV551 @ ( setadjoin @ SY2976 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1446,plain,
! [SV398: $i,SV552: $i > $i,SV170: $i] :
( ( ~ ! [SY2977: $i] :
( ~ ( in @ SY2977 @ SV170 )
| ( in @ ( SV552 @ SY2977 ) @ SV398 ) )
| ( ( lam @ SV170 @ SV398
@ ^ [SY2978: $i] : ( SV552 @ SY2978 ) )
= ( lam @ SV170 @ SV398
@ ^ [SY2979: $i] : ( SV552 @ SY2979 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1447,plain,
! [SV399: $o,SV171: $i,SV553: $i] :
( ( ~ ( in @ SV553 @ SV171 )
| ! [SY2980: $i] :
( ~ ( in @ SY2980 @ SV171 )
| ~ ~ SV399
| ( ( dsetconstr @ SV171
@ ^ [SY2981: $i] :
( ~ ( ~ SV399
| ( SY2981 != SV553 ) )
| ~ ( ~ ~ SV399
| ( SY2981 != SY2980 ) ) ) )
= ( setadjoin @ SY2980 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1448,plain,
! [SV171: $i,SV554: $i] :
( ( ~ ( in @ SV554 @ SV171 )
| ! [SY2982: $i] :
( ~ ( in @ SY2982 @ SV171 )
| ~ ~ $true
| ( ( dsetconstr @ SV171
@ ^ [SY2983: $i] :
( ~ ( ~ $true
| ( SY2983 != SV554 ) )
| ~ ( ~ ~ $true
| ( SY2983 != SY2982 ) ) ) )
= ( setadjoin @ SY2982 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1449,plain,
! [SV171: $i,SV555: $i] :
( ( ~ ( in @ SV555 @ SV171 )
| ! [SY2984: $i] :
( ~ ( in @ SY2984 @ SV171 )
| ~ ~ $false
| ( ( dsetconstr @ SV171
@ ^ [SY2985: $i] :
( ~ ( ~ $false
| ( SY2985 != SV555 ) )
| ~ ( ~ ~ $false
| ( SY2985 != SY2984 ) ) ) )
= ( setadjoin @ SY2984 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1450,plain,
! [SV172: $i,SV400: $i] :
( ( ~ ( ~ ( in @ SV400 @ ( powerset @ SV172 ) )
| ! [SY2727: $i] :
( ~ ( in @ SY2727 @ SV400 )
| ( in @ SY2727 @ SV172 ) ) )
| ~ ( ~ ! [SY2728: $i] :
( ~ ( in @ SY2728 @ SV400 )
| ( in @ SY2728 @ SV172 ) )
| ( in @ SV400 @ ( powerset @ SV172 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1451,plain,
! [SV556: $i,SV401: $i,SV173: $i] :
( ( ! [SY2986: $i] :
( ( ( setadjoin @ ( setadjoin @ SV173 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV173 @ ( setadjoin @ SV401 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV556 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV556 @ ( setadjoin @ SY2986 @ emptyset ) ) @ emptyset ) ) )
| ( SV401 = SY2986 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1452,plain,
! [SV402: $i,SV174: $i,SV557: $i] :
( ( ~ ( in @ SV557 @ SV174 )
| ! [SY2987: $i] :
( ~ ( in @ SY2987 @ SV402 )
| ( ( kfst @ ( kpair @ SV557 @ SY2987 ) )
= SV557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1453,plain,
! [SV403: $i,SV175: $i,SV558: $i] :
( ( ~ ( in @ SV558 @ ( funcSet @ SV175 @ SV403 ) )
| ! [SY2988: $i] :
( ~ ( in @ SY2988 @ SV175 )
| ( in @ ( ap @ SV175 @ SV403 @ SV558 @ SY2988 ) @ SV403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1454,plain,
! [SV176: $i,SV404: $i] :
( ( ( ~ ( in @ SV404 @ ( powerset @ SV176 ) ) )
= $true )
| ( ( ! [SY2735: $i] :
( ~ ( in @ SY2735 @ ( powerset @ SV176 ) )
| ~ ( subset @ SV404 @ SY2735 )
| ( subset @ ( setminus @ SV176 @ SY2735 ) @ ( setminus @ SV176 @ SV404 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1201]) ).
thf(1455,plain,
! [SV559: $i,SV405: $i,SV177: $i] :
( ( ~ ( subset @ SV177 @ SV405 )
| ~ ( subset @ SV405 @ SV559 )
| ( subset @ SV177 @ SV559 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1456,plain,
! [SV406: $i,SV178: $i,SV560: $i] :
( ( ~ ( in @ SV560 @ ( binintersect @ SV178 @ SV406 ) )
| ( in @ SV560 @ SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1457,plain,
! [SV179: $i,SV407: $i] :
( ( ( ~ ( in @ SV407 @ ( powerset @ SV179 ) ) )
= $true )
| ( ( subset @ SV407 @ ( setminus @ SV179 @ ( setminus @ SV179 @ SV407 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1458,plain,
! [SV408: $i > $o,SV180: $i] :
( ( ( ~ ~ ! [SY2738: $i] :
~ ~ ( ~ ( in @ SY2738 @ SV180 )
| ~ ( SV408 @ SY2738 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV180
@ ^ [SY2739: $i] : ( SV408 @ SY2739 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1205]) ).
thf(1459,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ( ~ ! [SY2740: $i] :
( ~ ( in @ SY2740 @ SV181 )
| ! [SY2741: $i] :
( ~ ( in @ SY2741 @ SV181 )
| ~ ( SV409 @ SY2740 )
| ~ ( SV409 @ SY2741 )
| ( SY2740 = SY2741 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) )
| ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1206]) ).
thf(1460,plain,
! [SV410: $i,SV182: $i] :
( ( ( ~ ( subset @ SV182 @ SV410 ) )
= $true )
| ( ( ( setminus @ SV182 @ SV410 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1207]) ).
thf(1461,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ! [SY2744: $i,SY2745: $i] :
( ( SY2744 != SY2745 )
| ~ ( ~ ( ~ ( SV183 @ SY2744 )
| ( SV411 @ SY2745 ) )
| ~ ( ~ ( SV411 @ SY2745 )
| ( SV183 @ SY2744 ) ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1462,plain,
! [SV412: $i,SV184: $i] :
( ( ( ~ ( subset @ SV184 @ SV412 ) )
= $true )
| ( ( in @ SV184 @ ( powerset @ SV412 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1463,plain,
! [SV413: $i,SV185: $i,SV561: $i] :
( ( ~ ( in @ SV561 @ ( funcSet @ SV185 @ SV413 ) )
| ! [SY2989: $i] :
( ~ ( in @ SY2989 @ SV185 )
| ! [SY2990: $i] :
( ~ ( in @ SY2990 @ SV413 )
| ~ ( in @ ( kpair @ SY2989 @ SY2990 ) @ SV561 )
| ( ( ap @ SV185 @ SV413 @ SV561 @ SY2989 )
= SY2990 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1464,plain,
! [SV186: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ ( powerset @ SV186 ) ) )
= $true )
| ( ( ! [SY2755: $i] :
( ~ ( in @ SY2755 @ ( powerset @ SV186 ) )
| ~ ! [SY2756: $i] :
( ~ ( in @ SY2756 @ SV186 )
| ~ ( in @ SY2756 @ SV414 )
| ( in @ SY2756 @ SY2755 ) )
| ~ ! [SY2757: $i] :
( ~ ( in @ SY2757 @ SV186 )
| ~ ( in @ SY2757 @ SY2755 )
| ( in @ SY2757 @ SV414 ) )
| ( SV414 = SY2755 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1465,plain,
! [SV415: $i > $o,SV187: $i,SV562: $i] :
( ( ~ ( in @ SV562 @ SV187 )
| ~ ( SV415 @ SV562 )
| ( ( dsetconstr @ SV187
@ ^ [SY2759: $i] : ( SV415 @ SY2759 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1466,plain,
! [SV188: $i > $o] :
( ( ( ~ ! [SY2314: $i] :
~ ~ ( ~ ( SV188 @ SY2314 )
| ~ ! [SY2315: $i] :
( ~ ( SV188 @ SY2315 )
| ( SY2314 = SY2315 ) ) ) )
= $false )
| ( ( ~ ! [SY2316: $i] :
~ ~ ( ~ ( SV188 @ SY2316 )
| ~ ! [SY2317: $i] :
( ~ ( SV188 @ SY2317 )
| ( SY2316 = SY2317 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1467,plain,
! [SV416: $i,SV189: $i,SV563: $i] :
( ( ~ ( in @ SV563 @ ( setadjoin @ SV189 @ SV416 ) )
| ( SV563 = SV189 )
| ( in @ SV563 @ SV416 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1468,plain,
! [SV417: $i,SV190: $i,SV564: $i] :
( ( ~ ( in @ SV564 @ ( funcSet @ SV190 @ SV417 ) )
| ! [SY2992: $i] :
( ~ ( in @ SY2992 @ SV190 )
| ( ( ap @ SV190 @ SV417 @ SV564 @ SY2992 )
= ( ap @ SV190 @ SV417 @ SV564 @ SY2992 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1469,plain,
! [SV191: $i,SV418: $i] :
( ( ( ~ ( in @ SV418 @ ( powerset @ SV191 ) ) )
= $true )
| ( ( ! [SY2763: $i] :
( ~ ( in @ SY2763 @ ( powerset @ SV191 ) )
| ! [SY2764: $i] :
( ~ ( in @ SY2764 @ ( powerset @ SV191 ) )
| ! [SY2765: $i] :
( ~ ( in @ SY2765 @ SV191 )
| ~ ( in @ SY2765 @ ( binintersect @ SV418 @ SY2763 ) )
| ( in @ SY2765 @ ( binintersect @ ( binunion @ SV418 @ SY2764 ) @ ( binunion @ SY2763 @ SY2764 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1216]) ).
thf(1470,plain,
! [SV192: $o,SV419: $i] :
( ( ( ~ ( in @ SV419 @ ( prop2set @ SV192 ) ) )
= $true )
| ( SV192 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1471,plain,
! [SV420: $i] :
( ( ( ~ ( in @ SV420 @ ( prop2set @ $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1472,plain,
! [SV421: $i] :
( ( ( ~ ( in @ SV421 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1473,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ! [SY2766: $i,SY2767: $i] :
( ( SY2766 != SY2767 )
| ~ ( ~ ( ~ ( SV193 @ SY2766 )
| ( SV422 @ SY2767 ) )
| ~ ( ~ ( SV422 @ SY2767 )
| ( SV193 @ SY2766 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1220]) ).
thf(1474,plain,
! [SV194: $i] :
( ( ( singleton @ SV194 )
= $false )
| ( ( ! [SY2339: $i] :
( ~ ( in @ SY2339 @ SV194 )
| ( ( setunion @ SV194 )
= SY2339 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1475,plain,
! [SV423: $i,SV195: $i,SV565: $i] :
( ( ~ ( in @ SV565 @ SV195 )
| ~ ~ ( in @ SV565 @ SV423 )
| ( in @ SV565 @ ( setminus @ SV195 @ SV423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1476,plain,
! [SV424: $i,SV196: $i,SV566: $i] :
( ( ~ ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) )
| ~ ! [SY2993: $i] :
~ ~ ( ~ ( in @ SY2993 @ SV196 )
| ~ ~ ! [SY2994: $i] :
~ ~ ( ~ ( in @ SY2994 @ SV424 )
| ( SV566
!= ( kpair @ SY2993 @ SY2994 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1477,plain,
! [SV425: $o,SV197: $i,SV567: $i] :
( ( ~ ( in @ SV567 @ SV197 )
| ! [SY2995: $i] :
( ~ ( in @ SY2995 @ SV197 )
| ~ SV425
| ( ( if @ SV197 @ SV425 @ SV567 @ SY2995 )
= SV567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1478,plain,
! [SV197: $i,SV568: $i] :
( ( ~ ( in @ SV568 @ SV197 )
| ! [SY2996: $i] :
( ~ ( in @ SY2996 @ SV197 )
| ~ $true
| ( ( if @ SV197 @ $true @ SV568 @ SY2996 )
= SV568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1479,plain,
! [SV197: $i,SV569: $i] :
( ( ~ ( in @ SV569 @ SV197 )
| ! [SY2997: $i] :
( ~ ( in @ SY2997 @ SV197 )
| ~ $false
| ( ( if @ SV197 @ $false @ SV569 @ SY2997 )
= SV569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1480,plain,
! [SV426: $i,SV198: $i,SV570: $i] :
( ( ~ ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
| ! [SY2998: $i] :
( ~ ( subset @ SY2998 @ ( cartprod @ SV198 @ SV426 ) )
| ~ ! [SY2999: $i] :
( ~ ( in @ SY2999 @ SV198 )
| ! [SY3000: $i] :
( ~ ( in @ SY3000 @ SV426 )
| ~ ( in @ ( kpair @ SY2999 @ SY3000 ) @ SV570 )
| ( in @ ( kpair @ SY2999 @ SY3000 ) @ SY2998 ) ) )
| ~ ! [SY3001: $i] :
( ~ ( in @ SY3001 @ SV198 )
| ! [SY3002: $i] :
( ~ ( in @ SY3002 @ SV426 )
| ~ ( in @ ( kpair @ SY3001 @ SY3002 ) @ SY2998 )
| ( in @ ( kpair @ SY3001 @ SY3002 ) @ SV570 ) ) )
| ( SV570 = SY2998 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1481,plain,
! [SV427: $i,SV199: $i] :
( ( ( ( binintersect @ SV199 @ SV427 )
!= SV427 )
= $true )
| ( ( subset @ SV427 @ SV199 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1228]) ).
thf(1482,plain,
! [SV428: $i,SV200: $i,SV571: $i] :
( ( ~ ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
| ! [SY3003: $i > $o] :
( ~ ! [SY3004: $i] :
( ~ ( in @ SY3004 @ SV200 )
| ! [SY3005: $i] :
( ~ ( in @ SY3005 @ SV428 )
| ~ ( in @ ( kpair @ SY3004 @ SY3005 ) @ SV571 )
| ( SY3003 @ ( kpair @ SY3004 @ SY3005 ) ) ) )
| ! [SY3006: $i] :
( ~ ( in @ SY3006 @ SV571 )
| ( SY3003 @ SY3006 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1483,plain,
! [SV429: $i > $o,SV201: $i] :
( ( ( ~ ~ ! [SY2793: $i] :
~ ~ ( ~ ( in @ SY2793 @ SV201 )
| ~ ~ ( SV429 @ SY2793 ) ) )
= $true )
| ( ( ~ ! [SY2794: $i] :
( ~ ( in @ SY2794 @ SV201 )
| ( SV429 @ SY2794 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1230]) ).
thf(1484,plain,
! [SV202: $i] :
( ( ( iskpair @ SV202 )
= $false )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV202 )
@ ^ [SY2366: $i] : ( in @ ( setadjoin @ SY2366 @ emptyset ) @ SV202 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1485,plain,
! [SV430: $i,SV572: $i > $i,SV203: $i] :
( ( ~ ! [SY3007: $i] :
( ~ ( in @ SY3007 @ SV203 )
| ( in @ ( SV572 @ SY3007 ) @ SV430 ) )
| ( func @ SV203 @ SV430
@ ( dpsetconstr @ SV203 @ SV430
@ ^ [SY3008: $i,SY3009: $i] :
( ( SV572 @ SY3008 )
= SY3009 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1486,plain,
! [SV204: $i] :
( ( ( ~ ! [SY2372: $i] :
~ ( in @ SY2372 @ SV204 ) )
= $false )
| ( ( SV204 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1487,plain,
! [SV205: $i] :
( ( ( in @ SV205 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV205 @ SV205 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1488,plain,
! [SV431: $i,SV206: $i,SV573: $i] :
( ( ~ ~ ( in @ SV573 @ SV206 )
| ~ ( in @ SV573 @ SV431 )
| ( in @ SV573 @ ( symdiff @ SV206 @ SV431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1489,plain,
! [SV432: $i,SV207: $i] :
( ( ( SV207 != SV432 )
= $true )
| ( ( subset @ SV432 @ SV207 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1236]) ).
thf(1490,plain,
! [SV208: $i] :
( ( ( in @ SV208 @ emptyset )
= $false )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1491,plain,
! [SV433: $i,SV574: $i > $i,SV209: $i] :
( ( ~ ! [SY3010: $i] :
( ~ ( in @ SY3010 @ SV209 )
| ( in @ ( SV574 @ SY3010 ) @ SV433 ) )
| ! [SY3011: $i] :
( ~ ( in @ SY3011 @ SV209 )
| ( ( ap @ SV209 @ SV433
@ ( lam @ SV209 @ SV433
@ ^ [SY3012: $i] : ( SV574 @ SY3012 ) )
@ SY3011 )
= ( SV574 @ SY3011 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1492,plain,
! [SV210: $i,SV434: $i] :
( ( ( ~ ( in @ SV434 @ ( powerset @ SV210 ) ) )
= $true )
| ( ( subset @ ( setminus @ SV210 @ ( setminus @ SV210 @ SV434 ) ) @ SV434 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1493,plain,
! [SV435: $i,SV211: $i] :
( ( ( SV211 != SV435 )
= $true )
| ( ( ! [SY2804: $i,SY2805: $i] :
( ( SY2804 != SY2805 )
| ( ( setadjoin @ SV211 @ SY2804 )
= ( setadjoin @ SV435 @ SY2805 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1494,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ( ~ ! [SY2806: $i] :
( ~ ( in @ SY2806 @ SV212 )
| ! [SY2807: $i] :
( ~ ( in @ SY2807 @ SV212 )
| ~ ( SV436 @ SY2806 )
| ~ ( SV436 @ SY2807 )
| ( SY2806 = SY2807 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) )
| ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1241]) ).
thf(1495,plain,
! [SV437: $i,SV213: $i] :
( ( ( ( setadjoin @ SV213 @ emptyset )
!= ( setadjoin @ SV437 @ emptyset ) )
= $true )
| ( ( SV213 = SV437 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1496,plain,
! [SV575: $i,SV438: $i,SV214: $i] :
( ( ! [SY3013: $i] :
( ( ( setadjoin @ ( setadjoin @ SV214 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV214 @ ( setadjoin @ SV438 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV575 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV575 @ ( setadjoin @ SY3013 @ emptyset ) ) @ emptyset ) ) )
| ( SV575 != SY3013 )
| ( SV438 = SY3013 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1497,plain,
! [SV215: $i] :
( ( ( ~ ( ~ ( in @ emptyset @ SV215 )
| ~ ! [SY2395: $i] :
( ~ ~ ( ~ ( in @ SY2395 @ omega )
| ~ ( in @ SY2395 @ SV215 ) )
| ( in @ ( setadjoin @ SY2395 @ SY2395 ) @ SV215 ) ) ) )
= $false )
| ( ( ! [SY2396: $i] :
( ~ ( in @ SY2396 @ omega )
| ( in @ SY2396 @ SV215 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1498,plain,
! [SV439: $i,SV216: $i,SV576: $i] :
( ( ~ ( in @ SV576 @ SV216 )
| ! [SY3014: $i] :
( ~ ( in @ SY3014 @ SV439 )
| ( in @ ( kpair @ SV576 @ SY3014 ) @ ( powerset @ ( powerset @ ( binunion @ SV216 @ SV439 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1499,plain,
! [SV577: $i > $i > $o,SV440: $i,SV217: $i] :
( ( ! [SY3015: $i] :
( ~ ( in @ SY3015 @ SV217 )
| ! [SY3016: $i] :
( ~ ( in @ SY3016 @ SV440 )
| ~ ( SV577 @ SY3015 @ SY3016 )
| ( in @ ( kpair @ SY3015 @ SY3016 )
@ ( dpsetconstr @ SV217 @ SV440
@ ^ [SY3017: $i,SY3018: $i] : ( SV577 @ SY3017 @ SY3018 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1500,plain,
! [SV441: $o,SV218: $i,SV578: $i] :
( ( ~ ( in @ SV578 @ SV218 )
| ! [SY3019: $i] :
( ~ ( in @ SY3019 @ SV218 )
| ( in @ ( if @ SV218 @ SV441 @ SV578 @ SY3019 ) @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1501,plain,
! [SV218: $i,SV579: $i] :
( ( ~ ( in @ SV579 @ SV218 )
| ! [SY3020: $i] :
( ~ ( in @ SY3020 @ SV218 )
| ( in @ ( if @ SV218 @ $true @ SV579 @ SY3020 ) @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1502,plain,
! [SV218: $i,SV580: $i] :
( ( ~ ( in @ SV580 @ SV218 )
| ! [SY3021: $i] :
( ~ ( in @ SY3021 @ SV218 )
| ( in @ ( if @ SV218 @ $false @ SV580 @ SY3021 ) @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1503,plain,
! [SV442: $i,SV219: $i,SV581: $i] :
( ( ~ ( in @ SV581 @ ( funcSet @ SV219 @ SV442 ) )
| ! [SY3022: $i] :
( ~ ( in @ SY3022 @ ( funcSet @ SV219 @ SV442 ) )
| ~ ! [SY3023: $i] :
( ~ ( in @ SY3023 @ SV219 )
| ( ( ap @ SV219 @ SV442 @ SV581 @ SY3023 )
= ( ap @ SV219 @ SV442 @ SY3022 @ SY3023 ) ) )
| ( SV581 = SY3022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1504,plain,
! [SV582: $i > $i > $o,SV443: $i,SV220: $i] :
( ( ! [SY3024: $i] :
( ~ ( in @ SY3024 @ SV220 )
| ! [SY3025: $i] :
( ~ ( in @ SY3025 @ SV443 )
| ~ ( in @ ( kpair @ SY3024 @ SY3025 )
@ ( dpsetconstr @ SV220 @ SV443
@ ^ [SY3026: $i,SY3027: $i] : ( SV582 @ SY3026 @ SY3027 ) ) )
| ( SV582 @ SY3024 @ SY3025 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1505,plain,
! [SV583: $i,SV444: $i,SV221: $i] :
( ( ~ ( func @ SV221 @ SV444 @ SV583 )
| ! [SY3028: $i] :
( ~ ( in @ SY3028 @ SV221 )
| ( in @ ( ap @ SV221 @ SV444 @ SV583 @ SY3028 ) @ SV444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1506,plain,
! [SV445: $i,SV222: $i,SV584: $i] :
( ( ~ ( in @ SV584 @ SV222 )
| ( in @ ( setadjoin @ SV584 @ emptyset ) @ ( powerset @ ( binunion @ SV222 @ SV445 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1507,plain,
! [SV446: $i > $o,SV223: $i] :
( ( ( ~ ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY2832: $i] : ( SV446 @ SY2832 ) ) ) )
= $true )
| ( ( ~ ! [SY2833: $i] :
~ ~ ( ~ ( in @ SY2833 @ SV223 )
| ~ ( SV446 @ SY2833 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1254]) ).
thf(1508,plain,
! [SV447: $i,SV224: $i] :
( ( ( ~ ( ( SV224 != SV447 ) ) )
= $true )
| ( ( ~ ( in @ SV447 @ ( setadjoin @ SV224 @ emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1255]) ).
thf(1509,plain,
! [SV448: $i,SV225: $i] :
( ( ( ~ ! [SY2834: $i] :
~ ( ~ ( ~ ( in @ SY2834 @ SV225 )
| ( in @ SY2834 @ SV448 ) )
| ~ ( ~ ( in @ SY2834 @ SV448 )
| ( in @ SY2834 @ SV225 ) ) ) )
= $true )
| ( ( SV225 = SV448 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1256]) ).
thf(1510,plain,
! [SV449: $i,SV226: $i,SV585: $i] :
( ( ~ ( in @ SV585 @ SV226 )
| ~ ( in @ SV585 @ SV449 )
| ~ ( in @ SV585 @ ( symdiff @ SV226 @ SV449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1511,plain,
! [SV227: $i,SV450: $i] :
( ( ( ~ ( in @ SV450 @ ( powerset @ SV227 ) ) )
= $true )
| ( ( ! [SY2836: $i] :
( ~ ( in @ SY2836 @ SV227 )
| ~ ( in @ SY2836 @ ( setminus @ SV227 @ ( setminus @ SV227 @ SV450 ) ) )
| ( in @ SY2836 @ SV450 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1258]) ).
thf(1512,plain,
! [SV586: $i,SV451: $i,SV228: $i] :
( ( ! [SY3029: $i] :
( ( ( setadjoin @ ( setadjoin @ SV228 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV228 @ ( setadjoin @ SV451 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV586 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV586 @ ( setadjoin @ SY3029 @ emptyset ) ) @ emptyset ) ) )
| ( SV228 = SV586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1513,plain,
! [SV229: $i,SV452: $i] :
( ( ( ~ ( in @ SV452 @ ( powerset @ SV229 ) ) )
= $true )
| ( ( ! [SY2839: $i] :
( ~ ( in @ SY2839 @ ( powerset @ SV229 ) )
| ! [SY2840: $i] :
( ~ ( in @ SY2840 @ ( powerset @ SV229 ) )
| ( in @ ( binintersect @ SV452 @ SY2839 ) @ ( powerset @ ( binintersect @ ( binunion @ SV452 @ SY2840 ) @ ( binunion @ SY2839 @ SY2840 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1260]) ).
thf(1514,plain,
! [SV230: $i] :
( ( ( SV230 != emptyset )
= $false )
| ( ( ~ ! [SY2440: $i] :
~ ~ ( ~ ( in @ SY2440 @ SV230 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1261]) ).
thf(1515,plain,
! [SV453: $o,SV231: $i,SV587: $i] :
( ( ~ ( in @ SV587 @ SV231 )
| ! [SY3030: $i] :
( ~ ( in @ SY3030 @ SV231 )
| ~ SV453
| ( ( dsetconstr @ SV231
@ ^ [SY3031: $i] :
( ~ ( ~ SV453
| ( SY3031 != SV587 ) )
| ~ ( ~ ~ SV453
| ( SY3031 != SY3030 ) ) ) )
= ( setadjoin @ SV587 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1516,plain,
! [SV231: $i,SV588: $i] :
( ( ~ ( in @ SV588 @ SV231 )
| ! [SY3032: $i] :
( ~ ( in @ SY3032 @ SV231 )
| ~ $true
| ( ( dsetconstr @ SV231
@ ^ [SY3033: $i] :
( ~ ( ~ $true
| ( SY3033 != SV588 ) )
| ~ ( ~ ~ $true
| ( SY3033 != SY3032 ) ) ) )
= ( setadjoin @ SV588 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1517,plain,
! [SV231: $i,SV589: $i] :
( ( ~ ( in @ SV589 @ SV231 )
| ! [SY3034: $i] :
( ~ ( in @ SY3034 @ SV231 )
| ~ $false
| ( ( dsetconstr @ SV231
@ ^ [SY3035: $i] :
( ~ ( ~ $false
| ( SY3035 != SV589 ) )
| ~ ( ~ ~ $false
| ( SY3035 != SY3034 ) ) ) )
= ( setadjoin @ SV589 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1518,plain,
! [SV590: $i,SV232: $i,SV454: $i] :
( ( ~ ( in @ SV454 @ ( powerset @ SV232 ) )
| ~ ( in @ SV590 @ SV454 )
| ( in @ SV590 @ SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1519,plain,
! [SV233: $i,SV455: $i] :
( ( ( ~ ( in @ SV455 @ ( powerset @ SV233 ) ) )
= $true )
| ( ( ! [SY2845: $i] :
( ~ ( in @ SY2845 @ SV233 )
| ~ ( in @ SY2845 @ SV455 )
| ~ ( in @ SY2845 @ ( setminus @ SV233 @ SV455 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1266]) ).
thf(1520,plain,
! [SV456: $i,SV591: $i > $i,SV234: $i] :
( ( ~ ! [SY3036: $i] :
( ~ ( in @ SY3036 @ SV234 )
| ( in @ ( SV591 @ SY3036 ) @ SV456 ) )
| ! [SY3037: $i] :
( ~ ( in @ SY3037 @ SV234 )
| ( ( ap @ SV234 @ SV456
@ ( lam @ SV234 @ SV456
@ ^ [SY3038: $i] : ( SV591 @ SY3038 ) )
@ SY3037 )
= ( SV591 @ SY3037 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1521,plain,
! [SV457: $i,SV235: $i] :
( ( ( ~ ~ ~ ! [SY2850: $i] :
~ ~ ( ~ ( in @ SY2850 @ SV235 )
| ~ ( in @ SY2850 @ SV457 ) ) )
= $true )
| ( ( ( binintersect @ SV235 @ SV457 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1268]) ).
thf(1522,plain,
! [SV592: $i,SV458: $i,SV236: $i] :
( ( ! [SY3039: $i] :
( ( ( kpair @ SV236 @ SV458 )
!= ( kpair @ SV592 @ SY3039 ) )
| ( SV236 = SV592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1523,plain,
! [SV459: $i,SV593: $i,SV237: $i] :
( ( ~ ( subset @ SV237 @ SV593 )
| ( subset @ SV237 @ ( setadjoin @ SV459 @ SV593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1524,plain,
! [SV460: $i,SV238: $i,SV594: $i] :
( ( ~ ( in @ SV594 @ ( setadjoin @ SV238 @ ( setadjoin @ SV460 @ emptyset ) ) )
| ( SV594 = SV238 )
| ( SV594 = SV460 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1525,plain,
! [SV595: $i,SV461: $i,SV239: $i] :
( ( ! [SY3040: $i] :
( ( ( kpair @ SV239 @ SV461 )
!= ( kpair @ SV595 @ SY3040 ) )
| ( SV461 = SY3040 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1526,plain,
! [SV462: $i,SV240: $i] :
( ( ( SV240 != SV462 )
= $true )
| ( ( ( setadjoin @ SV240 @ ( setadjoin @ SV462 @ emptyset ) )
= ( setadjoin @ SV240 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1273]) ).
thf(1527,plain,
! [SV463: $i,SV241: $i] :
( ( ( SV241 != SV463 )
= $true )
| ( ( ( powerset @ SV241 )
= ( powerset @ SV463 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1274]) ).
thf(1528,plain,
! [SV464: $i,SV596: $i > $i,SV242: $i] :
( ( ~ ! [SY3041: $i] :
( ~ ( in @ SY3041 @ SV242 )
| ( in @ ( SV596 @ SY3041 ) @ SV464 ) )
| ( func @ SV242 @ SV464
@ ( lam @ SV242 @ SV464
@ ^ [SY3042: $i] : ( SV596 @ SY3042 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1529,plain,
! [SV243: $i,SV465: $i] :
( ( ( ~ ( in @ SV465 @ ( powerset @ SV243 ) ) )
= $true )
| ( ( ! [SY2860: $i] :
( ~ ( in @ SY2860 @ ( powerset @ SV243 ) )
| ! [SY2861: $i] :
( ~ ( in @ SY2861 @ SV243 )
| ~ ( in @ SV465 @ ( powerset @ SY2860 ) )
| ~ ( in @ SY2861 @ SV465 )
| ( in @ SY2861 @ SY2860 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1276]) ).
thf(1530,plain,
! [SV466: $o,SV244: $i,SV597: $i] :
( ( ~ ( in @ SV597 @ SV244 )
| ! [SY3043: $i] :
( ~ ( in @ SY3043 @ SV244 )
| ~ ~ SV466
| ( in @ SY3043
@ ( dsetconstr @ SV244
@ ^ [SY3044: $i] :
( ~ ( ~ SV466
| ( SY3044 != SV597 ) )
| ~ ( ~ ~ SV466
| ( SY3044 != SY3043 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1531,plain,
! [SV244: $i,SV598: $i] :
( ( ~ ( in @ SV598 @ SV244 )
| ! [SY3045: $i] :
( ~ ( in @ SY3045 @ SV244 )
| ~ ~ $true
| ( in @ SY3045
@ ( dsetconstr @ SV244
@ ^ [SY3046: $i] :
( ~ ( ~ $true
| ( SY3046 != SV598 ) )
| ~ ( ~ ~ $true
| ( SY3046 != SY3045 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1532,plain,
! [SV244: $i,SV599: $i] :
( ( ~ ( in @ SV599 @ SV244 )
| ! [SY3047: $i] :
( ~ ( in @ SY3047 @ SV244 )
| ~ ~ $false
| ( in @ SY3047
@ ( dsetconstr @ SV244
@ ^ [SY3048: $i] :
( ~ ( ~ $false
| ( SY3048 != SV599 ) )
| ~ ( ~ ~ $false
| ( SY3048 != SY3047 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1533,plain,
! [SV245: $i,SV467: $i] :
( ( ( ~ ( in @ SV467 @ SV245 ) )
= $true )
| ( ( in @ ( setadjoin @ SV467 @ emptyset ) @ ( powerset @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1280]) ).
thf(1534,plain,
! [SV246: $i,SV468: $i] :
( ( ( ~ ( in @ SV468 @ SV246 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV468 @ emptyset ) @ SV246 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1281]) ).
thf(1535,plain,
! [SV600: $i,SV469: $i,SV247: $i] :
( ( ~ ( func @ SV247 @ SV469 @ SV600 )
| ! [SY3049: $i] :
( ~ ( func @ SV247 @ SV469 @ SY3049 )
| ~ ! [SY3050: $i] :
( ~ ( in @ SY3050 @ SV247 )
| ( ( ap @ SV247 @ SV469 @ SV600 @ SY3050 )
= ( ap @ SV247 @ SV469 @ SY3049 @ SY3050 ) ) )
| ! [SY3051: $i] :
( ~ ( in @ SY3051 @ SV247 )
| ! [SY3052: $i] :
( ~ ( in @ SY3052 @ SV469 )
| ~ ( in @ ( kpair @ SY3051 @ SY3052 ) @ SY3049 )
| ( in @ ( kpair @ SY3051 @ SY3052 ) @ SV600 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1536,plain,
! [SV248: $i,SV470: $i] :
( ( ( ~ ( in @ SV470 @ ( powerset @ SV248 ) ) )
= $true )
| ( ( ! [SY2870: $i] :
( ~ ( in @ SY2870 @ ( powerset @ SV248 ) )
| ( subset @ ( setminus @ SV248 @ SV470 ) @ ( setminus @ SV248 @ ( binintersect @ SV470 @ SY2870 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1283]) ).
thf(1537,plain,
! [SV249: $i > $i > $o,SV471: $i] :
( ( ( ~ ! [SY2871: $i] :
( ~ ( in @ SY2871 @ SV471 )
| ~ ! [SY2491: $i] :
~ ~ ( ~ ( SV249 @ SY2871 @ SY2491 )
| ~ ! [SY2492: $i] :
( ~ ( SV249 @ SY2871 @ SY2492 )
| ( SY2491 = SY2492 ) ) ) ) )
= $true )
| ( ( ~ ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1284]) ).
thf(1538,plain,
! [SV472: $i,SV250: $i] :
( ( ( SV250 != SV472 )
= $true )
| ( ( in @ SV250 @ ( setadjoin @ SV472 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1285]) ).
thf(1539,plain,
! [SV473: $i,SV251: $i] :
( ( ( ( setminus @ SV251 @ SV473 )
!= emptyset )
= $true )
| ( ( subset @ SV251 @ SV473 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1286]) ).
thf(1540,plain,
! [SV474: $o,SV252: $i,SV601: $i] :
( ( ~ ( in @ SV601 @ SV252 )
| ! [SY3053: $i] :
( ~ ( in @ SY3053 @ SV252 )
| ~ ~ SV474
| ( ( if @ SV252 @ SV474 @ SV601 @ SY3053 )
= SY3053 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1541,plain,
! [SV252: $i,SV602: $i] :
( ( ~ ( in @ SV602 @ SV252 )
| ! [SY3054: $i] :
( ~ ( in @ SY3054 @ SV252 )
| ~ ~ $true
| ( ( if @ SV252 @ $true @ SV602 @ SY3054 )
= SY3054 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1542,plain,
! [SV252: $i,SV603: $i] :
( ( ~ ( in @ SV603 @ SV252 )
| ! [SY3055: $i] :
( ~ ( in @ SY3055 @ SV252 )
| ~ ~ $false
| ( ( if @ SV252 @ $false @ SV603 @ SY3055 )
= SY3055 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1543,plain,
! [SV475: $i,SV253: $i,SV604: $i] :
( ( ~ ( in @ SV604 @ SV253 )
| ! [SY3056: $i] :
( ~ ( in @ SY3056 @ SV475 )
| ( in @ ( setadjoin @ ( setadjoin @ SV604 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV604 @ ( setadjoin @ SY3056 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV253 @ SV475 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1544,plain,
! [SV476: $i,SV254: $i] :
( ( ( SV254 != SV476 )
= $true )
| ( ( ! [SY2882: $i,SY2883: $i] :
( ( SY2882 != SY2883 )
| ~ ( ~ ( ~ ( in @ SY2882 @ SV254 )
| ( in @ SY2883 @ SV476 ) )
| ~ ( ~ ( in @ SY2883 @ SV476 )
| ( in @ SY2882 @ SV254 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1291]) ).
thf(1545,plain,
! [SV477: $i,SV255: $i] :
( ( ( ~ ( subset @ SV255 @ SV477 ) )
= $true )
| ( ( ~ ( subset @ SV477 @ SV255 )
| ( SV255 = SV477 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1292]) ).
thf(1546,plain,
! [SV256: $i > $o] :
( ( ( ~ ! [SY2509: $i] :
~ ~ ( ~ ( SV256 @ SY2509 )
| ~ ! [SY2510: $i] :
( ~ ( SV256 @ SY2510 )
| ( SY2509 = SY2510 ) ) ) )
= $false )
| ( ( ~ ! [SY2511: $i] :
~ ! [SY2512: $i] :
~ ( ~ ( ~ ( SV256 @ SY2512 )
| ( SY2512 = SY2511 ) )
| ~ ( ( SY2512 != SY2511 )
| ( SV256 @ SY2512 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1547,plain,
! [SV257: $i,SV478: $i] :
( ( ( ~ ( in @ SV478 @ ( powerset @ SV257 ) ) )
= $true )
| ( ( ! [SY2884: $i] :
( ~ ( in @ SY2884 @ ( powerset @ SV257 ) )
| ( in @ ( binunion @ SV478 @ SY2884 ) @ ( powerset @ SV257 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1294]) ).
thf(1548,plain,
! [SV479: $i,SV258: $i,SV605: $i] :
( ( ~ ( in @ SV605 @ SV258 )
| ! [SY3057: $i] :
( ~ ( in @ SY3057 @ SV479 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV605 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV605 @ ( setadjoin @ SY3057 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV258 @ SV479 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1549,plain,
! [SV483: $i,SV281: $i,SV34: $i] :
( ( ( ~ ( func @ SV34 @ SV281 @ SV483 ) )
= $true )
| ( ( in @ SV483 @ ( funcSet @ SV34 @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1299]) ).
thf(1550,plain,
! [SV35: $i > $o] :
( ( ( ! [SY1900: $i] :
~ ~ ( ~ ( SV35 @ SY1900 )
| ~ ! [SY1901: $i] :
( ~ ( SV35 @ SY1901 )
| ( SY1900 = SY1901 ) ) ) )
= $true )
| ( ( ~ ! [SY1902: $i] :
~ ~ ( ~ ( SV35 @ SY1902 )
| ~ ! [SY1903: $i] :
( ~ ( SV35 @ SY1903 )
| ( SY1902 = SY1903 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1300]) ).
thf(1551,plain,
! [SV36: $i,SV282: $i] :
( ( ( in @ SV282 @ ( powerset @ SV36 ) )
= $false )
| ( ( ! [SY2528: $i] :
( ~ ( in @ SY2528 @ ( powerset @ SV36 ) )
| ~ ( subset @ ( setminus @ SV36 @ SY2528 ) @ ( setminus @ SV36 @ SV282 ) )
| ( subset @ SV282 @ SY2528 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1552,plain,
! [SV283: $i,SV37: $i] :
( ( ( in @ SV37 @ ( setadjoin @ SV283 @ emptyset ) )
= $false )
| ( ( SV37 = SV283 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1553,plain,
! [SV484: $i,SV284: $i,SV38: $i] :
( ( ( ~ ( func @ SV38 @ SV284 @ SV484 ) )
= $true )
| ( ( ! [SY2891: $i] :
( ~ ( in @ SY2891 @ SV38 )
| ! [SY2892: $i] :
( ~ ( in @ SY2892 @ SV284 )
| ~ ( in @ ( kpair @ SY2891 @ SY2892 ) @ SV484 )
| ( ( ap @ SV38 @ SV284 @ SV484 @ SY2891 )
= SY2892 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1303]) ).
thf(1554,plain,
! [SV285: $o,SV39: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ SV39 ) )
= $true )
| ( ( ! [SY2893: $i] :
( ~ ( in @ SY2893 @ SV39 )
| ~ SV285
| ( in @ SV485
@ ( dsetconstr @ SV39
@ ^ [SY2894: $i] :
( ~ ( ~ SV285
| ( SY2894 != SV485 ) )
| ~ ( ~ ~ SV285
| ( SY2894 != SY2893 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1304]) ).
thf(1555,plain,
! [SV39: $i,SV486: $i] :
( ( ( ~ ( in @ SV486 @ SV39 ) )
= $true )
| ( ( ! [SY2895: $i] :
( ~ ( in @ SY2895 @ SV39 )
| ~ $true
| ( in @ SV486
@ ( dsetconstr @ SV39
@ ^ [SY2896: $i] :
( ~ ( ~ $true
| ( SY2896 != SV486 ) )
| ~ ( ~ ~ $true
| ( SY2896 != SY2895 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1305]) ).
thf(1556,plain,
! [SV39: $i,SV487: $i] :
( ( ( ~ ( in @ SV487 @ SV39 ) )
= $true )
| ( ( ! [SY2897: $i] :
( ~ ( in @ SY2897 @ SV39 )
| ~ $false
| ( in @ SV487
@ ( dsetconstr @ SV39
@ ^ [SY2898: $i] :
( ~ ( ~ $false
| ( SY2898 != SV487 ) )
| ~ ( ~ ~ $false
| ( SY2898 != SY2897 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1306]) ).
thf(1557,plain,
! [SV286: $i,SV40: $i] :
( ( ( SV40 = SV286 )
= $false )
| ( ( ! [SY2535: $i > $o,SY2536: $i > $o] :
( ~ ! [SY2537: $i] :
( ~ ( in @ SY2537 @ SV40 )
| ! [SY2538: $i] :
( ~ ( in @ SY2538 @ SV286 )
| ( SY2537 != SY2538 )
| ~ ( ~ ( ~ ( SY2535 @ SY2537 )
| ( SY2536 @ SY2538 ) )
| ~ ( ~ ( SY2536 @ SY2538 )
| ( SY2535 @ SY2537 ) ) ) ) )
| ( ( dsetconstr @ SV40
@ ^ [SX4: $i] : ( SY2535 @ SX4 ) )
= ( dsetconstr @ SV286
@ ^ [SX4: $i] : ( SY2536 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1558,plain,
! [SV287: $i > $o,SV41: $i] :
( ( ( ~ ~ ! [SY2541: $i] :
~ ~ ( ~ ( in @ SY2541 @ SV41 )
| ~ ( SV287 @ SY2541 ) ) )
= $false )
| ( ( ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV41 )
| ~ ( SV287 @ SY2542 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1559,plain,
! [SV288: $i,SV43: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV43 ) )
= $true )
| ( ( ~ ( in @ SV488 @ ( setminus @ SV43 @ SV288 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1312]) ).
thf(1560,plain,
! [SV44: $i > $o] :
( ( ( ! [SY1927: $i] :
~ ! [SY1928: $i] :
~ ( ~ ( ~ ( SV44 @ SY1928 )
| ( SY1928 = SY1927 ) )
| ~ ( ( SY1928 != SY1927 )
| ( SV44 @ SY1928 ) ) ) )
= $true )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1313]) ).
thf(1561,plain,
! [SV289: $i,SV45: $i,SV489: $i] :
( ( ( ~ ( in @ SV489 @ ( setminus @ SV45 @ SV289 ) ) )
= $true )
| ( ( ~ ( in @ SV489 @ SV289 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1314]) ).
thf(1562,plain,
! [SV290: $i,SV46: $i,SV490: $i] :
( ( ( ~ ( in @ SV490 @ SV46 ) )
= $true )
| ( ( ! [SY2899: $i] :
( ~ ( in @ SY2899 @ SV290 )
| ( in @ ( kpair @ SV490 @ SY2899 ) @ ( cartprod @ SV46 @ SV290 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1315]) ).
thf(1563,plain,
! [SV291: $i,SV47: $i,SV491: $i] :
( ( ~ ( ~ ( in @ SV491 @ ( setadjoin @ SV47 @ SV291 ) )
| ( SV491 = SV47 )
| ( in @ SV491 @ SV291 ) )
| ~ ( ~ ( ( SV491 = SV47 )
| ( in @ SV491 @ SV291 ) )
| ( in @ SV491 @ ( setadjoin @ SV47 @ SV291 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1316]) ).
thf(1564,plain,
! [SV49: $i,SV292: $i] :
( ( ( in @ SV292 @ ( powerset @ SV49 ) )
= $false )
| ( ( in @ ( setminus @ SV49 @ SV292 ) @ ( powerset @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1565,plain,
! [SV293: $i,SV50: $i,SV492: $i] :
( ( ( ~ ( in @ SV492 @ ( setminus @ SV50 @ SV293 ) ) )
= $true )
| ( ( in @ SV492 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1321]) ).
thf(1566,plain,
! [SV493: $i,SV294: $i,SV51: $i] :
( ( ( ~ ( func @ SV51 @ SV294 @ SV493 ) )
= $true )
| ( ( ! [SY2900: $i] :
( ~ ( in @ SY2900 @ SV51 )
| ( singleton
@ ( dsetconstr @ SV294
@ ^ [SY2901: $i] : ( in @ ( kpair @ SY2900 @ SY2901 ) @ SV493 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1567,plain,
! [SV52: $i,SV295: $i] :
( ( ( in @ SV295 @ ( powerset @ SV52 ) )
= $false )
| ( ( subset @ SV295 @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1568,plain,
! [SV296: $i,SV55: $i,SV494: $i] :
( ( ( ~ ( in @ SV494 @ SV55 ) )
= $true )
| ( ( ! [SY2902: $i] :
( ~ ( in @ SY2902 @ SV296 )
| ( ( kpair @ SV494 @ SY2902 )
= ( kpair @ SV494 @ SY2902 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1326]) ).
thf(1569,plain,
! [SV297: $i,SV56: $i,SV495: $i] :
( ( ( ~ ( in @ SV495 @ SV56 ) )
= $true )
| ( ( ! [SY2903: $i] :
( ~ ( in @ SY2903 @ SV297 )
| ( ( ksnd @ ( kpair @ SV495 @ SY2903 ) )
= SY2903 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1327]) ).
thf(1570,plain,
! [SV496: $i,SV298: $i,SV57: $i] :
( ( ( ~ ( func @ SV57 @ SV298 @ SV496 ) )
= $true )
| ( ( ! [SY2904: $i] :
( ~ ( in @ SY2904 @ SV57 )
| ( in @ ( kpair @ SY2904 @ ( ap @ SV57 @ SV298 @ SV496 @ SY2904 ) ) @ SV496 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1328]) ).
thf(1571,plain,
! [SV299: $i,SV58: $i,SV497: $i] :
( ( ( ~ ( in @ SV497 @ ( cartprod @ SV58 @ SV299 ) ) )
= $true )
| ( ( in @ ( kfst @ SV497 ) @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1329]) ).
thf(1572,plain,
! [SV498: $i,SV300: $i,SV59: $i] :
( ( ( ( setadjoin @ SV59 @ ( setadjoin @ SV300 @ emptyset ) )
!= ( setadjoin @ SV498 @ emptyset ) )
= $true )
| ( ( SV59 = SV300 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1330]) ).
thf(1573,plain,
! [SV301: $o,SV60: $i,SV499: $i] :
( ( ( ~ ( in @ SV499 @ SV60 ) )
= $true )
| ( ( ! [SY2905: $i] :
( ~ ( in @ SY2905 @ SV60 )
| ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY2906: $i] :
( ~ ( ~ SV301
| ( SY2906 != SV499 ) )
| ~ ( ~ ~ SV301
| ( SY2906 != SY2905 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1574,plain,
! [SV60: $i,SV500: $i] :
( ( ( ~ ( in @ SV500 @ SV60 ) )
= $true )
| ( ( ! [SY2907: $i] :
( ~ ( in @ SY2907 @ SV60 )
| ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY2908: $i] :
( ~ ( ~ $true
| ( SY2908 != SV500 ) )
| ~ ( ~ ~ $true
| ( SY2908 != SY2907 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1575,plain,
! [SV60: $i,SV501: $i] :
( ( ( ~ ( in @ SV501 @ SV60 ) )
= $true )
| ( ( ! [SY2909: $i] :
( ~ ( in @ SY2909 @ SV60 )
| ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY2910: $i] :
( ~ ( ~ $false
| ( SY2910 != SV501 ) )
| ~ ( ~ ~ $false
| ( SY2910 != SY2909 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1576,plain,
! [SV302: $i,SV61: $i,SV502: $i] :
( ( ( ~ ( in @ SV502 @ ( funcSet @ SV61 @ SV302 ) ) )
= $true )
| ( ( func @ SV61 @ SV302 @ SV502 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1577,plain,
! [SV303: $i,SV62: $i,SV503: $i] :
( ( ( ~ ( in @ SV503 @ SV62 ) )
= $true )
| ( ( ~ ( in @ SV503 @ SV303 )
| ( in @ SV503 @ ( binintersect @ SV62 @ SV303 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1335]) ).
thf(1578,plain,
! [SV304: $i,SV63: $i,SV504: $i] :
( ( ( ~ ( subset @ SV504 @ SV63 ) )
= $true )
| ( ( ~ ( subset @ SV504 @ SV304 )
| ( subset @ SV504 @ ( binintersect @ SV63 @ SV304 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1336]) ).
thf(1579,plain,
! [SV64: $i,SV305: $i] :
( ( ( in @ SV305 @ ( powerset @ SV64 ) )
= $false )
| ( ( ! [SY2566: $i] :
( ~ ( in @ SY2566 @ ( powerset @ SV64 ) )
| ! [SY2567: $i] :
( ~ ( in @ SY2567 @ SV64 )
| ~ ( in @ SY2567 @ ( setminus @ SV64 @ SV305 ) )
| ~ ( in @ SY2567 @ ( binintersect @ SV305 @ SY2566 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1580,plain,
! [SV306: $i,SV65: $i,SV505: $i] :
( ( ( ~ ( in @ SV505 @ ( binintersect @ SV65 @ SV306 ) ) )
= $true )
| ( ( in @ SV505 @ SV306 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1338]) ).
thf(1581,plain,
! [SV66: $i,SV307: $i] :
( ( ( in @ SV307 @ ( powerset @ SV66 ) )
= $false )
| ( ( ! [SY2569: $i] :
( ~ ( in @ SY2569 @ ( powerset @ SV66 ) )
| ! [SY2570: $i] :
( ~ ( in @ SY2570 @ SV66 )
| ~ ~ ( in @ SY2570 @ ( binunion @ SV307 @ SY2569 ) )
| ~ ( in @ SY2570 @ SY2569 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1582,plain,
! [SV506: $i,SV308: $i,SV67: $i] :
( ( ( ~ ( func @ SV67 @ SV308 @ SV506 ) )
= $true )
| ( ( ! [SY2911: $i] :
( ~ ( in @ SY2911 @ SV67 )
| ( ( ap @ SV67 @ SV308 @ SV506 @ SY2911 )
= ( ap @ SV67 @ SV308 @ SV506 @ SY2911 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1583,plain,
! [SV68: $i,SV309: $i,SV507: $i] :
( ( ( ~ ( in @ SV507 @ SV309 ) )
= $true )
| ( ( ~ ( in @ SV507 @ ( setminus @ SV68 @ SV309 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1584,plain,
! [SV69: $i,SV310: $i] :
( ( ~ ( ~ ( in @ SV310 @ ( setunion @ SV69 ) )
| ~ ! [SY2574: $i] :
~ ~ ( ~ ( in @ SV310 @ SY2574 )
| ~ ( in @ SY2574 @ SV69 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1342]) ).
thf(1585,plain,
! [SV69: $i,SV310: $i] :
( ( ~ ( ~ ~ ! [SY2575: $i] :
~ ~ ( ~ ( in @ SV310 @ SY2575 )
| ~ ( in @ SY2575 @ SV69 ) )
| ( in @ SV310 @ ( setunion @ SV69 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1342]) ).
thf(1586,plain,
! [SV70: $i,SV311: $i] :
( ( ( in @ SV311 @ ( powerset @ SV70 ) )
= $false )
| ( ( ! [SY2576: $i] :
( ~ ( in @ SY2576 @ ( powerset @ SV70 ) )
| ! [SY2577: $i] :
( ~ ( in @ SY2577 @ SV70 )
| ~ ( in @ SY2577 @ ( setminus @ SV70 @ ( binunion @ SV311 @ SY2576 ) ) )
| ~ ( in @ SY2577 @ SV311 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1587,plain,
! [SV312: $i,SV71: $i] :
( ( ( ! [SY2578: $i] :
( ~ ( in @ SY2578 @ SV71 )
| ( in @ SY2578 @ SV312 ) ) )
= $false )
| ( ( subset @ SV71 @ SV312 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1344]) ).
thf(1588,plain,
! [SV313: $i > $o,SV72: $i,SV508: $i] :
( ( ( ~ ( in @ SV508
@ ( dsetconstr @ SV72
@ ^ [SY2580: $i] : ( SV313 @ SY2580 ) ) ) )
= $true )
| ( ( SV313 @ SV508 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1345]) ).
thf(1589,plain,
! [SV73: $i,SV314: $i] :
( ( ( in @ SV314 @ ( powerset @ SV73 ) )
= $false )
| ( ( ! [SY2581: $i] :
( ~ ( in @ SY2581 @ ( powerset @ SV73 ) )
| ~ ! [SY2582: $i] :
( ~ ( in @ SY2582 @ SV73 )
| ~ ( in @ SY2582 @ SV314 )
| ( in @ SY2582 @ SY2581 ) )
| ( in @ SV314 @ ( powerset @ SY2581 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1346]) ).
thf(1590,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) ) )
= $true )
| ( ( ! [SY2913: $o] :
( ~ ( ~ ( in @ SV509 @ SV74 )
| ~ ~ ( in @ SV509 @ SV315 )
| SY2913 )
| ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SY2913 )
| SY2913 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1347]) ).
thf(1591,plain,
! [SV75: $i] :
( ( ( ~ ( in @ ( sK4_SY2000 @ SV75 ) @ SV75 ) )
= $false )
| ( ( SV75 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1348]) ).
thf(1592,plain,
! [SV510: $i,SV316: $i,SV76: $i] :
( ( ( ~ ( subset @ SV76 @ SV316 ) )
= $true )
| ( ( ~ ~ ( in @ SV510 @ SV316 )
| ~ ( in @ SV510 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1349]) ).
thf(1593,plain,
! [SV511: $i > $i > $o,SV317: $i,SV77: $i,SV606: $i] :
( ( ! [SY3058: $i] :
( ~ ( in @ ( kpair @ SV606 @ SY3058 )
@ ( dpsetconstr @ SV77 @ SV317
@ ^ [SY2916: $i,SY2917: $i] : ( SV511 @ SY2916 @ SY2917 ) ) )
| ( in @ SY3058 @ SV317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1594,plain,
! [SV78: $i] :
( ( ( SV78 = emptyset )
= $true )
| ( ( ~ ! [SY2009: $i] :
~ ( in @ SY2009 @ SV78 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1351]) ).
thf(1595,plain,
! [SV318: $i > $o,SV79: $i] :
( ( ( ~ ~ ! [SY2591: $i] :
~ ~ ( ~ ( in @ SY2591 @ SV79 )
| ~ ( SV318 @ SY2591 ) ) )
= $false )
| ( ( ! [SY2592: $i] :
( ~ ( in @ SY2592 @ SV79 )
| ~ ( SV318 @ SY2592 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1352]) ).
thf(1596,plain,
! [SV319: $i,SV80: $i,SV512: $i] :
( ( ( ~ ( in @ SV512 @ SV80 ) )
= $true )
| ( ( in @ SV512 @ ( binunion @ SV80 @ SV319 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1353]) ).
thf(1597,plain,
! [SV81: $i,SV320: $i] :
( ( ( in @ SV320 @ SV81 )
= $false )
| ( ( in @ SV320 @ ( powerset @ ( setunion @ SV81 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1598,plain,
! [SV82: $i] :
( ( ( ! [SY2016: $i] :
~ ( in @ SY2016 @ SV82 ) )
= $true )
| ( ( ~ ! [SY2017: $i] :
~ ~ ( ~ ( in @ SY2017 @ SV82 )
| ~ ~ ~ ! [SY2018: $i] :
~ ~ ( ~ ( in @ SY2018 @ SY2017 )
| ~ ( in @ SY2018 @ SV82 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1355]) ).
thf(1599,plain,
! [SV321: $i,SV83: $i] :
( ( ( ( binintersect @ SV83 @ SV321 )
= SV83 )
= $false )
| ( ( subset @ SV83 @ SV321 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1356]) ).
thf(1600,plain,
! [SV607: $o,SV322: $i,SV84: $i,SV513: $i] :
( ( ~ ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
| ~ ( ~ ( in @ SV513 @ SV84 )
| SV607 )
| ~ ( ~ ( in @ SV513 @ SV322 )
| SV607 )
| SV607 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1357]) ).
thf(1601,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( ~ ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
| ~ ( ~ ( in @ SV513 @ SV84 )
| $true )
| ~ ( ~ ( in @ SV513 @ SV322 )
| $true )
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1357]) ).
thf(1602,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( ~ ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
| ~ ( ~ ( in @ SV513 @ SV84 )
| $false )
| ~ ( ~ ( in @ SV513 @ SV322 )
| $false )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1357]) ).
thf(1603,plain,
! [SV85: $i,SV323: $i] :
( ( ( in @ SV323 @ ( powerset @ SV85 ) )
= $false )
| ( ( ! [SY2596: $i] :
( ~ ( in @ SY2596 @ ( powerset @ SV85 ) )
| ! [SY2597: $i] :
( ~ ( in @ SY2597 @ SV85 )
| ~ ~ ( in @ SY2597 @ ( binunion @ SV323 @ SY2596 ) )
| ~ ( in @ SY2597 @ SV323 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1604,plain,
! [SV86: $i > $o,SV324: $i] :
( ( ( in @ SV324 @ emptyset )
= $false )
| ( ( SV86 @ SV324 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1605,plain,
! [SV325: $i > $o,SV87: $i] :
( ( ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ SV87 )
| ( SV325 @ SY2598 ) ) )
= $false )
| ( ( ~ ! [SY2599: $i] :
~ ~ ( ~ ( in @ SY2599 @ SV87 )
| ~ ~ ( SV325 @ SY2599 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1606,plain,
! [SV326: $i,SV88: $i] :
( ( ( ! [SY2600: $i] :
( ~ ( in @ SY2600 @ SV88 )
| ( in @ SY2600 @ SV326 ) ) )
= $false )
| ( ( ~ ! [SY2601: $i] :
( ~ ( in @ SY2601 @ SV326 )
| ( in @ SY2601 @ SV88 ) )
| ( SV88 = SV326 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1607,plain,
! [SV327: $i,SV89: $i] :
( ( ( SV89 = SV327 )
= $false )
| ( ( subset @ SV89 @ SV327 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1608,plain,
! [SV90: $i,SV328: $i] :
( ( ( in @ SV328 @ ( powerset @ SV90 ) )
= $false )
| ( ( in @ ( powerset @ SV328 ) @ ( powerset @ ( powerset @ SV90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1609,plain,
! [SV91: $i > $o] :
( ( ( ! [SY2035: $i] :
~ ~ ( ~ ( SV91 @ SY2035 )
| ~ ! [SY2036: $i] :
( ~ ( SV91 @ SY2036 )
| ( SY2035 = SY2036 ) ) ) )
= $true )
| ( ( ! [SY2037: $i,SY2038: $i] :
( ~ ( SV91 @ SY2037 )
| ~ ( SV91 @ SY2038 )
| ( SY2037 = SY2038 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1364]) ).
thf(1610,plain,
! [SV514: $i,SV329: $i,SV92: $i] :
( ( ( ~ ( func @ SV92 @ SV329 @ SV514 ) )
= $true )
| ( ( ! [SY2919: $i] :
( ~ ( in @ SY2919 @ SV92 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV329
@ ^ [SY2920: $i] : ( in @ ( kpair @ SY2919 @ SY2920 ) @ SV514 ) ) )
@ SV329 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1365]) ).
thf(1611,plain,
! [SV330: $i,SV93: $i] :
( ( ( SV93 = SV330 )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ SV93 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV93 @ ( setadjoin @ SV330 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV93 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1366]) ).
thf(1612,plain,
! [SV331: $i,SV94: $i,SV515: $i] :
( ( ( ~ ( in @ SV515 @ SV94 ) )
= $true )
| ( ( ~ ~ ( in @ SV515 @ SV331 )
| ~ ( subset @ SV94 @ SV331 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1613,plain,
! [SV332: $i,SV95: $i,SV516: $i] :
( ( ( ~ ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) ) )
= $true )
| ( ( ! [SY2921: $i] :
( ~ ( subset @ SY2921 @ ( cartprod @ SV95 @ SV332 ) )
| ~ ! [SY2922: $i] :
( ~ ( in @ SY2922 @ SV95 )
| ! [SY2923: $i] :
( ~ ( in @ SY2923 @ SV332 )
| ~ ( in @ ( kpair @ SY2922 @ SY2923 ) @ SV516 )
| ( in @ ( kpair @ SY2922 @ SY2923 ) @ SY2921 ) ) )
| ( subset @ SV516 @ SY2921 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1614,plain,
! [SV96: $i,SV333: $i] :
( ( ( in @ SV333 @ ( setunion @ SV96 ) )
= $false )
| ( ( ~ ! [SY2610: $i] :
~ ~ ( ~ ( in @ SY2610 @ SV96 )
| ~ ( in @ SV333 @ SY2610 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1615,plain,
! [SV97: $i,SV334: $i] :
( ( ( in @ SV334 @ ( powerset @ SV97 ) )
= $false )
| ( ( ! [SY2611: $i] :
( ~ ( in @ SY2611 @ SV97 )
| ~ ~ ( in @ SY2611 @ ( setminus @ SV97 @ SV334 ) )
| ( in @ SY2611 @ SV334 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1370]) ).
thf(1616,plain,
! [SV335: $i > $o,SV98: $i,SV517: $i] :
( ( ( ~ ( in @ SV517 @ SV98 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV517
@ ( dsetconstr @ SV98
@ ^ [SY2613: $i] : ( SV335 @ SY2613 ) ) )
| ( SV335 @ SV517 ) )
| ~ ( ~ ( SV335 @ SV517 )
| ( in @ SV517
@ ( dsetconstr @ SV98
@ ^ [SY2614: $i] : ( SV335 @ SY2614 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1371]) ).
thf(1617,plain,
! [SV99: $i,SV336: $i] :
( ( ( ! [SY2615: $i] :
( ~ ( in @ SY2615 @ SV336 )
| ( in @ SY2615 @ SV99 ) ) )
= $false )
| ( ( in @ SV336 @ ( powerset @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1618,plain,
! [SV337: $i > $o,SV100: $i,SV518: $i] :
( ( ( ~ ( in @ SV518 @ SV100 ) )
= $true )
| ( ( ~ ( SV337 @ SV518 )
| ~ ! [SY2926: $i] :
( ~ ( in @ SY2926 @ SV100 )
| ~ ( SV337 @ SY2926 )
| ( SY2926 = SV518 ) )
| ( singleton
@ ( dsetconstr @ SV100
@ ^ [SY2618: $i] : ( SV337 @ SY2618 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1619,plain,
! [SV519: $i > $i > $o,SV338: $i,SV101: $i,SV608: $i] :
( ( ! [SY3061: $i] :
( ~ ( in @ ( kpair @ SV608 @ SY3061 )
@ ( dpsetconstr @ SV101 @ SV338
@ ^ [SY2930: $i,SY2931: $i] : ( SV519 @ SY2930 @ SY2931 ) ) )
| ( SV519 @ SV608 @ SY3061 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1620,plain,
( ( ~ ( in @ sK2_SY2624 @ ( powerset @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1375]) ).
thf(1621,plain,
( ( ! [SY2932: $i] :
( ~ ( in @ SY2932 @ ( powerset @ sK1_SX0 ) )
| ! [SY2933: $o,SY2934: $i] :
( ~ ( in @ SY2934 @ sK1_SX0 )
| ~ ( in @ SY2934 @ ( binunion @ sK2_SY2624 @ SY2932 ) )
| ~ ( ~ ( in @ SY2934 @ sK2_SY2624 )
| SY2933 )
| ~ ( ~ ( in @ SY2934 @ SY2932 )
| SY2933 )
| SY2933 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1375]) ).
thf(1622,plain,
! [SV339: $i,SV102: $i] :
( ( ( in @ SV102 @ ( setadjoin @ SV339 @ emptyset ) )
= $false )
| ( ( in @ SV339 @ ( setadjoin @ SV102 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1623,plain,
! [SV340: $i,SV103: $i,SV520: $i] :
( ( ( ~ ( in @ SV520 @ ( funcSet @ SV103 @ SV340 ) ) )
= $true )
| ( ( ( lam @ SV103 @ SV340
@ ^ [SY2935: $i] : ( ap @ SV103 @ SV340 @ SV520 @ SY2935 ) )
= SV520 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1377]) ).
thf(1624,plain,
! [SV341: $i,SV104: $i,SV521: $i] :
( ( ( ~ ( in @ SV521 @ SV104 ) )
= $true )
| ( ( ! [SY2936: $i] :
( ~ ( in @ SY2936 @ SV341 )
| ( subset @ ( setadjoin @ SV521 @ ( setadjoin @ SY2936 @ emptyset ) ) @ ( binunion @ SV104 @ SV341 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1378]) ).
thf(1625,plain,
! [SV342: $i,SV105: $i,SV522: $i] :
( ( ( ~ ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) ) )
= $true )
| ( ( ! [SY2937: $i > $o] :
( ~ ! [SY2938: $i] :
( ~ ( in @ SY2938 @ SV105 )
| ! [SY2939: $i] :
( ~ ( in @ SY2939 @ SV342 )
| ~ ( in @ ( kpair @ SY2938 @ SY2939 ) @ SV522 )
| ( SY2937 @ ( kpair @ SY2938 @ SY2939 ) ) ) )
| ! [SY2940: $i] :
( ~ ( in @ SY2940 @ SV522 )
| ( SY2937 @ SY2940 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1379]) ).
thf(1626,plain,
! [SV106: $i > $o] :
( ( ( ! [SY2084: $i] :
~ ~ ( ~ ( SV106 @ SY2084 )
| ~ ! [SY2085: $i] :
( ~ ( SV106 @ SY2085 )
| ( SY2084 = SY2085 ) ) ) )
= $true )
| ( ( ! [SY2086: $i,SY2087: $i] :
( ~ ( SV106 @ SY2086 )
| ~ ( SV106 @ SY2087 )
| ( SY2086 = SY2087 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1380]) ).
thf(1627,plain,
! [SV343: $i > $o,SV107: $i,SV523: $i] :
( ( ( ~ ( in @ SV523 @ SV107 ) )
= $true )
| ( ( ~ ( SV343 @ SV523 )
| ( in @ SV523
@ ( dsetconstr @ SV107
@ ^ [SY2638: $i] : ( SV343 @ SY2638 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1628,plain,
! [SV108: $i > $o] :
( ( ( ! [SY2091: $i] :
~ ~ ( ~ ( SV108 @ SY2091 )
| ~ ! [SY2092: $i] :
( ~ ( SV108 @ SY2092 )
| ( SY2091 = SY2092 ) ) ) )
= $true )
| ( ( SV108
@ ( descr
@ ^ [SY2093: $i] : ( SV108 @ SY2093 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1382]) ).
thf(1629,plain,
! [SV524: $i > $i > $o,SV344: $i,SV109: $i,SV609: $i] :
( ( ! [SY3064: $i] :
( ~ ( in @ ( kpair @ SV609 @ SY3064 )
@ ( dpsetconstr @ SV109 @ SV344
@ ^ [SY2944: $i,SY2945: $i] : ( SV524 @ SY2944 @ SY2945 ) ) )
| ( in @ SV609 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1630,plain,
! [SV345: $i,SV110: $i] :
( ( ( subset @ SV110 @ SV345 )
= $false )
| ( ( ( binintersect @ SV110 @ SV345 )
= SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1631,plain,
! [SV111: $i] :
( ( ( ~ ( in @ ( sK5_SY2101 @ SV111 ) @ SV111 ) )
= $false )
| ( ( SV111 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1385]) ).
thf(1632,plain,
! [SV112: $i,SV346: $i] :
( ( ( subset @ SV346 @ SV112 )
= $false )
| ( ( ( binintersect @ SV112 @ SV346 )
= SV346 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1633,plain,
! [SV347: $i,SV113: $i,SV525: $i] :
( ( ( ~ ~ ( in @ SV525 @ ( setminus @ SV113 @ SV347 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV525 @ SV347 )
| ~ ( in @ SV525 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1634,plain,
! [SV114: $i > $o] :
( ( ( ! [SY2105: $i] :
~ ~ ( ~ ( SV114 @ SY2105 )
| ~ ! [SY2106: $i] :
( ~ ( SV114 @ SY2106 )
| ( SY2105 = SY2106 ) ) ) )
= $true )
| ( ( ~ ! [SY2107: $i] :
~ ( SV114 @ SY2107 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1388]) ).
thf(1635,plain,
! [SV115: $i,SV348: $i] :
( ( ( in @ SV348 @ ( powerset @ SV115 ) )
= $false )
| ( ( ! [SY2645: $i] :
( ~ ( in @ SY2645 @ ( powerset @ SV115 ) )
| ! [SY2646: $i] :
( ~ ( in @ SY2646 @ ( powerset @ SV115 ) )
| ! [SY2647: $i] :
( ~ ( in @ SY2647 @ SV115 )
| ~ ( in @ SY2647 @ ( binintersect @ SV348 @ SY2645 ) )
| ( in @ SY2647 @ ( binunion @ SV348 @ SY2646 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1636,plain,
! [SV117: $i,SV349: $i] :
( ( ( in @ SV349 @ ( powerset @ SV117 ) )
= $false )
| ( ( ! [SY2648: $i] :
( ~ ( in @ SY2648 @ ( powerset @ SV117 ) )
| ( in @ ( binintersect @ SV349 @ SY2648 ) @ ( powerset @ SV117 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1391]) ).
thf(1637,plain,
! [SV350: $i > $o,SV118: $i] :
( ( ( ! [SY2649: $i] :
( ~ ( in @ SY2649 @ SV118 )
| ~ ( SV350 @ SY2649 ) ) )
= $false )
| ( ( ~ ~ ! [SY2650: $i] :
~ ~ ( ~ ( in @ SY2650 @ SV118 )
| ~ ( SV350 @ SY2650 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1638,plain,
! [SV351: $i > $o,SV119: $i] :
( ( ( ~ ! [SY2651: $i] :
( ~ ( in @ SY2651 @ SV119 )
| ( SV351 @ SY2651 ) ) )
= $false )
| ( ( ~ ! [SY2652: $i] :
~ ~ ( ~ ( in @ SY2652 @ SV119 )
| ~ ~ ( SV351 @ SY2652 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1639,plain,
! [SV120: $i,SV352: $i] :
( ( ( in @ SV352 @ ( powerset @ SV120 ) )
= $false )
| ( ( ! [SY2653: $i] :
( ~ ( in @ SY2653 @ ( powerset @ SV120 ) )
| ! [SY2654: $i] :
( ~ ( in @ SY2654 @ SV120 )
| ~ ~ ( in @ SY2654 @ SY2653 )
| ~ ( in @ SY2654 @ ( binintersect @ SV352 @ SY2653 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1640,plain,
! [SV121: $i,SV353: $i] :
( ( ( in @ SV353 @ ( powerset @ SV121 ) )
= $false )
| ( ( ! [SY2655: $i] :
( ~ ( in @ SY2655 @ ( powerset @ SV121 ) )
| ~ ( subset @ SV353 @ ( setminus @ SV121 @ SY2655 ) )
| ! [SY2656: $i] :
( ~ ( in @ SY2656 @ SV121 )
| ~ ( in @ SY2656 @ SY2655 )
| ( in @ SY2656 @ ( setminus @ SV121 @ SV353 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1395]) ).
thf(1641,plain,
! [SV354: $i,SV122: $i] :
( ( ( ~ ( subset @ SV122 @ SV354 ) )
= $false )
| ( ( SV122 != SV354 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1642,plain,
! [SV355: $i,SV526: $i > $i,SV123: $i] :
( ( ( ~ ! [SY2946: $i] :
( ~ ( in @ SY2946 @ SV123 )
| ( in @ ( SV526 @ SY2946 ) @ SV355 ) ) )
= $true )
| ( ( in
@ ( lam @ SV123 @ SV355
@ ^ [SY2947: $i] : ( SV526 @ SY2947 ) )
@ ( funcSet @ SV123 @ SV355 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1643,plain,
! [SV124: $i,SV527: $i,SV356: $i] :
( ( ( ~ ( in @ SV356 @ SV527 ) )
= $true )
| ( ( ~ ( in @ SV527 @ SV124 )
| ( in @ SV356 @ ( setunion @ SV124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1398]) ).
thf(1644,plain,
! [SV357: $i,SV125: $i,SV528: $i] :
( ( ( ~ ( in @ ( setadjoin @ SV528 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV125 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV125 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( SV125 = SV528 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1399]) ).
thf(1645,plain,
! [SV358: $i,SV126: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) ) )
= $true )
| ( ( ! [SY2948: $o] :
( ~ ( ( SV529 != SV126 )
| SY2948 )
| ~ ( ~ ( in @ SV529 @ SV358 )
| SY2948 )
| SY2948 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1400]) ).
thf(1646,plain,
! [SV359: $i,SV127: $i,SV530: $i] :
( ( ( ~ ~ ( in @ SV530 @ SV127 ) )
= $true )
| ( ( ~ ~ ( in @ SV530 @ SV359 )
| ~ ( in @ SV530 @ ( symdiff @ SV127 @ SV359 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1401]) ).
thf(1647,plain,
! [SV360: $i,SV128: $i,SV531: $i] :
( ( ( ~ ( in @ SV531 @ SV128 ) )
= $true )
| ( ( ! [SY2949: $i] :
( ~ ( in @ SY2949 @ SV360 )
| ( in @ ( setadjoin @ SV531 @ ( setadjoin @ SY2949 @ emptyset ) ) @ ( powerset @ ( binunion @ SV128 @ SV360 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1402]) ).
thf(1648,plain,
! [SV129: $i,SV361: $i] :
( ( ( in @ SV361 @ ( powerset @ SV129 ) )
= $false )
| ( ( ! [SY2667: $i] :
( ~ ( in @ SY2667 @ ( powerset @ SV129 ) )
| ~ ( subset @ SV361 @ ( setminus @ SV129 @ SY2667 ) )
| ( subset @ SY2667 @ ( setminus @ SV129 @ SV361 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1649,plain,
! [SV130: $i,SV362: $i] :
( ( ( in @ SV362 @ ( powerset @ SV130 ) )
= $false )
| ( ( ! [SY2668: $i] :
( ~ ( in @ SY2668 @ ( powerset @ SV130 ) )
| ! [SY2669: $i] :
( ~ ( in @ SY2669 @ SV130 )
| ~ ~ ( in @ SY2669 @ SV362 )
| ~ ( in @ SY2669 @ ( binintersect @ SV362 @ SY2668 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1650,plain,
! [SV131: $i,SV363: $i] :
( ( ( in @ SV363 @ ( powerset @ SV131 ) )
= $false )
| ( ( ! [SY2670: $i] :
( ~ ( in @ SY2670 @ ( powerset @ SV131 ) )
| ! [SY2671: $i] :
( ~ ( in @ SY2671 @ SV131 )
| ~ ( in @ SY2671 @ ( setminus @ SV131 @ SV363 ) )
| ( in @ SY2671 @ ( setminus @ SV131 @ ( binintersect @ SV363 @ SY2670 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1651,plain,
! [SV364: $i,SV132: $i,SV532: $i] :
( ( ( ~ ( in @ SV532 @ ( cartprod @ SV132 @ SV364 ) ) )
= $true )
| ( ( in @ ( ksnd @ SV532 ) @ SV364 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1652,plain,
! [SV133: $i,SV365: $i] :
( ( ( in @ SV365 @ ( powerset @ SV133 ) )
= $false )
| ( ( ! [SY2673: $i] :
( ~ ( in @ SY2673 @ SV133 )
| ~ ( in @ SY2673 @ SV365 )
| ( in @ SY2673 @ ( setminus @ SV133 @ ( setminus @ SV133 @ SV365 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1407]) ).
thf(1653,plain,
! [SV533: $i,SV366: $i,SV134: $i] :
( ( ( ~ ( func @ SV134 @ SV366 @ SV533 ) )
= $true )
| ( ( ( lam @ SV134 @ SV366
@ ^ [SY2950: $i] : ( ap @ SV134 @ SV366 @ SV533 @ SY2950 ) )
= SV533 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1408]) ).
thf(1654,plain,
! [SV367: $i > $o,SV135: $i] :
( ( ( singleton
@ ( dsetconstr @ SV135
@ ^ [SY2676: $i] : ( SV367 @ SY2676 ) ) )
= $false )
| ( ( ! [SY2677: $i] :
( ~ ( in @ SY2677 @ SV135 )
| ! [SY2678: $i] :
( ~ ( in @ SY2678 @ SV135 )
| ~ ( SV367 @ SY2677 )
| ~ ( SV367 @ SY2678 )
| ( SY2677 = SY2678 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1409]) ).
thf(1655,plain,
! [SV136: $i,SV368: $i] :
( ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false )
| ( ( ! [SY2679: $o] :
( ~ ! [SY2680: $i] :
( ~ ( in @ SV368 @ SY2680 )
| ~ ( in @ SY2680 @ SV136 )
| SY2679 )
| SY2679 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1656,plain,
! [SV137: $i,SV369: $i] :
( ( ( in @ SV369 @ ( powerset @ SV137 ) )
= $false )
| ( ( ! [SY2681: $i] :
( ~ ( in @ SY2681 @ ( powerset @ SV137 ) )
| ! [SY2682: $i] :
( ~ ( in @ SY2682 @ SV137 )
| ~ ( subset @ SV369 @ SY2681 )
| ~ ~ ( in @ SY2682 @ SY2681 )
| ~ ( in @ SY2682 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1411]) ).
thf(1657,plain,
! [SV370: $i,SV138: $i,SV534: $i] :
( ( ( ~ ( in @ SV534 @ ( setadjoin @ SV138 @ ( setadjoin @ SV370 @ emptyset ) ) ) )
= $true )
| ( ( ( SV534 = SV138 )
| ( SV534 = SV370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1412]) ).
thf(1658,plain,
! [SV371: $i,SV140: $i,SV535: $i] :
( ( ( ~ ( in @ SV535 @ ( cartprod @ SV140 @ SV371 ) ) )
= $true )
| ( ( iskpair @ SV535 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1414]) ).
thf(1659,plain,
! [SV141: $i,SV372: $i,SV536: $i] :
( ( ( ~ ( in @ SV536 @ SV372 ) )
= $true )
| ( ( in @ SV536 @ ( setadjoin @ SV141 @ SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1415]) ).
thf(1660,plain,
! [SV373: $i,SV142: $i,SV610: $i,SV537: $i] :
( ( ~ ( in @ ( kpair @ SV537 @ SV610 ) @ ( cartprod @ SV142 @ SV373 ) )
| ( in @ SV610 @ SV373 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(1661,plain,
! [SV374: $i,SV143: $i,SV538: $i] :
( ( ( ~ ( in @ SV538 @ ( funcSet @ SV143 @ SV374 ) ) )
= $true )
| ( ( ! [SY2952: $i] :
( ~ ( in @ SY2952 @ SV143 )
| ( in @ ( kpair @ SY2952 @ ( ap @ SV143 @ SV374 @ SV538 @ SY2952 ) ) @ SV538 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1417]) ).
thf(1662,plain,
! [SV375: $i,SV144: $i] :
( ( ( subset @ SV144 @ SV375 )
= $false )
| ( ( subset @ ( powerset @ SV144 ) @ ( powerset @ SV375 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1418]) ).
thf(1663,plain,
! [SV376: $i,SV145: $i,SV539: $i] :
( ( ( ~ ( in @ SV539 @ ( cartprod @ SV145 @ SV376 ) ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV539 ) @ ( ksnd @ SV539 ) )
= SV539 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1419]) ).
thf(1664,plain,
! [SV146: $i,SV377: $i] :
( ( ( in @ SV377 @ ( powerset @ SV146 ) )
= $false )
| ( ( ! [SY2691: $i] :
( ~ ( in @ SY2691 @ ( powerset @ SV146 ) )
| ~ ! [SY2692: $i] :
( ~ ( in @ SY2692 @ SV146 )
| ~ ( in @ SY2692 @ SV377 )
| ( in @ SY2692 @ SY2691 ) )
| ( subset @ SV377 @ SY2691 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1420]) ).
thf(1665,plain,
! [SV147: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY2953: $i] :
( ~ ( in @ SY2953 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY2188: $i] :
( ~ ( in @ SY2188 @ SY2953 )
| ( in @ SY2188 @ SV147 ) ) )
| ~ ! [SY2955: $i,SY2956: $i] :
( ~ ~ ( ~ ( in @ SY2955 @ SV147 )
| ~ ( in @ SY2956 @ SV147 ) )
| ~ ! [SY2957: $i] :
( ~ ( in @ SY2957 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SY2955 @ SY2957 )
| ( in @ SY2956 @ SY2957 ) )
| ~ ( ~ ( in @ SY2956 @ SY2957 )
| ( in @ SY2955 @ SY2957 ) ) ) )
| ( SY2955 = SY2956 ) ) )
| ~ ! [SY2958: $i,SY2959: $i] :
( ~ ~ ( ~ ( in @ SY2958 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY2959 @ ( sK3_SY2186 @ SV147 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2958 )
| ( in @ SX4 @ SY2959 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2959 )
| ( in @ SX4 @ SY2958 ) ) ) )
| ~ ! [SY2962: $i] :
( ~ ~ ( ~ ! [SY2197: $i] :
( ~ ( in @ SY2197 @ SY2962 )
| ( in @ SY2197 @ SV147 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY2962 ) )
| ~ ! [SY2965: $i] :
~ ~ ! [SY2966: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY2965 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY2966 @ SY2962 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY2965 )
| ~ ( in @ SX5 @ SY2962 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY2965 ) )
| ( in @ SY2966 @ SY2968 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1421]) ).
thf(1666,plain,
! [SV540: $i,SV378: $i,SV148: $i] :
( ( ( ~ ( subset @ SV148 @ SV378 ) )
= $true )
| ( ( ~ ( in @ SV540 @ SV148 )
| ( in @ SV540 @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1422]) ).
thf(1667,plain,
! [SV149: $i,SV379: $i] :
( ( ( subset @ SV379 @ SV149 )
= $false )
| ( ( in @ SV379 @ ( powerset @ SV149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1668,plain,
! [SV150: $i,SV380: $i,SV541: $i] :
( ( ( ~ ( in @ SV541 @ SV380 ) )
= $true )
| ( ( in @ SV541 @ ( binunion @ SV150 @ SV380 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1669,plain,
! [SV151: $i,SV381: $i] :
( ( ( in @ SV381 @ ( powerset @ SV151 ) )
= $false )
| ( ( ! [SY2695: $i] :
( ~ ( in @ SY2695 @ ( powerset @ SV151 ) )
| ! [SY2696: $i] :
( ~ ( in @ SY2696 @ ( powerset @ SV151 ) )
| ! [SY2697: $i] :
( ~ ( in @ SY2697 @ SV151 )
| ~ ( in @ SY2697 @ ( binintersect @ SV381 @ SY2695 ) )
| ( in @ SY2697 @ ( binunion @ SY2695 @ SY2696 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1670,plain,
! [SV382: $i,SV152: $i] :
( ( ( SV152 = SV382 )
= $false )
| ( ( ( setunion @ SV152 )
= ( setunion @ SV382 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1671,plain,
! [SV383: $i,SV153: $i,SV611: $i,SV542: $i] :
( ( ~ ( in @ ( kpair @ SV542 @ SV611 ) @ ( cartprod @ SV153 @ SV383 ) )
| ( in @ SV542 @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1672,plain,
! [SV384: $i,SV154: $i,SV543: $i] :
( ( ( ~ ( in @ SV543 @ ( binunion @ SV154 @ SV384 ) ) )
= $true )
| ( ( ( in @ SV543 @ SV154 )
| ( in @ SV543 @ SV384 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1428]) ).
thf(1673,plain,
! [SV385: $i,SV155: $i] :
( ( ( ! [SY2701: $i] :
( ~ ( in @ SY2701 @ SV155 )
| ( in @ SY2701 @ SV385 ) ) )
= $false )
| ( ( subset @ SV155 @ SV385 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1674,plain,
! [SV156: $i,SV386: $i] :
( ( ( in @ SV386 @ ( powerset @ SV156 ) )
= $false )
| ( ( ! [SY2702: $i] :
( ~ ( in @ SY2702 @ ( powerset @ SV156 ) )
| ! [SY2703: $i] :
( ~ ( in @ SY2703 @ SV156 )
| ~ ( subset @ SV386 @ ( setminus @ SV156 @ SY2702 ) )
| ~ ( in @ SY2703 @ SY2702 )
| ~ ( in @ SY2703 @ SV386 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1430]) ).
thf(1675,plain,
! [SV387: $i > $o,SV157: $i,SV544: $i] :
( ( ( ~ ( in @ SV544
@ ( dsetconstr @ SV157
@ ^ [SY2705: $i] : ( SV387 @ SY2705 ) ) ) )
= $true )
| ( ( in @ SV544 @ SV157 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1431]) ).
thf(1676,plain,
! [SV388: $i,SV158: $i,SV545: $i] :
( ( ( ~ ~ ( in @ SV545 @ ( setminus @ SV158 @ SV388 ) ) )
= $true )
| ( ( ~ ( in @ SV545 @ SV158 )
| ( in @ SV545 @ SV388 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1432]) ).
thf(1677,plain,
! [SV159: $i,SV389: $i] :
( ( ( in @ SV389 @ ( powerset @ SV159 ) )
= $false )
| ( ( SV389
= ( setminus @ SV159 @ ( setminus @ SV159 @ SV389 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1678,plain,
! [SV160: $i > $o] :
( ( ( ! [SY2230: $i] :
~ ( SV160 @ SY2230 ) )
= $true )
| ( ( ~ ! [SY2231: $i,SY2232: $i] :
( ~ ( SV160 @ SY2231 )
| ~ ( SV160 @ SY2232 )
| ( SY2231 = SY2232 ) )
| ~ ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1434]) ).
thf(1679,plain,
! [SV161: $i,SV390: $i] :
( ( ( in @ SV390 @ ( powerset @ SV161 ) )
= $false )
| ( ( ! [SY2707: $i] :
( ~ ( in @ SY2707 @ ( powerset @ SV161 ) )
| ( in @ ( setminus @ SV161 @ SV390 ) @ ( powerset @ ( setminus @ SV161 @ ( binintersect @ SV390 @ SY2707 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1435]) ).
thf(1680,plain,
! [SV162: $i,SV391: $i] :
( ( ( in @ SV391 @ ( powerset @ SV162 ) )
= $false )
| ( ( ! [SY2708: $i] :
( ~ ( in @ SY2708 @ ( powerset @ SV162 ) )
| ( in @ ( setminus @ SV391 @ SY2708 ) @ ( powerset @ SV162 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1681,plain,
! [SV392: $i,SV164: $i,SV546: $i] :
( ( ( ~ ( in @ SV546 @ SV164 ) )
= $true )
| ( ( ~ ~ ( in @ SV546 @ SV392 )
| ( in @ SV546 @ ( symdiff @ SV164 @ SV392 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1438]) ).
thf(1682,plain,
! [SV393: $i,SV165: $i] :
( ( ( SV165 = SV393 )
= $false )
| ( ( ! [SY2710: $i,SY2711: $i] :
( ( SY2710 != SY2711 )
| ~ ( in @ SY2710 @ SV165 )
| ( in @ SY2711 @ SV393 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1439]) ).
thf(1683,plain,
! [SV394: $i,SV166: $i,SV547: $i] :
( ( ( ~ ( in @ SV547 @ SV166 ) )
= $true )
| ( ( ~ ~ ( in @ SV547 @ SV394 )
| ( SV166 != SV394 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1440]) ).
thf(1684,plain,
! [SV167: $i,SV395: $i] :
( ( ( in @ SV395 @ ( powerset @ SV167 ) )
= $false )
| ( ( ! [SY2713: $i] :
( ~ ( in @ SY2713 @ ( powerset @ SV167 ) )
| ! [SY2714: $i] :
( ~ ( in @ SY2714 @ SV167 )
| ~ ( in @ SY2714 @ ( setminus @ SV167 @ ( binunion @ SV395 @ SY2713 ) ) )
| ( in @ SY2714 @ ( setminus @ SV167 @ SV395 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1685,plain,
! [SV548: $i,SV396: $i,SV168: $i] :
( ( ( ~ ( func @ SV168 @ SV396 @ SV548 ) )
= $true )
| ( ( ! [SY2972: $i] :
( ~ ( func @ SV168 @ SV396 @ SY2972 )
| ~ ! [SY2973: $i] :
( ~ ( in @ SY2973 @ SV168 )
| ( ( ap @ SV168 @ SV396 @ SV548 @ SY2973 )
= ( ap @ SV168 @ SV396 @ SY2972 @ SY2973 ) ) )
| ( SV548 = SY2972 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1442]) ).
thf(1686,plain,
! [SV397: $o,SV169: $i,SV549: $i] :
( ( ( ~ ( in @ SV549 @ SV169 ) )
= $true )
| ( ( ! [SY2974: $i] :
( ~ ( in @ SY2974 @ SV169 )
| ( in @ ( if @ SV169 @ SV397 @ SV549 @ SY2974 ) @ ( setadjoin @ SV549 @ ( setadjoin @ SY2974 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1443]) ).
thf(1687,plain,
! [SV169: $i,SV550: $i] :
( ( ( ~ ( in @ SV550 @ SV169 ) )
= $true )
| ( ( ! [SY2975: $i] :
( ~ ( in @ SY2975 @ SV169 )
| ( in @ ( if @ SV169 @ $true @ SV550 @ SY2975 ) @ ( setadjoin @ SV550 @ ( setadjoin @ SY2975 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1444]) ).
thf(1688,plain,
! [SV169: $i,SV551: $i] :
( ( ( ~ ( in @ SV551 @ SV169 ) )
= $true )
| ( ( ! [SY2976: $i] :
( ~ ( in @ SY2976 @ SV169 )
| ( in @ ( if @ SV169 @ $false @ SV551 @ SY2976 ) @ ( setadjoin @ SV551 @ ( setadjoin @ SY2976 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1445]) ).
thf(1689,plain,
! [SV398: $i,SV552: $i > $i,SV170: $i] :
( ( ( ~ ! [SY2977: $i] :
( ~ ( in @ SY2977 @ SV170 )
| ( in @ ( SV552 @ SY2977 ) @ SV398 ) ) )
= $true )
| ( ( ( lam @ SV170 @ SV398
@ ^ [SY2978: $i] : ( SV552 @ SY2978 ) )
= ( lam @ SV170 @ SV398
@ ^ [SY2979: $i] : ( SV552 @ SY2979 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1446]) ).
thf(1690,plain,
! [SV399: $o,SV171: $i,SV553: $i] :
( ( ( ~ ( in @ SV553 @ SV171 ) )
= $true )
| ( ( ! [SY2980: $i] :
( ~ ( in @ SY2980 @ SV171 )
| ~ ~ SV399
| ( ( dsetconstr @ SV171
@ ^ [SY2981: $i] :
( ~ ( ~ SV399
| ( SY2981 != SV553 ) )
| ~ ( ~ ~ SV399
| ( SY2981 != SY2980 ) ) ) )
= ( setadjoin @ SY2980 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1447]) ).
thf(1691,plain,
! [SV171: $i,SV554: $i] :
( ( ( ~ ( in @ SV554 @ SV171 ) )
= $true )
| ( ( ! [SY2982: $i] :
( ~ ( in @ SY2982 @ SV171 )
| ~ ~ $true
| ( ( dsetconstr @ SV171
@ ^ [SY2983: $i] :
( ~ ( ~ $true
| ( SY2983 != SV554 ) )
| ~ ( ~ ~ $true
| ( SY2983 != SY2982 ) ) ) )
= ( setadjoin @ SY2982 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1448]) ).
thf(1692,plain,
! [SV171: $i,SV555: $i] :
( ( ( ~ ( in @ SV555 @ SV171 ) )
= $true )
| ( ( ! [SY2984: $i] :
( ~ ( in @ SY2984 @ SV171 )
| ~ ~ $false
| ( ( dsetconstr @ SV171
@ ^ [SY2985: $i] :
( ~ ( ~ $false
| ( SY2985 != SV555 ) )
| ~ ( ~ ~ $false
| ( SY2985 != SY2984 ) ) ) )
= ( setadjoin @ SY2984 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1693,plain,
! [SV172: $i,SV400: $i] :
( ( ~ ( ~ ( in @ SV400 @ ( powerset @ SV172 ) )
| ! [SY2727: $i] :
( ~ ( in @ SY2727 @ SV400 )
| ( in @ SY2727 @ SV172 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1694,plain,
! [SV172: $i,SV400: $i] :
( ( ~ ( ~ ! [SY2728: $i] :
( ~ ( in @ SY2728 @ SV400 )
| ( in @ SY2728 @ SV172 ) )
| ( in @ SV400 @ ( powerset @ SV172 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1695,plain,
! [SV612: $i,SV556: $i,SV401: $i,SV173: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV173 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV173 @ ( setadjoin @ SV401 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV556 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV556 @ ( setadjoin @ SV612 @ emptyset ) ) @ emptyset ) ) )
| ( SV401 = SV612 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1696,plain,
! [SV402: $i,SV174: $i,SV557: $i] :
( ( ( ~ ( in @ SV557 @ SV174 ) )
= $true )
| ( ( ! [SY2987: $i] :
( ~ ( in @ SY2987 @ SV402 )
| ( ( kfst @ ( kpair @ SV557 @ SY2987 ) )
= SV557 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1452]) ).
thf(1697,plain,
! [SV403: $i,SV175: $i,SV558: $i] :
( ( ( ~ ( in @ SV558 @ ( funcSet @ SV175 @ SV403 ) ) )
= $true )
| ( ( ! [SY2988: $i] :
( ~ ( in @ SY2988 @ SV175 )
| ( in @ ( ap @ SV175 @ SV403 @ SV558 @ SY2988 ) @ SV403 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1453]) ).
thf(1698,plain,
! [SV176: $i,SV404: $i] :
( ( ( in @ SV404 @ ( powerset @ SV176 ) )
= $false )
| ( ( ! [SY2735: $i] :
( ~ ( in @ SY2735 @ ( powerset @ SV176 ) )
| ~ ( subset @ SV404 @ SY2735 )
| ( subset @ ( setminus @ SV176 @ SY2735 ) @ ( setminus @ SV176 @ SV404 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1454]) ).
thf(1699,plain,
! [SV559: $i,SV405: $i,SV177: $i] :
( ( ( ~ ( subset @ SV177 @ SV405 ) )
= $true )
| ( ( ~ ( subset @ SV405 @ SV559 )
| ( subset @ SV177 @ SV559 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1455]) ).
thf(1700,plain,
! [SV406: $i,SV178: $i,SV560: $i] :
( ( ( ~ ( in @ SV560 @ ( binintersect @ SV178 @ SV406 ) ) )
= $true )
| ( ( in @ SV560 @ SV178 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1456]) ).
thf(1701,plain,
! [SV179: $i,SV407: $i] :
( ( ( in @ SV407 @ ( powerset @ SV179 ) )
= $false )
| ( ( subset @ SV407 @ ( setminus @ SV179 @ ( setminus @ SV179 @ SV407 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1457]) ).
thf(1702,plain,
! [SV408: $i > $o,SV180: $i] :
( ( ( ~ ! [SY2738: $i] :
~ ~ ( ~ ( in @ SY2738 @ SV180 )
| ~ ( SV408 @ SY2738 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV180
@ ^ [SY2739: $i] : ( SV408 @ SY2739 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1458]) ).
thf(1703,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ( ! [SY2740: $i] :
( ~ ( in @ SY2740 @ SV181 )
| ! [SY2741: $i] :
( ~ ( in @ SY2741 @ SV181 )
| ~ ( SV409 @ SY2740 )
| ~ ( SV409 @ SY2741 )
| ( SY2740 = SY2741 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) )
| ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1459]) ).
thf(1704,plain,
! [SV410: $i,SV182: $i] :
( ( ( subset @ SV182 @ SV410 )
= $false )
| ( ( ( setminus @ SV182 @ SV410 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1460]) ).
thf(1705,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ! [SY2744: $i,SY2745: $i] :
( ( SY2744 != SY2745 )
| ~ ( ~ ( ~ ( SV183 @ SY2744 )
| ( SV411 @ SY2745 ) )
| ~ ( ~ ( SV411 @ SY2745 )
| ( SV183 @ SY2744 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1706,plain,
! [SV412: $i,SV184: $i] :
( ( ( subset @ SV184 @ SV412 )
= $false )
| ( ( in @ SV184 @ ( powerset @ SV412 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1462]) ).
thf(1707,plain,
! [SV413: $i,SV185: $i,SV561: $i] :
( ( ( ~ ( in @ SV561 @ ( funcSet @ SV185 @ SV413 ) ) )
= $true )
| ( ( ! [SY2989: $i] :
( ~ ( in @ SY2989 @ SV185 )
| ! [SY2990: $i] :
( ~ ( in @ SY2990 @ SV413 )
| ~ ( in @ ( kpair @ SY2989 @ SY2990 ) @ SV561 )
| ( ( ap @ SV185 @ SV413 @ SV561 @ SY2989 )
= SY2990 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1463]) ).
thf(1708,plain,
! [SV186: $i,SV414: $i] :
( ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false )
| ( ( ! [SY2755: $i] :
( ~ ( in @ SY2755 @ ( powerset @ SV186 ) )
| ~ ! [SY2756: $i] :
( ~ ( in @ SY2756 @ SV186 )
| ~ ( in @ SY2756 @ SV414 )
| ( in @ SY2756 @ SY2755 ) )
| ~ ! [SY2757: $i] :
( ~ ( in @ SY2757 @ SV186 )
| ~ ( in @ SY2757 @ SY2755 )
| ( in @ SY2757 @ SV414 ) )
| ( SV414 = SY2755 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1464]) ).
thf(1709,plain,
! [SV415: $i > $o,SV187: $i,SV562: $i] :
( ( ( ~ ( in @ SV562 @ SV187 ) )
= $true )
| ( ( ~ ( SV415 @ SV562 )
| ( ( dsetconstr @ SV187
@ ^ [SY2759: $i] : ( SV415 @ SY2759 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1465]) ).
thf(1710,plain,
! [SV188: $i > $o] :
( ( ( ! [SY2314: $i] :
~ ~ ( ~ ( SV188 @ SY2314 )
| ~ ! [SY2315: $i] :
( ~ ( SV188 @ SY2315 )
| ( SY2314 = SY2315 ) ) ) )
= $true )
| ( ( ~ ! [SY2316: $i] :
~ ~ ( ~ ( SV188 @ SY2316 )
| ~ ! [SY2317: $i] :
( ~ ( SV188 @ SY2317 )
| ( SY2316 = SY2317 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1466]) ).
thf(1711,plain,
! [SV416: $i,SV189: $i,SV563: $i] :
( ( ( ~ ( in @ SV563 @ ( setadjoin @ SV189 @ SV416 ) ) )
= $true )
| ( ( ( SV563 = SV189 )
| ( in @ SV563 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1467]) ).
thf(1712,plain,
! [SV417: $i,SV190: $i,SV564: $i] :
( ( ( ~ ( in @ SV564 @ ( funcSet @ SV190 @ SV417 ) ) )
= $true )
| ( ( ! [SY2992: $i] :
( ~ ( in @ SY2992 @ SV190 )
| ( ( ap @ SV190 @ SV417 @ SV564 @ SY2992 )
= ( ap @ SV190 @ SV417 @ SV564 @ SY2992 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1468]) ).
thf(1713,plain,
! [SV191: $i,SV418: $i] :
( ( ( in @ SV418 @ ( powerset @ SV191 ) )
= $false )
| ( ( ! [SY2763: $i] :
( ~ ( in @ SY2763 @ ( powerset @ SV191 ) )
| ! [SY2764: $i] :
( ~ ( in @ SY2764 @ ( powerset @ SV191 ) )
| ! [SY2765: $i] :
( ~ ( in @ SY2765 @ SV191 )
| ~ ( in @ SY2765 @ ( binintersect @ SV418 @ SY2763 ) )
| ( in @ SY2765 @ ( binintersect @ ( binunion @ SV418 @ SY2764 ) @ ( binunion @ SY2763 @ SY2764 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1469]) ).
thf(1714,plain,
! [SV192: $o,SV419: $i] :
( ( ( in @ SV419 @ ( prop2set @ SV192 ) )
= $false )
| ( SV192 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1715,plain,
! [SV420: $i] :
( ( ( in @ SV420 @ ( prop2set @ $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1471]) ).
thf(1716,plain,
! [SV421: $i] :
( ( ( in @ SV421 @ ( prop2set @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1717,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ! [SY2766: $i,SY2767: $i] :
( ( SY2766 != SY2767 )
| ~ ( ~ ( ~ ( SV193 @ SY2766 )
| ( SV422 @ SY2767 ) )
| ~ ( ~ ( SV422 @ SY2767 )
| ( SV193 @ SY2766 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1718,plain,
! [SV194: $i,SV613: $i] :
( ( ( ~ ( in @ SV613 @ SV194 )
| ( ( setunion @ SV194 )
= SV613 ) )
= $true )
| ( ( singleton @ SV194 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1719,plain,
! [SV423: $i,SV195: $i,SV565: $i] :
( ( ( ~ ( in @ SV565 @ SV195 ) )
= $true )
| ( ( ~ ~ ( in @ SV565 @ SV423 )
| ( in @ SV565 @ ( setminus @ SV195 @ SV423 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1475]) ).
thf(1720,plain,
! [SV424: $i,SV196: $i,SV566: $i] :
( ( ( ~ ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) ) )
= $true )
| ( ( ~ ! [SY2993: $i] :
~ ~ ( ~ ( in @ SY2993 @ SV196 )
| ~ ~ ! [SY2994: $i] :
~ ~ ( ~ ( in @ SY2994 @ SV424 )
| ( SV566
!= ( kpair @ SY2993 @ SY2994 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1476]) ).
thf(1721,plain,
! [SV425: $o,SV197: $i,SV567: $i] :
( ( ( ~ ( in @ SV567 @ SV197 ) )
= $true )
| ( ( ! [SY2995: $i] :
( ~ ( in @ SY2995 @ SV197 )
| ~ SV425
| ( ( if @ SV197 @ SV425 @ SV567 @ SY2995 )
= SV567 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1477]) ).
thf(1722,plain,
! [SV197: $i,SV568: $i] :
( ( ( ~ ( in @ SV568 @ SV197 ) )
= $true )
| ( ( ! [SY2996: $i] :
( ~ ( in @ SY2996 @ SV197 )
| ~ $true
| ( ( if @ SV197 @ $true @ SV568 @ SY2996 )
= SV568 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1478]) ).
thf(1723,plain,
! [SV197: $i,SV569: $i] :
( ( ( ~ ( in @ SV569 @ SV197 ) )
= $true )
| ( ( ! [SY2997: $i] :
( ~ ( in @ SY2997 @ SV197 )
| ~ $false
| ( ( if @ SV197 @ $false @ SV569 @ SY2997 )
= SV569 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1479]) ).
thf(1724,plain,
! [SV426: $i,SV198: $i,SV570: $i] :
( ( ( ~ ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) ) )
= $true )
| ( ( ! [SY2998: $i] :
( ~ ( subset @ SY2998 @ ( cartprod @ SV198 @ SV426 ) )
| ~ ! [SY2999: $i] :
( ~ ( in @ SY2999 @ SV198 )
| ! [SY3000: $i] :
( ~ ( in @ SY3000 @ SV426 )
| ~ ( in @ ( kpair @ SY2999 @ SY3000 ) @ SV570 )
| ( in @ ( kpair @ SY2999 @ SY3000 ) @ SY2998 ) ) )
| ~ ! [SY3001: $i] :
( ~ ( in @ SY3001 @ SV198 )
| ! [SY3002: $i] :
( ~ ( in @ SY3002 @ SV426 )
| ~ ( in @ ( kpair @ SY3001 @ SY3002 ) @ SY2998 )
| ( in @ ( kpair @ SY3001 @ SY3002 ) @ SV570 ) ) )
| ( SV570 = SY2998 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1725,plain,
! [SV427: $i,SV199: $i] :
( ( ( ( binintersect @ SV199 @ SV427 )
= SV427 )
= $false )
| ( ( subset @ SV427 @ SV199 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1726,plain,
! [SV428: $i,SV200: $i,SV571: $i] :
( ( ( ~ ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) ) )
= $true )
| ( ( ! [SY3003: $i > $o] :
( ~ ! [SY3004: $i] :
( ~ ( in @ SY3004 @ SV200 )
| ! [SY3005: $i] :
( ~ ( in @ SY3005 @ SV428 )
| ~ ( in @ ( kpair @ SY3004 @ SY3005 ) @ SV571 )
| ( SY3003 @ ( kpair @ SY3004 @ SY3005 ) ) ) )
| ! [SY3006: $i] :
( ~ ( in @ SY3006 @ SV571 )
| ( SY3003 @ SY3006 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1482]) ).
thf(1727,plain,
! [SV429: $i > $o,SV201: $i] :
( ( ( ~ ! [SY2793: $i] :
~ ~ ( ~ ( in @ SY2793 @ SV201 )
| ~ ~ ( SV429 @ SY2793 ) ) )
= $false )
| ( ( ~ ! [SY2794: $i] :
( ~ ( in @ SY2794 @ SV201 )
| ( SV429 @ SY2794 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1728,plain,
! [SV430: $i,SV572: $i > $i,SV203: $i] :
( ( ( ~ ! [SY3007: $i] :
( ~ ( in @ SY3007 @ SV203 )
| ( in @ ( SV572 @ SY3007 ) @ SV430 ) ) )
= $true )
| ( ( func @ SV203 @ SV430
@ ( dpsetconstr @ SV203 @ SV430
@ ^ [SY3008: $i,SY3009: $i] :
( ( SV572 @ SY3008 )
= SY3009 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1485]) ).
thf(1729,plain,
! [SV204: $i] :
( ( ( ! [SY2372: $i] :
~ ( in @ SY2372 @ SV204 ) )
= $true )
| ( ( SV204 != emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1486]) ).
thf(1730,plain,
! [SV431: $i,SV206: $i,SV573: $i] :
( ( ( ~ ~ ( in @ SV573 @ SV206 ) )
= $true )
| ( ( ~ ( in @ SV573 @ SV431 )
| ( in @ SV573 @ ( symdiff @ SV206 @ SV431 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1488]) ).
thf(1731,plain,
! [SV432: $i,SV207: $i] :
( ( ( SV207 = SV432 )
= $false )
| ( ( subset @ SV432 @ SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1732,plain,
! [SV208: $i,SV614: $o] :
( ( SV614 = $true )
| ( ( in @ SV208 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1490]) ).
thf(1733,plain,
! [SV208: $i] :
( ( $true = $true )
| ( ( in @ SV208 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1490]) ).
thf(1734,plain,
! [SV208: $i] :
( ( $false = $true )
| ( ( in @ SV208 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1490]) ).
thf(1735,plain,
! [SV433: $i,SV574: $i > $i,SV209: $i] :
( ( ( ~ ! [SY3010: $i] :
( ~ ( in @ SY3010 @ SV209 )
| ( in @ ( SV574 @ SY3010 ) @ SV433 ) ) )
= $true )
| ( ( ! [SY3011: $i] :
( ~ ( in @ SY3011 @ SV209 )
| ( ( ap @ SV209 @ SV433
@ ( lam @ SV209 @ SV433
@ ^ [SY3012: $i] : ( SV574 @ SY3012 ) )
@ SY3011 )
= ( SV574 @ SY3011 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1491]) ).
thf(1736,plain,
! [SV210: $i,SV434: $i] :
( ( ( in @ SV434 @ ( powerset @ SV210 ) )
= $false )
| ( ( subset @ ( setminus @ SV210 @ ( setminus @ SV210 @ SV434 ) ) @ SV434 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1737,plain,
! [SV435: $i,SV211: $i] :
( ( ( SV211 = SV435 )
= $false )
| ( ( ! [SY2804: $i,SY2805: $i] :
( ( SY2804 != SY2805 )
| ( ( setadjoin @ SV211 @ SY2804 )
= ( setadjoin @ SV435 @ SY2805 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1738,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ( ! [SY2806: $i] :
( ~ ( in @ SY2806 @ SV212 )
| ! [SY2807: $i] :
( ~ ( in @ SY2807 @ SV212 )
| ~ ( SV436 @ SY2806 )
| ~ ( SV436 @ SY2807 )
| ( SY2806 = SY2807 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) )
| ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1494]) ).
thf(1739,plain,
! [SV437: $i,SV213: $i] :
( ( ( ( setadjoin @ SV213 @ emptyset )
= ( setadjoin @ SV437 @ emptyset ) )
= $false )
| ( ( SV213 = SV437 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1740,plain,
! [SV615: $i,SV575: $i,SV438: $i,SV214: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV214 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV214 @ ( setadjoin @ SV438 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV575 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV575 @ ( setadjoin @ SV615 @ emptyset ) ) @ emptyset ) ) )
| ( SV575 != SV615 )
| ( SV438 = SV615 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1741,plain,
! [SV215: $i] :
( ( ( ~ ( in @ emptyset @ SV215 )
| ~ ! [SY2395: $i] :
( ~ ~ ( ~ ( in @ SY2395 @ omega )
| ~ ( in @ SY2395 @ SV215 ) )
| ( in @ ( setadjoin @ SY2395 @ SY2395 ) @ SV215 ) ) )
= $true )
| ( ( ! [SY2396: $i] :
( ~ ( in @ SY2396 @ omega )
| ( in @ SY2396 @ SV215 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1497]) ).
thf(1742,plain,
! [SV439: $i,SV216: $i,SV576: $i] :
( ( ( ~ ( in @ SV576 @ SV216 ) )
= $true )
| ( ( ! [SY3014: $i] :
( ~ ( in @ SY3014 @ SV439 )
| ( in @ ( kpair @ SV576 @ SY3014 ) @ ( powerset @ ( powerset @ ( binunion @ SV216 @ SV439 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1498]) ).
thf(1743,plain,
! [SV577: $i > $i > $o,SV440: $i,SV217: $i,SV616: $i] :
( ( ~ ( in @ SV616 @ SV217 )
| ! [SY3067: $i] :
( ~ ( in @ SY3067 @ SV440 )
| ~ ( SV577 @ SV616 @ SY3067 )
| ( in @ ( kpair @ SV616 @ SY3067 )
@ ( dpsetconstr @ SV217 @ SV440
@ ^ [SY3017: $i,SY3018: $i] : ( SV577 @ SY3017 @ SY3018 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1744,plain,
! [SV441: $o,SV218: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV218 ) )
= $true )
| ( ( ! [SY3019: $i] :
( ~ ( in @ SY3019 @ SV218 )
| ( in @ ( if @ SV218 @ SV441 @ SV578 @ SY3019 ) @ SV218 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1500]) ).
thf(1745,plain,
! [SV218: $i,SV579: $i] :
( ( ( ~ ( in @ SV579 @ SV218 ) )
= $true )
| ( ( ! [SY3020: $i] :
( ~ ( in @ SY3020 @ SV218 )
| ( in @ ( if @ SV218 @ $true @ SV579 @ SY3020 ) @ SV218 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1501]) ).
thf(1746,plain,
! [SV218: $i,SV580: $i] :
( ( ( ~ ( in @ SV580 @ SV218 ) )
= $true )
| ( ( ! [SY3021: $i] :
( ~ ( in @ SY3021 @ SV218 )
| ( in @ ( if @ SV218 @ $false @ SV580 @ SY3021 ) @ SV218 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1502]) ).
thf(1747,plain,
! [SV442: $i,SV219: $i,SV581: $i] :
( ( ( ~ ( in @ SV581 @ ( funcSet @ SV219 @ SV442 ) ) )
= $true )
| ( ( ! [SY3022: $i] :
( ~ ( in @ SY3022 @ ( funcSet @ SV219 @ SV442 ) )
| ~ ! [SY3023: $i] :
( ~ ( in @ SY3023 @ SV219 )
| ( ( ap @ SV219 @ SV442 @ SV581 @ SY3023 )
= ( ap @ SV219 @ SV442 @ SY3022 @ SY3023 ) ) )
| ( SV581 = SY3022 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1503]) ).
thf(1748,plain,
! [SV582: $i > $i > $o,SV443: $i,SV220: $i,SV617: $i] :
( ( ~ ( in @ SV617 @ SV220 )
| ! [SY3070: $i] :
( ~ ( in @ SY3070 @ SV443 )
| ~ ( in @ ( kpair @ SV617 @ SY3070 )
@ ( dpsetconstr @ SV220 @ SV443
@ ^ [SY3026: $i,SY3027: $i] : ( SV582 @ SY3026 @ SY3027 ) ) )
| ( SV582 @ SV617 @ SY3070 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1749,plain,
! [SV583: $i,SV444: $i,SV221: $i] :
( ( ( ~ ( func @ SV221 @ SV444 @ SV583 ) )
= $true )
| ( ( ! [SY3028: $i] :
( ~ ( in @ SY3028 @ SV221 )
| ( in @ ( ap @ SV221 @ SV444 @ SV583 @ SY3028 ) @ SV444 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1505]) ).
thf(1750,plain,
! [SV445: $i,SV222: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV222 ) )
= $true )
| ( ( in @ ( setadjoin @ SV584 @ emptyset ) @ ( powerset @ ( binunion @ SV222 @ SV445 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1506]) ).
thf(1751,plain,
! [SV446: $i > $o,SV223: $i] :
( ( ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY2832: $i] : ( SV446 @ SY2832 ) ) )
= $false )
| ( ( ~ ! [SY2833: $i] :
~ ~ ( ~ ( in @ SY2833 @ SV223 )
| ~ ( SV446 @ SY2833 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1752,plain,
! [SV447: $i,SV224: $i] :
( ( ( SV224 != SV447 )
= $false )
| ( ( ~ ( in @ SV447 @ ( setadjoin @ SV224 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1508]) ).
thf(1753,plain,
! [SV448: $i,SV225: $i] :
( ( ( ! [SY2834: $i] :
~ ( ~ ( ~ ( in @ SY2834 @ SV225 )
| ( in @ SY2834 @ SV448 ) )
| ~ ( ~ ( in @ SY2834 @ SV448 )
| ( in @ SY2834 @ SV225 ) ) ) )
= $false )
| ( ( SV225 = SV448 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1754,plain,
! [SV449: $i,SV226: $i,SV585: $i] :
( ( ( ~ ( in @ SV585 @ SV226 ) )
= $true )
| ( ( ~ ( in @ SV585 @ SV449 )
| ~ ( in @ SV585 @ ( symdiff @ SV226 @ SV449 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1510]) ).
thf(1755,plain,
! [SV227: $i,SV450: $i] :
( ( ( in @ SV450 @ ( powerset @ SV227 ) )
= $false )
| ( ( ! [SY2836: $i] :
( ~ ( in @ SY2836 @ SV227 )
| ~ ( in @ SY2836 @ ( setminus @ SV227 @ ( setminus @ SV227 @ SV450 ) ) )
| ( in @ SY2836 @ SV450 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1511]) ).
thf(1756,plain,
! [SV618: $i,SV586: $i,SV451: $i,SV228: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV228 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV228 @ ( setadjoin @ SV451 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV586 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV586 @ ( setadjoin @ SV618 @ emptyset ) ) @ emptyset ) ) )
| ( SV228 = SV586 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1757,plain,
! [SV229: $i,SV452: $i] :
( ( ( in @ SV452 @ ( powerset @ SV229 ) )
= $false )
| ( ( ! [SY2839: $i] :
( ~ ( in @ SY2839 @ ( powerset @ SV229 ) )
| ! [SY2840: $i] :
( ~ ( in @ SY2840 @ ( powerset @ SV229 ) )
| ( in @ ( binintersect @ SV452 @ SY2839 ) @ ( powerset @ ( binintersect @ ( binunion @ SV452 @ SY2840 ) @ ( binunion @ SY2839 @ SY2840 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1513]) ).
thf(1758,plain,
! [SV230: $i] :
( ( ( SV230 = emptyset )
= $true )
| ( ( ~ ! [SY2440: $i] :
~ ~ ( ~ ( in @ SY2440 @ SV230 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1514]) ).
thf(1759,plain,
! [SV453: $o,SV231: $i,SV587: $i] :
( ( ( ~ ( in @ SV587 @ SV231 ) )
= $true )
| ( ( ! [SY3030: $i] :
( ~ ( in @ SY3030 @ SV231 )
| ~ SV453
| ( ( dsetconstr @ SV231
@ ^ [SY3031: $i] :
( ~ ( ~ SV453
| ( SY3031 != SV587 ) )
| ~ ( ~ ~ SV453
| ( SY3031 != SY3030 ) ) ) )
= ( setadjoin @ SV587 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1515]) ).
thf(1760,plain,
! [SV231: $i,SV588: $i] :
( ( ( ~ ( in @ SV588 @ SV231 ) )
= $true )
| ( ( ! [SY3032: $i] :
( ~ ( in @ SY3032 @ SV231 )
| ~ $true
| ( ( dsetconstr @ SV231
@ ^ [SY3033: $i] :
( ~ ( ~ $true
| ( SY3033 != SV588 ) )
| ~ ( ~ ~ $true
| ( SY3033 != SY3032 ) ) ) )
= ( setadjoin @ SV588 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1516]) ).
thf(1761,plain,
! [SV231: $i,SV589: $i] :
( ( ( ~ ( in @ SV589 @ SV231 ) )
= $true )
| ( ( ! [SY3034: $i] :
( ~ ( in @ SY3034 @ SV231 )
| ~ $false
| ( ( dsetconstr @ SV231
@ ^ [SY3035: $i] :
( ~ ( ~ $false
| ( SY3035 != SV589 ) )
| ~ ( ~ ~ $false
| ( SY3035 != SY3034 ) ) ) )
= ( setadjoin @ SV589 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1517]) ).
thf(1762,plain,
! [SV590: $i,SV232: $i,SV454: $i] :
( ( ( ~ ( in @ SV454 @ ( powerset @ SV232 ) ) )
= $true )
| ( ( ~ ( in @ SV590 @ SV454 )
| ( in @ SV590 @ SV232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1518]) ).
thf(1763,plain,
! [SV233: $i,SV455: $i] :
( ( ( in @ SV455 @ ( powerset @ SV233 ) )
= $false )
| ( ( ! [SY2845: $i] :
( ~ ( in @ SY2845 @ SV233 )
| ~ ( in @ SY2845 @ SV455 )
| ~ ( in @ SY2845 @ ( setminus @ SV233 @ SV455 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1764,plain,
! [SV456: $i,SV591: $i > $i,SV234: $i] :
( ( ( ~ ! [SY3036: $i] :
( ~ ( in @ SY3036 @ SV234 )
| ( in @ ( SV591 @ SY3036 ) @ SV456 ) ) )
= $true )
| ( ( ! [SY3037: $i] :
( ~ ( in @ SY3037 @ SV234 )
| ( ( ap @ SV234 @ SV456
@ ( lam @ SV234 @ SV456
@ ^ [SY3038: $i] : ( SV591 @ SY3038 ) )
@ SY3037 )
= ( SV591 @ SY3037 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1520]) ).
thf(1765,plain,
! [SV457: $i,SV235: $i] :
( ( ( ~ ~ ! [SY2850: $i] :
~ ~ ( ~ ( in @ SY2850 @ SV235 )
| ~ ( in @ SY2850 @ SV457 ) ) )
= $false )
| ( ( ( binintersect @ SV235 @ SV457 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1521]) ).
thf(1766,plain,
! [SV619: $i,SV592: $i,SV458: $i,SV236: $i] :
( ( ( ( kpair @ SV236 @ SV458 )
!= ( kpair @ SV592 @ SV619 ) )
| ( SV236 = SV592 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1767,plain,
! [SV459: $i,SV593: $i,SV237: $i] :
( ( ( ~ ( subset @ SV237 @ SV593 ) )
= $true )
| ( ( subset @ SV237 @ ( setadjoin @ SV459 @ SV593 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1523]) ).
thf(1768,plain,
! [SV460: $i,SV238: $i,SV594: $i] :
( ( ( ~ ( in @ SV594 @ ( setadjoin @ SV238 @ ( setadjoin @ SV460 @ emptyset ) ) ) )
= $true )
| ( ( ( SV594 = SV238 )
| ( SV594 = SV460 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1524]) ).
thf(1769,plain,
! [SV620: $i,SV595: $i,SV461: $i,SV239: $i] :
( ( ( ( kpair @ SV239 @ SV461 )
!= ( kpair @ SV595 @ SV620 ) )
| ( SV461 = SV620 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1770,plain,
! [SV462: $i,SV240: $i] :
( ( ( SV240 = SV462 )
= $false )
| ( ( ( setadjoin @ SV240 @ ( setadjoin @ SV462 @ emptyset ) )
= ( setadjoin @ SV240 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1771,plain,
! [SV463: $i,SV241: $i] :
( ( ( SV241 = SV463 )
= $false )
| ( ( ( powerset @ SV241 )
= ( powerset @ SV463 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1772,plain,
! [SV464: $i,SV596: $i > $i,SV242: $i] :
( ( ( ~ ! [SY3041: $i] :
( ~ ( in @ SY3041 @ SV242 )
| ( in @ ( SV596 @ SY3041 ) @ SV464 ) ) )
= $true )
| ( ( func @ SV242 @ SV464
@ ( lam @ SV242 @ SV464
@ ^ [SY3042: $i] : ( SV596 @ SY3042 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1528]) ).
thf(1773,plain,
! [SV243: $i,SV465: $i] :
( ( ( in @ SV465 @ ( powerset @ SV243 ) )
= $false )
| ( ( ! [SY2860: $i] :
( ~ ( in @ SY2860 @ ( powerset @ SV243 ) )
| ! [SY2861: $i] :
( ~ ( in @ SY2861 @ SV243 )
| ~ ( in @ SV465 @ ( powerset @ SY2860 ) )
| ~ ( in @ SY2861 @ SV465 )
| ( in @ SY2861 @ SY2860 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1529]) ).
thf(1774,plain,
! [SV466: $o,SV244: $i,SV597: $i] :
( ( ( ~ ( in @ SV597 @ SV244 ) )
= $true )
| ( ( ! [SY3043: $i] :
( ~ ( in @ SY3043 @ SV244 )
| ~ ~ SV466
| ( in @ SY3043
@ ( dsetconstr @ SV244
@ ^ [SY3044: $i] :
( ~ ( ~ SV466
| ( SY3044 != SV597 ) )
| ~ ( ~ ~ SV466
| ( SY3044 != SY3043 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1530]) ).
thf(1775,plain,
! [SV244: $i,SV598: $i] :
( ( ( ~ ( in @ SV598 @ SV244 ) )
= $true )
| ( ( ! [SY3045: $i] :
( ~ ( in @ SY3045 @ SV244 )
| ~ ~ $true
| ( in @ SY3045
@ ( dsetconstr @ SV244
@ ^ [SY3046: $i] :
( ~ ( ~ $true
| ( SY3046 != SV598 ) )
| ~ ( ~ ~ $true
| ( SY3046 != SY3045 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1531]) ).
thf(1776,plain,
! [SV244: $i,SV599: $i] :
( ( ( ~ ( in @ SV599 @ SV244 ) )
= $true )
| ( ( ! [SY3047: $i] :
( ~ ( in @ SY3047 @ SV244 )
| ~ ~ $false
| ( in @ SY3047
@ ( dsetconstr @ SV244
@ ^ [SY3048: $i] :
( ~ ( ~ $false
| ( SY3048 != SV599 ) )
| ~ ( ~ ~ $false
| ( SY3048 != SY3047 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1777,plain,
! [SV245: $i,SV467: $i] :
( ( ( in @ SV467 @ SV245 )
= $false )
| ( ( in @ ( setadjoin @ SV467 @ emptyset ) @ ( powerset @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1778,plain,
! [SV246: $i,SV468: $i] :
( ( ( in @ SV468 @ SV246 )
= $false )
| ( ( subset @ ( setadjoin @ SV468 @ emptyset ) @ SV246 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1534]) ).
thf(1779,plain,
! [SV600: $i,SV469: $i,SV247: $i] :
( ( ( ~ ( func @ SV247 @ SV469 @ SV600 ) )
= $true )
| ( ( ! [SY3049: $i] :
( ~ ( func @ SV247 @ SV469 @ SY3049 )
| ~ ! [SY3050: $i] :
( ~ ( in @ SY3050 @ SV247 )
| ( ( ap @ SV247 @ SV469 @ SV600 @ SY3050 )
= ( ap @ SV247 @ SV469 @ SY3049 @ SY3050 ) ) )
| ! [SY3051: $i] :
( ~ ( in @ SY3051 @ SV247 )
| ! [SY3052: $i] :
( ~ ( in @ SY3052 @ SV469 )
| ~ ( in @ ( kpair @ SY3051 @ SY3052 ) @ SY3049 )
| ( in @ ( kpair @ SY3051 @ SY3052 ) @ SV600 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1535]) ).
thf(1780,plain,
! [SV248: $i,SV470: $i] :
( ( ( in @ SV470 @ ( powerset @ SV248 ) )
= $false )
| ( ( ! [SY2870: $i] :
( ~ ( in @ SY2870 @ ( powerset @ SV248 ) )
| ( subset @ ( setminus @ SV248 @ SV470 ) @ ( setminus @ SV248 @ ( binintersect @ SV470 @ SY2870 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1781,plain,
! [SV249: $i > $i > $o,SV471: $i] :
( ( ( ! [SY2871: $i] :
( ~ ( in @ SY2871 @ SV471 )
| ~ ! [SY2491: $i] :
~ ~ ( ~ ( SV249 @ SY2871 @ SY2491 )
| ~ ! [SY2492: $i] :
( ~ ( SV249 @ SY2871 @ SY2492 )
| ( SY2491 = SY2492 ) ) ) ) )
= $false )
| ( ( ~ ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1782,plain,
! [SV472: $i,SV250: $i] :
( ( ( SV250 = SV472 )
= $false )
| ( ( in @ SV250 @ ( setadjoin @ SV472 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1783,plain,
! [SV473: $i,SV251: $i] :
( ( ( ( setminus @ SV251 @ SV473 )
= emptyset )
= $false )
| ( ( subset @ SV251 @ SV473 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1784,plain,
! [SV474: $o,SV252: $i,SV601: $i] :
( ( ( ~ ( in @ SV601 @ SV252 ) )
= $true )
| ( ( ! [SY3053: $i] :
( ~ ( in @ SY3053 @ SV252 )
| ~ ~ SV474
| ( ( if @ SV252 @ SV474 @ SV601 @ SY3053 )
= SY3053 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1540]) ).
thf(1785,plain,
! [SV252: $i,SV602: $i] :
( ( ( ~ ( in @ SV602 @ SV252 ) )
= $true )
| ( ( ! [SY3054: $i] :
( ~ ( in @ SY3054 @ SV252 )
| ~ ~ $true
| ( ( if @ SV252 @ $true @ SV602 @ SY3054 )
= SY3054 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1541]) ).
thf(1786,plain,
! [SV252: $i,SV603: $i] :
( ( ( ~ ( in @ SV603 @ SV252 ) )
= $true )
| ( ( ! [SY3055: $i] :
( ~ ( in @ SY3055 @ SV252 )
| ~ ~ $false
| ( ( if @ SV252 @ $false @ SV603 @ SY3055 )
= SY3055 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1542]) ).
thf(1787,plain,
! [SV475: $i,SV253: $i,SV604: $i] :
( ( ( ~ ( in @ SV604 @ SV253 ) )
= $true )
| ( ( ! [SY3056: $i] :
( ~ ( in @ SY3056 @ SV475 )
| ( in @ ( setadjoin @ ( setadjoin @ SV604 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV604 @ ( setadjoin @ SY3056 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV253 @ SV475 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1543]) ).
thf(1788,plain,
! [SV476: $i,SV254: $i] :
( ( ( SV254 = SV476 )
= $false )
| ( ( ! [SY2882: $i,SY2883: $i] :
( ( SY2882 != SY2883 )
| ~ ( ~ ( ~ ( in @ SY2882 @ SV254 )
| ( in @ SY2883 @ SV476 ) )
| ~ ( ~ ( in @ SY2883 @ SV476 )
| ( in @ SY2882 @ SV254 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1544]) ).
thf(1789,plain,
! [SV477: $i,SV255: $i] :
( ( ( subset @ SV255 @ SV477 )
= $false )
| ( ( ~ ( subset @ SV477 @ SV255 )
| ( SV255 = SV477 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1545]) ).
thf(1790,plain,
! [SV256: $i > $o] :
( ( ( ! [SY2509: $i] :
~ ~ ( ~ ( SV256 @ SY2509 )
| ~ ! [SY2510: $i] :
( ~ ( SV256 @ SY2510 )
| ( SY2509 = SY2510 ) ) ) )
= $true )
| ( ( ~ ! [SY2511: $i] :
~ ! [SY2512: $i] :
~ ( ~ ( ~ ( SV256 @ SY2512 )
| ( SY2512 = SY2511 ) )
| ~ ( ( SY2512 != SY2511 )
| ( SV256 @ SY2512 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1546]) ).
thf(1791,plain,
! [SV257: $i,SV478: $i] :
( ( ( in @ SV478 @ ( powerset @ SV257 ) )
= $false )
| ( ( ! [SY2884: $i] :
( ~ ( in @ SY2884 @ ( powerset @ SV257 ) )
| ( in @ ( binunion @ SV478 @ SY2884 ) @ ( powerset @ SV257 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1792,plain,
! [SV479: $i,SV258: $i,SV605: $i] :
( ( ( ~ ( in @ SV605 @ SV258 ) )
= $true )
| ( ( ! [SY3057: $i] :
( ~ ( in @ SY3057 @ SV479 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV605 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV605 @ ( setadjoin @ SY3057 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV258 @ SV479 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1548]) ).
thf(1793,plain,
! [SV483: $i,SV281: $i,SV34: $i] :
( ( ( func @ SV34 @ SV281 @ SV483 )
= $false )
| ( ( in @ SV483 @ ( funcSet @ SV34 @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1794,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ~ ~ ( ~ ( SV35 @ SV621 )
| ~ ! [SY3073: $i] :
( ~ ( SV35 @ SY3073 )
| ( SV621 = SY3073 ) ) ) )
= $true )
| ( ( ~ ! [SY1902: $i] :
~ ~ ( ~ ( SV35 @ SY1902 )
| ~ ! [SY1903: $i] :
( ~ ( SV35 @ SY1903 )
| ( SY1902 = SY1903 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1795,plain,
! [SV282: $i,SV36: $i,SV622: $i] :
( ( ( ~ ( in @ SV622 @ ( powerset @ SV36 ) )
| ~ ( subset @ ( setminus @ SV36 @ SV622 ) @ ( setminus @ SV36 @ SV282 ) )
| ( subset @ SV282 @ SV622 ) )
= $true )
| ( ( in @ SV282 @ ( powerset @ SV36 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1796,plain,
! [SV484: $i,SV284: $i,SV38: $i] :
( ( ( func @ SV38 @ SV284 @ SV484 )
= $false )
| ( ( ! [SY2891: $i] :
( ~ ( in @ SY2891 @ SV38 )
| ! [SY2892: $i] :
( ~ ( in @ SY2892 @ SV284 )
| ~ ( in @ ( kpair @ SY2891 @ SY2892 ) @ SV484 )
| ( ( ap @ SV38 @ SV284 @ SV484 @ SY2891 )
= SY2892 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1797,plain,
! [SV285: $o,SV39: $i,SV485: $i] :
( ( ( in @ SV485 @ SV39 )
= $false )
| ( ( ! [SY2893: $i] :
( ~ ( in @ SY2893 @ SV39 )
| ~ SV285
| ( in @ SV485
@ ( dsetconstr @ SV39
@ ^ [SY2894: $i] :
( ~ ( ~ SV285
| ( SY2894 != SV485 ) )
| ~ ( ~ ~ SV285
| ( SY2894 != SY2893 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1798,plain,
! [SV39: $i,SV486: $i] :
( ( ( in @ SV486 @ SV39 )
= $false )
| ( ( ! [SY2895: $i] :
( ~ ( in @ SY2895 @ SV39 )
| ~ $true
| ( in @ SV486
@ ( dsetconstr @ SV39
@ ^ [SY2896: $i] :
( ~ ( ~ $true
| ( SY2896 != SV486 ) )
| ~ ( ~ ~ $true
| ( SY2896 != SY2895 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1799,plain,
! [SV39: $i,SV487: $i] :
( ( ( in @ SV487 @ SV39 )
= $false )
| ( ( ! [SY2897: $i] :
( ~ ( in @ SY2897 @ SV39 )
| ~ $false
| ( in @ SV487
@ ( dsetconstr @ SV39
@ ^ [SY2898: $i] :
( ~ ( ~ $false
| ( SY2898 != SV487 ) )
| ~ ( ~ ~ $false
| ( SY2898 != SY2897 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1556]) ).
thf(1800,plain,
! [SV623: $i > $o,SV286: $i,SV40: $i] :
( ( ( ! [SY3074: $i > $o] :
( ~ ! [SY3075: $i] :
( ~ ( in @ SY3075 @ SV40 )
| ! [SY3076: $i] :
( ~ ( in @ SY3076 @ SV286 )
| ( SY3075 != SY3076 )
| ~ ( ~ ( ~ ( SV623 @ SY3075 )
| ( SY3074 @ SY3076 ) )
| ~ ( ~ ( SY3074 @ SY3076 )
| ( SV623 @ SY3075 ) ) ) ) )
| ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SX4: $i] : ( SY3074 @ SX4 ) ) ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1801,plain,
! [SV287: $i > $o,SV41: $i] :
( ( ( ~ ! [SY2541: $i] :
~ ~ ( ~ ( in @ SY2541 @ SV41 )
| ~ ( SV287 @ SY2541 ) ) )
= $true )
| ( ( ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV41 )
| ~ ( SV287 @ SY2542 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1558]) ).
thf(1802,plain,
! [SV288: $i,SV43: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV43 ) )
= $false )
| ( ( ~ ( in @ SV488 @ ( setminus @ SV43 @ SV288 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1803,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ! [SY3079: $i] :
~ ( ~ ( ~ ( SV44 @ SY3079 )
| ( SY3079 = SV624 ) )
| ~ ( ( SY3079 != SV624 )
| ( SV44 @ SY3079 ) ) ) )
= $true )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1804,plain,
! [SV289: $i,SV45: $i,SV489: $i] :
( ( ( in @ SV489 @ ( setminus @ SV45 @ SV289 ) )
= $false )
| ( ( ~ ( in @ SV489 @ SV289 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1805,plain,
! [SV290: $i,SV46: $i,SV490: $i] :
( ( ( in @ SV490 @ SV46 )
= $false )
| ( ( ! [SY2899: $i] :
( ~ ( in @ SY2899 @ SV290 )
| ( in @ ( kpair @ SV490 @ SY2899 ) @ ( cartprod @ SV46 @ SV290 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1806,plain,
! [SV291: $i,SV47: $i,SV491: $i] :
( ( ~ ( ~ ( in @ SV491 @ ( setadjoin @ SV47 @ SV291 ) )
| ( SV491 = SV47 )
| ( in @ SV491 @ SV291 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1563]) ).
thf(1807,plain,
! [SV291: $i,SV47: $i,SV491: $i] :
( ( ~ ( ~ ( ( SV491 = SV47 )
| ( in @ SV491 @ SV291 ) )
| ( in @ SV491 @ ( setadjoin @ SV47 @ SV291 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1563]) ).
thf(1808,plain,
! [SV293: $i,SV50: $i,SV492: $i] :
( ( ( in @ SV492 @ ( setminus @ SV50 @ SV293 ) )
= $false )
| ( ( in @ SV492 @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1565]) ).
thf(1809,plain,
! [SV493: $i,SV294: $i,SV51: $i] :
( ( ( func @ SV51 @ SV294 @ SV493 )
= $false )
| ( ( ! [SY2900: $i] :
( ~ ( in @ SY2900 @ SV51 )
| ( singleton
@ ( dsetconstr @ SV294
@ ^ [SY2901: $i] : ( in @ ( kpair @ SY2900 @ SY2901 ) @ SV493 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1810,plain,
! [SV296: $i,SV55: $i,SV494: $i] :
( ( ( in @ SV494 @ SV55 )
= $false )
| ( ( ! [SY2902: $i] :
( ~ ( in @ SY2902 @ SV296 )
| ( ( kpair @ SV494 @ SY2902 )
= ( kpair @ SV494 @ SY2902 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1568]) ).
thf(1811,plain,
! [SV297: $i,SV56: $i,SV495: $i] :
( ( ( in @ SV495 @ SV56 )
= $false )
| ( ( ! [SY2903: $i] :
( ~ ( in @ SY2903 @ SV297 )
| ( ( ksnd @ ( kpair @ SV495 @ SY2903 ) )
= SY2903 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1812,plain,
! [SV496: $i,SV298: $i,SV57: $i] :
( ( ( func @ SV57 @ SV298 @ SV496 )
= $false )
| ( ( ! [SY2904: $i] :
( ~ ( in @ SY2904 @ SV57 )
| ( in @ ( kpair @ SY2904 @ ( ap @ SV57 @ SV298 @ SV496 @ SY2904 ) ) @ SV496 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1570]) ).
thf(1813,plain,
! [SV299: $i,SV58: $i,SV497: $i] :
( ( ( in @ SV497 @ ( cartprod @ SV58 @ SV299 ) )
= $false )
| ( ( in @ ( kfst @ SV497 ) @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1814,plain,
! [SV498: $i,SV300: $i,SV59: $i] :
( ( ( ( setadjoin @ SV59 @ ( setadjoin @ SV300 @ emptyset ) )
= ( setadjoin @ SV498 @ emptyset ) )
= $false )
| ( ( SV59 = SV300 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1572]) ).
thf(1815,plain,
! [SV301: $o,SV60: $i,SV499: $i] :
( ( ( in @ SV499 @ SV60 )
= $false )
| ( ( ! [SY2905: $i] :
( ~ ( in @ SY2905 @ SV60 )
| ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY2906: $i] :
( ~ ( ~ SV301
| ( SY2906 != SV499 ) )
| ~ ( ~ ~ SV301
| ( SY2906 != SY2905 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1573]) ).
thf(1816,plain,
! [SV60: $i,SV500: $i] :
( ( ( in @ SV500 @ SV60 )
= $false )
| ( ( ! [SY2907: $i] :
( ~ ( in @ SY2907 @ SV60 )
| ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY2908: $i] :
( ~ ( ~ $true
| ( SY2908 != SV500 ) )
| ~ ( ~ ~ $true
| ( SY2908 != SY2907 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1817,plain,
! [SV60: $i,SV501: $i] :
( ( ( in @ SV501 @ SV60 )
= $false )
| ( ( ! [SY2909: $i] :
( ~ ( in @ SY2909 @ SV60 )
| ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY2910: $i] :
( ~ ( ~ $false
| ( SY2910 != SV501 ) )
| ~ ( ~ ~ $false
| ( SY2910 != SY2909 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1575]) ).
thf(1818,plain,
! [SV302: $i,SV61: $i,SV502: $i] :
( ( ( in @ SV502 @ ( funcSet @ SV61 @ SV302 ) )
= $false )
| ( ( func @ SV61 @ SV302 @ SV502 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1576]) ).
thf(1819,plain,
! [SV303: $i,SV62: $i,SV503: $i] :
( ( ( in @ SV503 @ SV62 )
= $false )
| ( ( ~ ( in @ SV503 @ SV303 )
| ( in @ SV503 @ ( binintersect @ SV62 @ SV303 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1577]) ).
thf(1820,plain,
! [SV304: $i,SV63: $i,SV504: $i] :
( ( ( subset @ SV504 @ SV63 )
= $false )
| ( ( ~ ( subset @ SV504 @ SV304 )
| ( subset @ SV504 @ ( binintersect @ SV63 @ SV304 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1821,plain,
! [SV305: $i,SV64: $i,SV625: $i] :
( ( ( ~ ( in @ SV625 @ ( powerset @ SV64 ) )
| ! [SY3080: $i] :
( ~ ( in @ SY3080 @ SV64 )
| ~ ( in @ SY3080 @ ( setminus @ SV64 @ SV305 ) )
| ~ ( in @ SY3080 @ ( binintersect @ SV305 @ SV625 ) ) ) )
= $true )
| ( ( in @ SV305 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1822,plain,
! [SV306: $i,SV65: $i,SV505: $i] :
( ( ( in @ SV505 @ ( binintersect @ SV65 @ SV306 ) )
= $false )
| ( ( in @ SV505 @ SV306 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1823,plain,
! [SV307: $i,SV66: $i,SV626: $i] :
( ( ( ~ ( in @ SV626 @ ( powerset @ SV66 ) )
| ! [SY3081: $i] :
( ~ ( in @ SY3081 @ SV66 )
| ~ ~ ( in @ SY3081 @ ( binunion @ SV307 @ SV626 ) )
| ~ ( in @ SY3081 @ SV626 ) ) )
= $true )
| ( ( in @ SV307 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(1824,plain,
! [SV506: $i,SV308: $i,SV67: $i] :
( ( ( func @ SV67 @ SV308 @ SV506 )
= $false )
| ( ( ! [SY2911: $i] :
( ~ ( in @ SY2911 @ SV67 )
| ( ( ap @ SV67 @ SV308 @ SV506 @ SY2911 )
= ( ap @ SV67 @ SV308 @ SV506 @ SY2911 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1582]) ).
thf(1825,plain,
! [SV68: $i,SV309: $i,SV507: $i] :
( ( ( in @ SV507 @ SV309 )
= $false )
| ( ( ~ ( in @ SV507 @ ( setminus @ SV68 @ SV309 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1583]) ).
thf(1826,plain,
! [SV69: $i,SV310: $i] :
( ( ~ ( in @ SV310 @ ( setunion @ SV69 ) )
| ~ ! [SY2574: $i] :
~ ~ ( ~ ( in @ SV310 @ SY2574 )
| ~ ( in @ SY2574 @ SV69 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1584]) ).
thf(1827,plain,
! [SV69: $i,SV310: $i] :
( ( ~ ~ ! [SY2575: $i] :
~ ~ ( ~ ( in @ SV310 @ SY2575 )
| ~ ( in @ SY2575 @ SV69 ) )
| ( in @ SV310 @ ( setunion @ SV69 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1585]) ).
thf(1828,plain,
! [SV311: $i,SV70: $i,SV627: $i] :
( ( ( ~ ( in @ SV627 @ ( powerset @ SV70 ) )
| ! [SY3082: $i] :
( ~ ( in @ SY3082 @ SV70 )
| ~ ( in @ SY3082 @ ( setminus @ SV70 @ ( binunion @ SV311 @ SV627 ) ) )
| ~ ( in @ SY3082 @ SV311 ) ) )
= $true )
| ( ( in @ SV311 @ ( powerset @ SV70 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1829,plain,
! [SV71: $i,SV312: $i] :
( ( ( ~ ( in @ ( sK6_SY2578 @ SV312 @ SV71 ) @ SV71 )
| ( in @ ( sK6_SY2578 @ SV312 @ SV71 ) @ SV312 ) )
= $false )
| ( ( subset @ SV71 @ SV312 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1587]) ).
thf(1830,plain,
! [SV313: $i > $o,SV72: $i,SV508: $i] :
( ( ( in @ SV508
@ ( dsetconstr @ SV72
@ ^ [SY2580: $i] : ( SV313 @ SY2580 ) ) )
= $false )
| ( ( SV313 @ SV508 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1588]) ).
thf(1831,plain,
! [SV314: $i,SV73: $i,SV628: $i] :
( ( ( ~ ( in @ SV628 @ ( powerset @ SV73 ) )
| ~ ! [SY3083: $i] :
( ~ ( in @ SY3083 @ SV73 )
| ~ ( in @ SY3083 @ SV314 )
| ( in @ SY3083 @ SV628 ) )
| ( in @ SV314 @ ( powerset @ SV628 ) ) )
= $true )
| ( ( in @ SV314 @ ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(1832,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false )
| ( ( ! [SY2913: $o] :
( ~ ( ~ ( in @ SV509 @ SV74 )
| ~ ~ ( in @ SV509 @ SV315 )
| SY2913 )
| ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SY2913 )
| SY2913 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1833,plain,
! [SV75: $i] :
( ( ( in @ ( sK4_SY2000 @ SV75 ) @ SV75 )
= $true )
| ( ( SV75 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1591]) ).
thf(1834,plain,
! [SV510: $i,SV316: $i,SV76: $i] :
( ( ( subset @ SV76 @ SV316 )
= $false )
| ( ( ~ ~ ( in @ SV510 @ SV316 )
| ~ ( in @ SV510 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1835,plain,
! [SV511: $i > $i > $o,SV317: $i,SV77: $i,SV629: $i,SV606: $i] :
( ( ~ ( in @ ( kpair @ SV606 @ SV629 )
@ ( dpsetconstr @ SV77 @ SV317
@ ^ [SY2916: $i,SY2917: $i] : ( SV511 @ SY2916 @ SY2917 ) ) )
| ( in @ SV629 @ SV317 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1836,plain,
! [SV78: $i] :
( ( ( ! [SY2009: $i] :
~ ( in @ SY2009 @ SV78 ) )
= $false )
| ( ( SV78 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1837,plain,
! [SV318: $i > $o,SV79: $i] :
( ( ( ~ ! [SY2591: $i] :
~ ~ ( ~ ( in @ SY2591 @ SV79 )
| ~ ( SV318 @ SY2591 ) ) )
= $true )
| ( ( ! [SY2592: $i] :
( ~ ( in @ SY2592 @ SV79 )
| ~ ( SV318 @ SY2592 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1595]) ).
thf(1838,plain,
! [SV319: $i,SV80: $i,SV512: $i] :
( ( ( in @ SV512 @ SV80 )
= $false )
| ( ( in @ SV512 @ ( binunion @ SV80 @ SV319 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1596]) ).
thf(1839,plain,
! [SV82: $i,SV630: $i] :
( ( ( ~ ( in @ SV630 @ SV82 ) )
= $true )
| ( ( ~ ! [SY2017: $i] :
~ ~ ( ~ ( in @ SY2017 @ SV82 )
| ~ ~ ~ ! [SY2018: $i] :
~ ~ ( ~ ( in @ SY2018 @ SY2017 )
| ~ ( in @ SY2018 @ SV82 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(1840,plain,
! [SV607: $o,SV322: $i,SV84: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV513 @ SV84 )
| SV607 )
| ~ ( ~ ( in @ SV513 @ SV322 )
| SV607 )
| SV607 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1600]) ).
thf(1841,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV513 @ SV84 )
| $true )
| ~ ( ~ ( in @ SV513 @ SV322 )
| $true )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1601]) ).
thf(1842,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV513 @ SV84 )
| $false )
| ~ ( ~ ( in @ SV513 @ SV322 )
| $false )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1602]) ).
thf(1843,plain,
! [SV323: $i,SV85: $i,SV631: $i] :
( ( ( ~ ( in @ SV631 @ ( powerset @ SV85 ) )
| ! [SY3086: $i] :
( ~ ( in @ SY3086 @ SV85 )
| ~ ~ ( in @ SY3086 @ ( binunion @ SV323 @ SV631 ) )
| ~ ( in @ SY3086 @ SV323 ) ) )
= $true )
| ( ( in @ SV323 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(1844,plain,
! [SV325: $i > $o,SV87: $i] :
( ( ( ! [SY2598: $i] :
( ~ ( in @ SY2598 @ SV87 )
| ( SV325 @ SY2598 ) ) )
= $true )
| ( ( ~ ! [SY2599: $i] :
~ ~ ( ~ ( in @ SY2599 @ SV87 )
| ~ ~ ( SV325 @ SY2599 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1605]) ).
thf(1845,plain,
! [SV88: $i,SV326: $i] :
( ( ( ~ ( in @ ( sK7_SY2600 @ SV326 @ SV88 ) @ SV88 )
| ( in @ ( sK7_SY2600 @ SV326 @ SV88 ) @ SV326 ) )
= $false )
| ( ( ~ ! [SY2601: $i] :
( ~ ( in @ SY2601 @ SV326 )
| ( in @ SY2601 @ SV88 ) )
| ( SV88 = SV326 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1606]) ).
thf(1846,plain,
! [SV632: $i,SV91: $i > $o] :
( ( ( ~ ~ ( ~ ( SV91 @ SV632 )
| ~ ! [SY3087: $i] :
( ~ ( SV91 @ SY3087 )
| ( SV632 = SY3087 ) ) ) )
= $true )
| ( ( ! [SY2037: $i,SY2038: $i] :
( ~ ( SV91 @ SY2037 )
| ~ ( SV91 @ SY2038 )
| ( SY2037 = SY2038 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1847,plain,
! [SV514: $i,SV329: $i,SV92: $i] :
( ( ( func @ SV92 @ SV329 @ SV514 )
= $false )
| ( ( ! [SY2919: $i] :
( ~ ( in @ SY2919 @ SV92 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV329
@ ^ [SY2920: $i] : ( in @ ( kpair @ SY2919 @ SY2920 ) @ SV514 ) ) )
@ SV329 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1848,plain,
! [SV331: $i,SV94: $i,SV515: $i] :
( ( ( in @ SV515 @ SV94 )
= $false )
| ( ( ~ ~ ( in @ SV515 @ SV331 )
| ~ ( subset @ SV94 @ SV331 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1612]) ).
thf(1849,plain,
! [SV332: $i,SV95: $i,SV516: $i] :
( ( ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) )
= $false )
| ( ( ! [SY2921: $i] :
( ~ ( subset @ SY2921 @ ( cartprod @ SV95 @ SV332 ) )
| ~ ! [SY2922: $i] :
( ~ ( in @ SY2922 @ SV95 )
| ! [SY2923: $i] :
( ~ ( in @ SY2923 @ SV332 )
| ~ ( in @ ( kpair @ SY2922 @ SY2923 ) @ SV516 )
| ( in @ ( kpair @ SY2922 @ SY2923 ) @ SY2921 ) ) )
| ( subset @ SV516 @ SY2921 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1613]) ).
thf(1850,plain,
! [SV333: $i,SV96: $i] :
( ( ( ! [SY2610: $i] :
~ ~ ( ~ ( in @ SY2610 @ SV96 )
| ~ ( in @ SV333 @ SY2610 ) ) )
= $false )
| ( ( in @ SV333 @ ( setunion @ SV96 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1851,plain,
! [SV334: $i,SV97: $i,SV633: $i] :
( ( ( ~ ( in @ SV633 @ SV97 )
| ~ ~ ( in @ SV633 @ ( setminus @ SV97 @ SV334 ) )
| ( in @ SV633 @ SV334 ) )
= $true )
| ( ( in @ SV334 @ ( powerset @ SV97 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(1852,plain,
! [SV335: $i > $o,SV98: $i,SV517: $i] :
( ( ( in @ SV517 @ SV98 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV517
@ ( dsetconstr @ SV98
@ ^ [SY2613: $i] : ( SV335 @ SY2613 ) ) )
| ( SV335 @ SV517 ) )
| ~ ( ~ ( SV335 @ SV517 )
| ( in @ SV517
@ ( dsetconstr @ SV98
@ ^ [SY2614: $i] : ( SV335 @ SY2614 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1853,plain,
! [SV336: $i,SV99: $i] :
( ( ( ~ ( in @ ( sK8_SY2615 @ SV99 @ SV336 ) @ SV336 )
| ( in @ ( sK8_SY2615 @ SV99 @ SV336 ) @ SV99 ) )
= $false )
| ( ( in @ SV336 @ ( powerset @ SV99 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1617]) ).
thf(1854,plain,
! [SV337: $i > $o,SV100: $i,SV518: $i] :
( ( ( in @ SV518 @ SV100 )
= $false )
| ( ( ~ ( SV337 @ SV518 )
| ~ ! [SY2926: $i] :
( ~ ( in @ SY2926 @ SV100 )
| ~ ( SV337 @ SY2926 )
| ( SY2926 = SV518 ) )
| ( singleton
@ ( dsetconstr @ SV100
@ ^ [SY2618: $i] : ( SV337 @ SY2618 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1855,plain,
! [SV519: $i > $i > $o,SV338: $i,SV101: $i,SV634: $i,SV608: $i] :
( ( ~ ( in @ ( kpair @ SV608 @ SV634 )
@ ( dpsetconstr @ SV101 @ SV338
@ ^ [SY2930: $i,SY2931: $i] : ( SV519 @ SY2930 @ SY2931 ) ) )
| ( SV519 @ SV608 @ SV634 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(1856,plain,
( ( in @ sK2_SY2624 @ ( powerset @ sK1_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1620]) ).
thf(1857,plain,
( ( ~ ( in @ sK9_SY2932 @ ( powerset @ sK1_SX0 ) )
| ! [SY3090: $o,SY3091: $i] :
( ~ ( in @ SY3091 @ sK1_SX0 )
| ~ ( in @ SY3091 @ ( binunion @ sK2_SY2624 @ sK9_SY2932 ) )
| ~ ( ~ ( in @ SY3091 @ sK2_SY2624 )
| SY3090 )
| ~ ( ~ ( in @ SY3091 @ sK9_SY2932 )
| SY3090 )
| SY3090 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1621]) ).
thf(1858,plain,
! [SV340: $i,SV103: $i,SV520: $i] :
( ( ( in @ SV520 @ ( funcSet @ SV103 @ SV340 ) )
= $false )
| ( ( ( lam @ SV103 @ SV340
@ ^ [SY2935: $i] : ( ap @ SV103 @ SV340 @ SV520 @ SY2935 ) )
= SV520 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1623]) ).
thf(1859,plain,
! [SV341: $i,SV104: $i,SV521: $i] :
( ( ( in @ SV521 @ SV104 )
= $false )
| ( ( ! [SY2936: $i] :
( ~ ( in @ SY2936 @ SV341 )
| ( subset @ ( setadjoin @ SV521 @ ( setadjoin @ SY2936 @ emptyset ) ) @ ( binunion @ SV104 @ SV341 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1860,plain,
! [SV342: $i,SV105: $i,SV522: $i] :
( ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false )
| ( ( ! [SY2937: $i > $o] :
( ~ ! [SY2938: $i] :
( ~ ( in @ SY2938 @ SV105 )
| ! [SY2939: $i] :
( ~ ( in @ SY2939 @ SV342 )
| ~ ( in @ ( kpair @ SY2938 @ SY2939 ) @ SV522 )
| ( SY2937 @ ( kpair @ SY2938 @ SY2939 ) ) ) )
| ! [SY2940: $i] :
( ~ ( in @ SY2940 @ SV522 )
| ( SY2937 @ SY2940 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1861,plain,
! [SV635: $i,SV106: $i > $o] :
( ( ( ~ ~ ( ~ ( SV106 @ SV635 )
| ~ ! [SY3092: $i] :
( ~ ( SV106 @ SY3092 )
| ( SV635 = SY3092 ) ) ) )
= $true )
| ( ( ! [SY2086: $i,SY2087: $i] :
( ~ ( SV106 @ SY2086 )
| ~ ( SV106 @ SY2087 )
| ( SY2086 = SY2087 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(1862,plain,
! [SV343: $i > $o,SV107: $i,SV523: $i] :
( ( ( in @ SV523 @ SV107 )
= $false )
| ( ( ~ ( SV343 @ SV523 )
| ( in @ SV523
@ ( dsetconstr @ SV107
@ ^ [SY2638: $i] : ( SV343 @ SY2638 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1627]) ).
thf(1863,plain,
! [SV636: $i,SV108: $i > $o] :
( ( ( ~ ~ ( ~ ( SV108 @ SV636 )
| ~ ! [SY3093: $i] :
( ~ ( SV108 @ SY3093 )
| ( SV636 = SY3093 ) ) ) )
= $true )
| ( ( SV108
@ ( descr
@ ^ [SY2093: $i] : ( SV108 @ SY2093 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(1864,plain,
! [SV524: $i > $i > $o,SV344: $i,SV109: $i,SV637: $i,SV609: $i] :
( ( ~ ( in @ ( kpair @ SV609 @ SV637 )
@ ( dpsetconstr @ SV109 @ SV344
@ ^ [SY2944: $i,SY2945: $i] : ( SV524 @ SY2944 @ SY2945 ) ) )
| ( in @ SV609 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(1865,plain,
! [SV111: $i] :
( ( ( in @ ( sK5_SY2101 @ SV111 ) @ SV111 )
= $true )
| ( ( SV111 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1631]) ).
thf(1866,plain,
! [SV347: $i,SV113: $i,SV525: $i] :
( ( ( ~ ( in @ SV525 @ ( setminus @ SV113 @ SV347 ) ) )
= $false )
| ( ( ~ ~ ( in @ SV525 @ SV347 )
| ~ ( in @ SV525 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1633]) ).
thf(1867,plain,
! [SV638: $i,SV114: $i > $o] :
( ( ( ~ ~ ( ~ ( SV114 @ SV638 )
| ~ ! [SY3096: $i] :
( ~ ( SV114 @ SY3096 )
| ( SV638 = SY3096 ) ) ) )
= $true )
| ( ( ~ ! [SY2107: $i] :
~ ( SV114 @ SY2107 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1868,plain,
! [SV348: $i,SV115: $i,SV639: $i] :
( ( ( ~ ( in @ SV639 @ ( powerset @ SV115 ) )
| ! [SY3097: $i] :
( ~ ( in @ SY3097 @ ( powerset @ SV115 ) )
| ! [SY3098: $i] :
( ~ ( in @ SY3098 @ SV115 )
| ~ ( in @ SY3098 @ ( binintersect @ SV348 @ SV639 ) )
| ( in @ SY3098 @ ( binunion @ SV348 @ SY3097 ) ) ) ) )
= $true )
| ( ( in @ SV348 @ ( powerset @ SV115 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(1869,plain,
! [SV349: $i,SV117: $i,SV640: $i] :
( ( ( ~ ( in @ SV640 @ ( powerset @ SV117 ) )
| ( in @ ( binintersect @ SV349 @ SV640 ) @ ( powerset @ SV117 ) ) )
= $true )
| ( ( in @ SV349 @ ( powerset @ SV117 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(1870,plain,
! [SV118: $i,SV350: $i > $o] :
( ( ( ~ ( in @ ( sK10_SY2649 @ SV350 @ SV118 ) @ SV118 )
| ~ ( SV350 @ ( sK10_SY2649 @ SV350 @ SV118 ) ) )
= $false )
| ( ( ~ ~ ! [SY2650: $i] :
~ ~ ( ~ ( in @ SY2650 @ SV118 )
| ~ ( SV350 @ SY2650 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1637]) ).
thf(1871,plain,
! [SV351: $i > $o,SV119: $i] :
( ( ( ! [SY2651: $i] :
( ~ ( in @ SY2651 @ SV119 )
| ( SV351 @ SY2651 ) ) )
= $true )
| ( ( ~ ! [SY2652: $i] :
~ ~ ( ~ ( in @ SY2652 @ SV119 )
| ~ ~ ( SV351 @ SY2652 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1638]) ).
thf(1872,plain,
! [SV352: $i,SV120: $i,SV641: $i] :
( ( ( ~ ( in @ SV641 @ ( powerset @ SV120 ) )
| ! [SY3099: $i] :
( ~ ( in @ SY3099 @ SV120 )
| ~ ~ ( in @ SY3099 @ SV641 )
| ~ ( in @ SY3099 @ ( binintersect @ SV352 @ SV641 ) ) ) )
= $true )
| ( ( in @ SV352 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(1873,plain,
! [SV353: $i,SV121: $i,SV642: $i] :
( ( ( ~ ( in @ SV642 @ ( powerset @ SV121 ) )
| ~ ( subset @ SV353 @ ( setminus @ SV121 @ SV642 ) )
| ! [SY3100: $i] :
( ~ ( in @ SY3100 @ SV121 )
| ~ ( in @ SY3100 @ SV642 )
| ( in @ SY3100 @ ( setminus @ SV121 @ SV353 ) ) ) )
= $true )
| ( ( in @ SV353 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1874,plain,
! [SV354: $i,SV122: $i] :
( ( ( subset @ SV122 @ SV354 )
= $true )
| ( ( SV122 != SV354 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1641]) ).
thf(1875,plain,
! [SV355: $i,SV526: $i > $i,SV123: $i] :
( ( ( ! [SY2946: $i] :
( ~ ( in @ SY2946 @ SV123 )
| ( in @ ( SV526 @ SY2946 ) @ SV355 ) ) )
= $false )
| ( ( in
@ ( lam @ SV123 @ SV355
@ ^ [SY2947: $i] : ( SV526 @ SY2947 ) )
@ ( funcSet @ SV123 @ SV355 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1642]) ).
thf(1876,plain,
! [SV124: $i,SV527: $i,SV356: $i] :
( ( ( in @ SV356 @ SV527 )
= $false )
| ( ( ~ ( in @ SV527 @ SV124 )
| ( in @ SV356 @ ( setunion @ SV124 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1643]) ).
thf(1877,plain,
! [SV357: $i,SV125: $i,SV528: $i] :
( ( ( in @ ( setadjoin @ SV528 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV125 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV125 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV125 = SV528 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1644]) ).
thf(1878,plain,
! [SV358: $i,SV126: $i,SV529: $i] :
( ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false )
| ( ( ! [SY2948: $o] :
( ~ ( ( SV529 != SV126 )
| SY2948 )
| ~ ( ~ ( in @ SV529 @ SV358 )
| SY2948 )
| SY2948 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1645]) ).
thf(1879,plain,
! [SV359: $i,SV127: $i,SV530: $i] :
( ( ( ~ ( in @ SV530 @ SV127 ) )
= $false )
| ( ( ~ ~ ( in @ SV530 @ SV359 )
| ~ ( in @ SV530 @ ( symdiff @ SV127 @ SV359 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1880,plain,
! [SV360: $i,SV128: $i,SV531: $i] :
( ( ( in @ SV531 @ SV128 )
= $false )
| ( ( ! [SY2949: $i] :
( ~ ( in @ SY2949 @ SV360 )
| ( in @ ( setadjoin @ SV531 @ ( setadjoin @ SY2949 @ emptyset ) ) @ ( powerset @ ( binunion @ SV128 @ SV360 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1647]) ).
thf(1881,plain,
! [SV361: $i,SV129: $i,SV643: $i] :
( ( ( ~ ( in @ SV643 @ ( powerset @ SV129 ) )
| ~ ( subset @ SV361 @ ( setminus @ SV129 @ SV643 ) )
| ( subset @ SV643 @ ( setminus @ SV129 @ SV361 ) ) )
= $true )
| ( ( in @ SV361 @ ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(1882,plain,
! [SV362: $i,SV130: $i,SV644: $i] :
( ( ( ~ ( in @ SV644 @ ( powerset @ SV130 ) )
| ! [SY3101: $i] :
( ~ ( in @ SY3101 @ SV130 )
| ~ ~ ( in @ SY3101 @ SV362 )
| ~ ( in @ SY3101 @ ( binintersect @ SV362 @ SV644 ) ) ) )
= $true )
| ( ( in @ SV362 @ ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(1883,plain,
! [SV363: $i,SV131: $i,SV645: $i] :
( ( ( ~ ( in @ SV645 @ ( powerset @ SV131 ) )
| ! [SY3102: $i] :
( ~ ( in @ SY3102 @ SV131 )
| ~ ( in @ SY3102 @ ( setminus @ SV131 @ SV363 ) )
| ( in @ SY3102 @ ( setminus @ SV131 @ ( binintersect @ SV363 @ SV645 ) ) ) ) )
= $true )
| ( ( in @ SV363 @ ( powerset @ SV131 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(1884,plain,
! [SV364: $i,SV132: $i,SV532: $i] :
( ( ( in @ SV532 @ ( cartprod @ SV132 @ SV364 ) )
= $false )
| ( ( in @ ( ksnd @ SV532 ) @ SV364 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1651]) ).
thf(1885,plain,
! [SV365: $i,SV133: $i,SV646: $i] :
( ( ( ~ ( in @ SV646 @ SV133 )
| ~ ( in @ SV646 @ SV365 )
| ( in @ SV646 @ ( setminus @ SV133 @ ( setminus @ SV133 @ SV365 ) ) ) )
= $true )
| ( ( in @ SV365 @ ( powerset @ SV133 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(1886,plain,
! [SV533: $i,SV366: $i,SV134: $i] :
( ( ( func @ SV134 @ SV366 @ SV533 )
= $false )
| ( ( ( lam @ SV134 @ SV366
@ ^ [SY2950: $i] : ( ap @ SV134 @ SV366 @ SV533 @ SY2950 ) )
= SV533 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1653]) ).
thf(1887,plain,
! [SV367: $i > $o,SV135: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV135 )
| ! [SY3103: $i] :
( ~ ( in @ SY3103 @ SV135 )
| ~ ( SV367 @ SV647 )
| ~ ( SV367 @ SY3103 )
| ( SV647 = SY3103 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV135
@ ^ [SY2676: $i] : ( SV367 @ SY2676 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(1888,plain,
! [SV648: $o,SV136: $i,SV368: $i] :
( ( ( ~ ! [SY3104: $i] :
( ~ ( in @ SV368 @ SY3104 )
| ~ ( in @ SY3104 @ SV136 )
| SV648 )
| SV648 )
= $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1655]) ).
thf(1889,plain,
! [SV136: $i,SV368: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV368 @ SX0 )
| ~ ( in @ SX0 @ SV136 )
| $true )
| $true )
= $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1655]) ).
thf(1890,plain,
! [SV136: $i,SV368: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV368 @ SX0 )
| ~ ( in @ SX0 @ SV136 )
| $false )
| $false )
= $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1655]) ).
thf(1891,plain,
! [SV369: $i,SV137: $i,SV649: $i] :
( ( ( ~ ( in @ SV649 @ ( powerset @ SV137 ) )
| ! [SY3105: $i] :
( ~ ( in @ SY3105 @ SV137 )
| ~ ( subset @ SV369 @ SV649 )
| ~ ~ ( in @ SY3105 @ SV649 )
| ~ ( in @ SY3105 @ SV369 ) ) )
= $true )
| ( ( in @ SV369 @ ( powerset @ SV137 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(1892,plain,
! [SV370: $i,SV138: $i,SV534: $i] :
( ( ( in @ SV534 @ ( setadjoin @ SV138 @ ( setadjoin @ SV370 @ emptyset ) ) )
= $false )
| ( ( ( SV534 = SV138 )
| ( SV534 = SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1893,plain,
! [SV371: $i,SV140: $i,SV535: $i] :
( ( ( in @ SV535 @ ( cartprod @ SV140 @ SV371 ) )
= $false )
| ( ( iskpair @ SV535 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1658]) ).
thf(1894,plain,
! [SV141: $i,SV372: $i,SV536: $i] :
( ( ( in @ SV536 @ SV372 )
= $false )
| ( ( in @ SV536 @ ( setadjoin @ SV141 @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1895,plain,
! [SV373: $i,SV142: $i,SV610: $i,SV537: $i] :
( ( ( ~ ( in @ ( kpair @ SV537 @ SV610 ) @ ( cartprod @ SV142 @ SV373 ) ) )
= $true )
| ( ( in @ SV610 @ SV373 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1660]) ).
thf(1896,plain,
! [SV374: $i,SV143: $i,SV538: $i] :
( ( ( in @ SV538 @ ( funcSet @ SV143 @ SV374 ) )
= $false )
| ( ( ! [SY2952: $i] :
( ~ ( in @ SY2952 @ SV143 )
| ( in @ ( kpair @ SY2952 @ ( ap @ SV143 @ SV374 @ SV538 @ SY2952 ) ) @ SV538 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1661]) ).
thf(1897,plain,
! [SV376: $i,SV145: $i,SV539: $i] :
( ( ( in @ SV539 @ ( cartprod @ SV145 @ SV376 ) )
= $false )
| ( ( ( kpair @ ( kfst @ SV539 ) @ ( ksnd @ SV539 ) )
= SV539 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1898,plain,
! [SV377: $i,SV146: $i,SV650: $i] :
( ( ( ~ ( in @ SV650 @ ( powerset @ SV146 ) )
| ~ ! [SY3106: $i] :
( ~ ( in @ SY3106 @ SV146 )
| ~ ( in @ SY3106 @ SV377 )
| ( in @ SY3106 @ SV650 ) )
| ( subset @ SV377 @ SV650 ) )
= $true )
| ( ( in @ SV377 @ ( powerset @ SV146 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(1899,plain,
! [SV147: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY2953: $i] :
( ~ ( in @ SY2953 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY2188: $i] :
( ~ ( in @ SY2188 @ SY2953 )
| ( in @ SY2188 @ SV147 ) ) )
| ~ ! [SY2955: $i,SY2956: $i] :
( ~ ~ ( ~ ( in @ SY2955 @ SV147 )
| ~ ( in @ SY2956 @ SV147 ) )
| ~ ! [SY2957: $i] :
( ~ ( in @ SY2957 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SY2955 @ SY2957 )
| ( in @ SY2956 @ SY2957 ) )
| ~ ( ~ ( in @ SY2956 @ SY2957 )
| ( in @ SY2955 @ SY2957 ) ) ) )
| ( SY2955 = SY2956 ) ) )
| ~ ! [SY2958: $i,SY2959: $i] :
( ~ ~ ( ~ ( in @ SY2958 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY2959 @ ( sK3_SY2186 @ SV147 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2958 )
| ( in @ SX4 @ SY2959 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2959 )
| ( in @ SX4 @ SY2958 ) ) ) )
| ~ ! [SY2962: $i] :
( ~ ~ ( ~ ! [SY2197: $i] :
( ~ ( in @ SY2197 @ SY2962 )
| ( in @ SY2197 @ SV147 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY2962 ) )
| ~ ! [SY2965: $i] :
~ ~ ! [SY2966: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY2965 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY2966 @ SY2962 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY2965 )
| ~ ( in @ SX5 @ SY2962 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY2965 ) )
| ( in @ SY2966 @ SY2968 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1665]) ).
thf(1900,plain,
! [SV540: $i,SV378: $i,SV148: $i] :
( ( ( subset @ SV148 @ SV378 )
= $false )
| ( ( ~ ( in @ SV540 @ SV148 )
| ( in @ SV540 @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1666]) ).
thf(1901,plain,
! [SV150: $i,SV380: $i,SV541: $i] :
( ( ( in @ SV541 @ SV380 )
= $false )
| ( ( in @ SV541 @ ( binunion @ SV150 @ SV380 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1902,plain,
! [SV381: $i,SV151: $i,SV651: $i] :
( ( ( ~ ( in @ SV651 @ ( powerset @ SV151 ) )
| ! [SY3107: $i] :
( ~ ( in @ SY3107 @ ( powerset @ SV151 ) )
| ! [SY3108: $i] :
( ~ ( in @ SY3108 @ SV151 )
| ~ ( in @ SY3108 @ ( binintersect @ SV381 @ SV651 ) )
| ( in @ SY3108 @ ( binunion @ SV651 @ SY3107 ) ) ) ) )
= $true )
| ( ( in @ SV381 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(1903,plain,
! [SV383: $i,SV153: $i,SV611: $i,SV542: $i] :
( ( ( ~ ( in @ ( kpair @ SV542 @ SV611 ) @ ( cartprod @ SV153 @ SV383 ) ) )
= $true )
| ( ( in @ SV542 @ SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1671]) ).
thf(1904,plain,
! [SV384: $i,SV154: $i,SV543: $i] :
( ( ( in @ SV543 @ ( binunion @ SV154 @ SV384 ) )
= $false )
| ( ( ( in @ SV543 @ SV154 )
| ( in @ SV543 @ SV384 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1672]) ).
thf(1905,plain,
! [SV155: $i,SV385: $i] :
( ( ( ~ ( in @ ( sK11_SY2701 @ SV385 @ SV155 ) @ SV155 )
| ( in @ ( sK11_SY2701 @ SV385 @ SV155 ) @ SV385 ) )
= $false )
| ( ( subset @ SV155 @ SV385 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1673]) ).
thf(1906,plain,
! [SV386: $i,SV156: $i,SV652: $i] :
( ( ( ~ ( in @ SV652 @ ( powerset @ SV156 ) )
| ! [SY3109: $i] :
( ~ ( in @ SY3109 @ SV156 )
| ~ ( subset @ SV386 @ ( setminus @ SV156 @ SV652 ) )
| ~ ( in @ SY3109 @ SV652 )
| ~ ( in @ SY3109 @ SV386 ) ) )
= $true )
| ( ( in @ SV386 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(1907,plain,
! [SV387: $i > $o,SV157: $i,SV544: $i] :
( ( ( in @ SV544
@ ( dsetconstr @ SV157
@ ^ [SY2705: $i] : ( SV387 @ SY2705 ) ) )
= $false )
| ( ( in @ SV544 @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1675]) ).
thf(1908,plain,
! [SV388: $i,SV158: $i,SV545: $i] :
( ( ( ~ ( in @ SV545 @ ( setminus @ SV158 @ SV388 ) ) )
= $false )
| ( ( ~ ( in @ SV545 @ SV158 )
| ( in @ SV545 @ SV388 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1676]) ).
thf(1909,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ( SV160 @ SV653 ) )
= $true )
| ( ( ~ ! [SY2231: $i,SY2232: $i] :
( ~ ( SV160 @ SY2231 )
| ~ ( SV160 @ SY2232 )
| ( SY2231 = SY2232 ) )
| ~ ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(1910,plain,
! [SV390: $i,SV161: $i,SV654: $i] :
( ( ( ~ ( in @ SV654 @ ( powerset @ SV161 ) )
| ( in @ ( setminus @ SV161 @ SV390 ) @ ( powerset @ ( setminus @ SV161 @ ( binintersect @ SV390 @ SV654 ) ) ) ) )
= $true )
| ( ( in @ SV390 @ ( powerset @ SV161 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(1911,plain,
! [SV391: $i,SV162: $i,SV655: $i] :
( ( ( ~ ( in @ SV655 @ ( powerset @ SV162 ) )
| ( in @ ( setminus @ SV391 @ SV655 ) @ ( powerset @ SV162 ) ) )
= $true )
| ( ( in @ SV391 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(1912,plain,
! [SV392: $i,SV164: $i,SV546: $i] :
( ( ( in @ SV546 @ SV164 )
= $false )
| ( ( ~ ~ ( in @ SV546 @ SV392 )
| ( in @ SV546 @ ( symdiff @ SV164 @ SV392 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1681]) ).
thf(1913,plain,
! [SV393: $i,SV165: $i,SV656: $i] :
( ( ( ! [SY3110: $i] :
( ( SV656 != SY3110 )
| ~ ( in @ SV656 @ SV165 )
| ( in @ SY3110 @ SV393 ) ) )
= $true )
| ( ( SV165 = SV393 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(1914,plain,
! [SV394: $i,SV166: $i,SV547: $i] :
( ( ( in @ SV547 @ SV166 )
= $false )
| ( ( ~ ~ ( in @ SV547 @ SV394 )
| ( SV166 != SV394 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1683]) ).
thf(1915,plain,
! [SV395: $i,SV167: $i,SV657: $i] :
( ( ( ~ ( in @ SV657 @ ( powerset @ SV167 ) )
| ! [SY3111: $i] :
( ~ ( in @ SY3111 @ SV167 )
| ~ ( in @ SY3111 @ ( setminus @ SV167 @ ( binunion @ SV395 @ SV657 ) ) )
| ( in @ SY3111 @ ( setminus @ SV167 @ SV395 ) ) ) )
= $true )
| ( ( in @ SV395 @ ( powerset @ SV167 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(1916,plain,
! [SV548: $i,SV396: $i,SV168: $i] :
( ( ( func @ SV168 @ SV396 @ SV548 )
= $false )
| ( ( ! [SY2972: $i] :
( ~ ( func @ SV168 @ SV396 @ SY2972 )
| ~ ! [SY2973: $i] :
( ~ ( in @ SY2973 @ SV168 )
| ( ( ap @ SV168 @ SV396 @ SV548 @ SY2973 )
= ( ap @ SV168 @ SV396 @ SY2972 @ SY2973 ) ) )
| ( SV548 = SY2972 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1917,plain,
! [SV397: $o,SV169: $i,SV549: $i] :
( ( ( in @ SV549 @ SV169 )
= $false )
| ( ( ! [SY2974: $i] :
( ~ ( in @ SY2974 @ SV169 )
| ( in @ ( if @ SV169 @ SV397 @ SV549 @ SY2974 ) @ ( setadjoin @ SV549 @ ( setadjoin @ SY2974 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1686]) ).
thf(1918,plain,
! [SV169: $i,SV550: $i] :
( ( ( in @ SV550 @ SV169 )
= $false )
| ( ( ! [SY2975: $i] :
( ~ ( in @ SY2975 @ SV169 )
| ( in @ ( if @ SV169 @ $true @ SV550 @ SY2975 ) @ ( setadjoin @ SV550 @ ( setadjoin @ SY2975 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1687]) ).
thf(1919,plain,
! [SV169: $i,SV551: $i] :
( ( ( in @ SV551 @ SV169 )
= $false )
| ( ( ! [SY2976: $i] :
( ~ ( in @ SY2976 @ SV169 )
| ( in @ ( if @ SV169 @ $false @ SV551 @ SY2976 ) @ ( setadjoin @ SV551 @ ( setadjoin @ SY2976 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1920,plain,
! [SV398: $i,SV552: $i > $i,SV170: $i] :
( ( ( ! [SY2977: $i] :
( ~ ( in @ SY2977 @ SV170 )
| ( in @ ( SV552 @ SY2977 ) @ SV398 ) ) )
= $false )
| ( ( ( lam @ SV170 @ SV398
@ ^ [SY2978: $i] : ( SV552 @ SY2978 ) )
= ( lam @ SV170 @ SV398
@ ^ [SY2979: $i] : ( SV552 @ SY2979 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1689]) ).
thf(1921,plain,
! [SV399: $o,SV171: $i,SV553: $i] :
( ( ( in @ SV553 @ SV171 )
= $false )
| ( ( ! [SY2980: $i] :
( ~ ( in @ SY2980 @ SV171 )
| ~ ~ SV399
| ( ( dsetconstr @ SV171
@ ^ [SY2981: $i] :
( ~ ( ~ SV399
| ( SY2981 != SV553 ) )
| ~ ( ~ ~ SV399
| ( SY2981 != SY2980 ) ) ) )
= ( setadjoin @ SY2980 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1690]) ).
thf(1922,plain,
! [SV171: $i,SV554: $i] :
( ( ( in @ SV554 @ SV171 )
= $false )
| ( ( ! [SY2982: $i] :
( ~ ( in @ SY2982 @ SV171 )
| ~ ~ $true
| ( ( dsetconstr @ SV171
@ ^ [SY2983: $i] :
( ~ ( ~ $true
| ( SY2983 != SV554 ) )
| ~ ( ~ ~ $true
| ( SY2983 != SY2982 ) ) ) )
= ( setadjoin @ SY2982 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1691]) ).
thf(1923,plain,
! [SV171: $i,SV555: $i] :
( ( ( in @ SV555 @ SV171 )
= $false )
| ( ( ! [SY2984: $i] :
( ~ ( in @ SY2984 @ SV171 )
| ~ ~ $false
| ( ( dsetconstr @ SV171
@ ^ [SY2985: $i] :
( ~ ( ~ $false
| ( SY2985 != SV555 ) )
| ~ ( ~ ~ $false
| ( SY2985 != SY2984 ) ) ) )
= ( setadjoin @ SY2984 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1692]) ).
thf(1924,plain,
! [SV172: $i,SV400: $i] :
( ( ~ ( in @ SV400 @ ( powerset @ SV172 ) )
| ! [SY2727: $i] :
( ~ ( in @ SY2727 @ SV400 )
| ( in @ SY2727 @ SV172 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1693]) ).
thf(1925,plain,
! [SV172: $i,SV400: $i] :
( ( ~ ! [SY2728: $i] :
( ~ ( in @ SY2728 @ SV400 )
| ( in @ SY2728 @ SV172 ) )
| ( in @ SV400 @ ( powerset @ SV172 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1694]) ).
thf(1926,plain,
! [SV612: $i,SV556: $i,SV401: $i,SV173: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV173 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV173 @ ( setadjoin @ SV401 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV556 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV556 @ ( setadjoin @ SV612 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV401 = SV612 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1695]) ).
thf(1927,plain,
! [SV402: $i,SV174: $i,SV557: $i] :
( ( ( in @ SV557 @ SV174 )
= $false )
| ( ( ! [SY2987: $i] :
( ~ ( in @ SY2987 @ SV402 )
| ( ( kfst @ ( kpair @ SV557 @ SY2987 ) )
= SV557 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(1928,plain,
! [SV403: $i,SV175: $i,SV558: $i] :
( ( ( in @ SV558 @ ( funcSet @ SV175 @ SV403 ) )
= $false )
| ( ( ! [SY2988: $i] :
( ~ ( in @ SY2988 @ SV175 )
| ( in @ ( ap @ SV175 @ SV403 @ SV558 @ SY2988 ) @ SV403 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1697]) ).
thf(1929,plain,
! [SV404: $i,SV176: $i,SV658: $i] :
( ( ( ~ ( in @ SV658 @ ( powerset @ SV176 ) )
| ~ ( subset @ SV404 @ SV658 )
| ( subset @ ( setminus @ SV176 @ SV658 ) @ ( setminus @ SV176 @ SV404 ) ) )
= $true )
| ( ( in @ SV404 @ ( powerset @ SV176 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(1930,plain,
! [SV559: $i,SV405: $i,SV177: $i] :
( ( ( subset @ SV177 @ SV405 )
= $false )
| ( ( ~ ( subset @ SV405 @ SV559 )
| ( subset @ SV177 @ SV559 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1931,plain,
! [SV406: $i,SV178: $i,SV560: $i] :
( ( ( in @ SV560 @ ( binintersect @ SV178 @ SV406 ) )
= $false )
| ( ( in @ SV560 @ SV178 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1932,plain,
! [SV408: $i > $o,SV180: $i] :
( ( ( ! [SY2738: $i] :
~ ~ ( ~ ( in @ SY2738 @ SV180 )
| ~ ( SV408 @ SY2738 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV180
@ ^ [SY2739: $i] : ( SV408 @ SY2739 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1702]) ).
thf(1933,plain,
! [SV181: $i,SV409: $i > $o] :
( ( ( ~ ( in @ ( sK12_SY2740 @ SV409 @ SV181 ) @ SV181 )
| ! [SY3112: $i] :
( ~ ( in @ SY3112 @ SV181 )
| ~ ( SV409 @ ( sK12_SY2740 @ SV409 @ SV181 ) )
| ~ ( SV409 @ SY3112 )
| ( ( sK12_SY2740 @ SV409 @ SV181 )
= SY3112 ) ) )
= $false )
| ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) )
| ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1703]) ).
thf(1934,plain,
! [SV183: $i > $o,SV411: $i > $o] :
( ( ( ! [SY3113: $i] :
( ( ( sK13_SY2744 @ SV411 @ SV183 )
!= SY3113 )
| ~ ( ~ ( ~ ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
| ( SV411 @ SY3113 ) )
| ~ ( ~ ( SV411 @ SY3113 )
| ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1705]) ).
thf(1935,plain,
! [SV413: $i,SV185: $i,SV561: $i] :
( ( ( in @ SV561 @ ( funcSet @ SV185 @ SV413 ) )
= $false )
| ( ( ! [SY2989: $i] :
( ~ ( in @ SY2989 @ SV185 )
| ! [SY2990: $i] :
( ~ ( in @ SY2990 @ SV413 )
| ~ ( in @ ( kpair @ SY2989 @ SY2990 ) @ SV561 )
| ( ( ap @ SV185 @ SV413 @ SV561 @ SY2989 )
= SY2990 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1707]) ).
thf(1936,plain,
! [SV414: $i,SV186: $i,SV659: $i] :
( ( ( ~ ( in @ SV659 @ ( powerset @ SV186 ) )
| ~ ! [SY3114: $i] :
( ~ ( in @ SY3114 @ SV186 )
| ~ ( in @ SY3114 @ SV414 )
| ( in @ SY3114 @ SV659 ) )
| ~ ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV186 )
| ~ ( in @ SY3115 @ SV659 )
| ( in @ SY3115 @ SV414 ) )
| ( SV414 = SV659 ) )
= $true )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(1937,plain,
! [SV415: $i > $o,SV187: $i,SV562: $i] :
( ( ( in @ SV562 @ SV187 )
= $false )
| ( ( ~ ( SV415 @ SV562 )
| ( ( dsetconstr @ SV187
@ ^ [SY2759: $i] : ( SV415 @ SY2759 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(1938,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ~ ~ ( ~ ( SV188 @ SV660 )
| ~ ! [SY3116: $i] :
( ~ ( SV188 @ SY3116 )
| ( SV660 = SY3116 ) ) ) )
= $true )
| ( ( ~ ! [SY2316: $i] :
~ ~ ( ~ ( SV188 @ SY2316 )
| ~ ! [SY2317: $i] :
( ~ ( SV188 @ SY2317 )
| ( SY2316 = SY2317 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(1939,plain,
! [SV416: $i,SV189: $i,SV563: $i] :
( ( ( in @ SV563 @ ( setadjoin @ SV189 @ SV416 ) )
= $false )
| ( ( ( SV563 = SV189 )
| ( in @ SV563 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(1940,plain,
! [SV417: $i,SV190: $i,SV564: $i] :
( ( ( in @ SV564 @ ( funcSet @ SV190 @ SV417 ) )
= $false )
| ( ( ! [SY2992: $i] :
( ~ ( in @ SY2992 @ SV190 )
| ( ( ap @ SV190 @ SV417 @ SV564 @ SY2992 )
= ( ap @ SV190 @ SV417 @ SV564 @ SY2992 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1941,plain,
! [SV418: $i,SV191: $i,SV661: $i] :
( ( ( ~ ( in @ SV661 @ ( powerset @ SV191 ) )
| ! [SY3117: $i] :
( ~ ( in @ SY3117 @ ( powerset @ SV191 ) )
| ! [SY3118: $i] :
( ~ ( in @ SY3118 @ SV191 )
| ~ ( in @ SY3118 @ ( binintersect @ SV418 @ SV661 ) )
| ( in @ SY3118 @ ( binintersect @ ( binunion @ SV418 @ SY3117 ) @ ( binunion @ SV661 @ SY3117 ) ) ) ) ) )
= $true )
| ( ( in @ SV418 @ ( powerset @ SV191 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(1942,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ! [SY3119: $i] :
( ( ( sK14_SY2766 @ SV422 @ SV193 )
!= SY3119 )
| ~ ( ~ ( ~ ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
| ( SV422 @ SY3119 ) )
| ~ ( ~ ( SV422 @ SY3119 )
| ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1717]) ).
thf(1943,plain,
! [SV194: $i,SV613: $i] :
( ( ( ~ ( in @ SV613 @ SV194 ) )
= $true )
| ( ( ( setunion @ SV194 )
= SV613 )
= $true )
| ( ( singleton @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1718]) ).
thf(1944,plain,
! [SV423: $i,SV195: $i,SV565: $i] :
( ( ( in @ SV565 @ SV195 )
= $false )
| ( ( ~ ~ ( in @ SV565 @ SV423 )
| ( in @ SV565 @ ( setminus @ SV195 @ SV423 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1945,plain,
! [SV424: $i,SV196: $i,SV566: $i] :
( ( ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) )
= $false )
| ( ( ~ ! [SY2993: $i] :
~ ~ ( ~ ( in @ SY2993 @ SV196 )
| ~ ~ ! [SY2994: $i] :
~ ~ ( ~ ( in @ SY2994 @ SV424 )
| ( SV566
!= ( kpair @ SY2993 @ SY2994 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1720]) ).
thf(1946,plain,
! [SV425: $o,SV197: $i,SV567: $i] :
( ( ( in @ SV567 @ SV197 )
= $false )
| ( ( ! [SY2995: $i] :
( ~ ( in @ SY2995 @ SV197 )
| ~ SV425
| ( ( if @ SV197 @ SV425 @ SV567 @ SY2995 )
= SV567 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1947,plain,
! [SV197: $i,SV568: $i] :
( ( ( in @ SV568 @ SV197 )
= $false )
| ( ( ! [SY2996: $i] :
( ~ ( in @ SY2996 @ SV197 )
| ~ $true
| ( ( if @ SV197 @ $true @ SV568 @ SY2996 )
= SV568 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1948,plain,
! [SV197: $i,SV569: $i] :
( ( ( in @ SV569 @ SV197 )
= $false )
| ( ( ! [SY2997: $i] :
( ~ ( in @ SY2997 @ SV197 )
| ~ $false
| ( ( if @ SV197 @ $false @ SV569 @ SY2997 )
= SV569 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1723]) ).
thf(1949,plain,
! [SV426: $i,SV198: $i,SV570: $i] :
( ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( ! [SY2998: $i] :
( ~ ( subset @ SY2998 @ ( cartprod @ SV198 @ SV426 ) )
| ~ ! [SY2999: $i] :
( ~ ( in @ SY2999 @ SV198 )
| ! [SY3000: $i] :
( ~ ( in @ SY3000 @ SV426 )
| ~ ( in @ ( kpair @ SY2999 @ SY3000 ) @ SV570 )
| ( in @ ( kpair @ SY2999 @ SY3000 ) @ SY2998 ) ) )
| ~ ! [SY3001: $i] :
( ~ ( in @ SY3001 @ SV198 )
| ! [SY3002: $i] :
( ~ ( in @ SY3002 @ SV426 )
| ~ ( in @ ( kpair @ SY3001 @ SY3002 ) @ SY2998 )
| ( in @ ( kpair @ SY3001 @ SY3002 ) @ SV570 ) ) )
| ( SV570 = SY2998 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(1950,plain,
! [SV428: $i,SV200: $i,SV571: $i] :
( ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false )
| ( ( ! [SY3003: $i > $o] :
( ~ ! [SY3004: $i] :
( ~ ( in @ SY3004 @ SV200 )
| ! [SY3005: $i] :
( ~ ( in @ SY3005 @ SV428 )
| ~ ( in @ ( kpair @ SY3004 @ SY3005 ) @ SV571 )
| ( SY3003 @ ( kpair @ SY3004 @ SY3005 ) ) ) )
| ! [SY3006: $i] :
( ~ ( in @ SY3006 @ SV571 )
| ( SY3003 @ SY3006 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1726]) ).
thf(1951,plain,
! [SV429: $i > $o,SV201: $i] :
( ( ( ! [SY2793: $i] :
~ ~ ( ~ ( in @ SY2793 @ SV201 )
| ~ ~ ( SV429 @ SY2793 ) ) )
= $true )
| ( ( ~ ! [SY2794: $i] :
( ~ ( in @ SY2794 @ SV201 )
| ( SV429 @ SY2794 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1727]) ).
thf(1952,plain,
! [SV430: $i,SV572: $i > $i,SV203: $i] :
( ( ( ! [SY3007: $i] :
( ~ ( in @ SY3007 @ SV203 )
| ( in @ ( SV572 @ SY3007 ) @ SV430 ) ) )
= $false )
| ( ( func @ SV203 @ SV430
@ ( dpsetconstr @ SV203 @ SV430
@ ^ [SY3008: $i,SY3009: $i] :
( ( SV572 @ SY3008 )
= SY3009 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1728]) ).
thf(1953,plain,
! [SV204: $i,SV662: $i] :
( ( ( ~ ( in @ SV662 @ SV204 ) )
= $true )
| ( ( SV204 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(1954,plain,
! [SV431: $i,SV206: $i,SV573: $i] :
( ( ( ~ ( in @ SV573 @ SV206 ) )
= $false )
| ( ( ~ ( in @ SV573 @ SV431 )
| ( in @ SV573 @ ( symdiff @ SV206 @ SV431 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(1955,plain,
! [SV433: $i,SV574: $i > $i,SV209: $i] :
( ( ( ! [SY3010: $i] :
( ~ ( in @ SY3010 @ SV209 )
| ( in @ ( SV574 @ SY3010 ) @ SV433 ) ) )
= $false )
| ( ( ! [SY3011: $i] :
( ~ ( in @ SY3011 @ SV209 )
| ( ( ap @ SV209 @ SV433
@ ( lam @ SV209 @ SV433
@ ^ [SY3012: $i] : ( SV574 @ SY3012 ) )
@ SY3011 )
= ( SV574 @ SY3011 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1735]) ).
thf(1956,plain,
! [SV435: $i,SV211: $i,SV663: $i] :
( ( ( ! [SY3120: $i] :
( ( SV663 != SY3120 )
| ( ( setadjoin @ SV211 @ SV663 )
= ( setadjoin @ SV435 @ SY3120 ) ) ) )
= $true )
| ( ( SV211 = SV435 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(1957,plain,
! [SV212: $i,SV436: $i > $o] :
( ( ( ~ ( in @ ( sK15_SY2806 @ SV436 @ SV212 ) @ SV212 )
| ! [SY3121: $i] :
( ~ ( in @ SY3121 @ SV212 )
| ~ ( SV436 @ ( sK15_SY2806 @ SV436 @ SV212 ) )
| ~ ( SV436 @ SY3121 )
| ( ( sK15_SY2806 @ SV436 @ SV212 )
= SY3121 ) ) )
= $false )
| ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) )
| ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1738]) ).
thf(1958,plain,
! [SV615: $i,SV575: $i,SV438: $i,SV214: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV214 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV214 @ ( setadjoin @ SV438 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV575 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV575 @ ( setadjoin @ SV615 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( ( SV575 != SV615 )
| ( SV438 = SV615 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1740]) ).
thf(1959,plain,
! [SV215: $i] :
( ( ( ~ ( in @ emptyset @ SV215 ) )
= $true )
| ( ( ~ ! [SY2395: $i] :
( ~ ~ ( ~ ( in @ SY2395 @ omega )
| ~ ( in @ SY2395 @ SV215 ) )
| ( in @ ( setadjoin @ SY2395 @ SY2395 ) @ SV215 ) ) )
= $true )
| ( ( ! [SY2396: $i] :
( ~ ( in @ SY2396 @ omega )
| ( in @ SY2396 @ SV215 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1741]) ).
thf(1960,plain,
! [SV439: $i,SV216: $i,SV576: $i] :
( ( ( in @ SV576 @ SV216 )
= $false )
| ( ( ! [SY3014: $i] :
( ~ ( in @ SY3014 @ SV439 )
| ( in @ ( kpair @ SV576 @ SY3014 ) @ ( powerset @ ( powerset @ ( binunion @ SV216 @ SV439 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1742]) ).
thf(1961,plain,
! [SV577: $i > $i > $o,SV440: $i,SV217: $i,SV616: $i] :
( ( ( ~ ( in @ SV616 @ SV217 ) )
= $true )
| ( ( ! [SY3067: $i] :
( ~ ( in @ SY3067 @ SV440 )
| ~ ( SV577 @ SV616 @ SY3067 )
| ( in @ ( kpair @ SV616 @ SY3067 )
@ ( dpsetconstr @ SV217 @ SV440
@ ^ [SY3017: $i,SY3018: $i] : ( SV577 @ SY3017 @ SY3018 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1743]) ).
thf(1962,plain,
! [SV441: $o,SV218: $i,SV578: $i] :
( ( ( in @ SV578 @ SV218 )
= $false )
| ( ( ! [SY3019: $i] :
( ~ ( in @ SY3019 @ SV218 )
| ( in @ ( if @ SV218 @ SV441 @ SV578 @ SY3019 ) @ SV218 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1963,plain,
! [SV218: $i,SV579: $i] :
( ( ( in @ SV579 @ SV218 )
= $false )
| ( ( ! [SY3020: $i] :
( ~ ( in @ SY3020 @ SV218 )
| ( in @ ( if @ SV218 @ $true @ SV579 @ SY3020 ) @ SV218 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1745]) ).
thf(1964,plain,
! [SV218: $i,SV580: $i] :
( ( ( in @ SV580 @ SV218 )
= $false )
| ( ( ! [SY3021: $i] :
( ~ ( in @ SY3021 @ SV218 )
| ( in @ ( if @ SV218 @ $false @ SV580 @ SY3021 ) @ SV218 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(1965,plain,
! [SV442: $i,SV219: $i,SV581: $i] :
( ( ( in @ SV581 @ ( funcSet @ SV219 @ SV442 ) )
= $false )
| ( ( ! [SY3022: $i] :
( ~ ( in @ SY3022 @ ( funcSet @ SV219 @ SV442 ) )
| ~ ! [SY3023: $i] :
( ~ ( in @ SY3023 @ SV219 )
| ( ( ap @ SV219 @ SV442 @ SV581 @ SY3023 )
= ( ap @ SV219 @ SV442 @ SY3022 @ SY3023 ) ) )
| ( SV581 = SY3022 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(1966,plain,
! [SV582: $i > $i > $o,SV443: $i,SV220: $i,SV617: $i] :
( ( ( ~ ( in @ SV617 @ SV220 ) )
= $true )
| ( ( ! [SY3070: $i] :
( ~ ( in @ SY3070 @ SV443 )
| ~ ( in @ ( kpair @ SV617 @ SY3070 )
@ ( dpsetconstr @ SV220 @ SV443
@ ^ [SY3026: $i,SY3027: $i] : ( SV582 @ SY3026 @ SY3027 ) ) )
| ( SV582 @ SV617 @ SY3070 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1748]) ).
thf(1967,plain,
! [SV583: $i,SV444: $i,SV221: $i] :
( ( ( func @ SV221 @ SV444 @ SV583 )
= $false )
| ( ( ! [SY3028: $i] :
( ~ ( in @ SY3028 @ SV221 )
| ( in @ ( ap @ SV221 @ SV444 @ SV583 @ SY3028 ) @ SV444 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1968,plain,
! [SV445: $i,SV222: $i,SV584: $i] :
( ( ( in @ SV584 @ SV222 )
= $false )
| ( ( in @ ( setadjoin @ SV584 @ emptyset ) @ ( powerset @ ( binunion @ SV222 @ SV445 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1750]) ).
thf(1969,plain,
! [SV446: $i > $o,SV223: $i] :
( ( ( ! [SY2833: $i] :
~ ~ ( ~ ( in @ SY2833 @ SV223 )
| ~ ( SV446 @ SY2833 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY2832: $i] : ( SV446 @ SY2832 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1751]) ).
thf(1970,plain,
! [SV447: $i,SV224: $i] :
( ( ( SV224 = SV447 )
= $true )
| ( ( ~ ( in @ SV447 @ ( setadjoin @ SV224 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1752]) ).
thf(1971,plain,
! [SV225: $i,SV448: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 )
| ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 ) )
| ~ ( ~ ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 )
| ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 ) ) ) )
= $false )
| ( ( SV225 = SV448 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1753]) ).
thf(1972,plain,
! [SV449: $i,SV226: $i,SV585: $i] :
( ( ( in @ SV585 @ SV226 )
= $false )
| ( ( ~ ( in @ SV585 @ SV449 )
| ~ ( in @ SV585 @ ( symdiff @ SV226 @ SV449 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1754]) ).
thf(1973,plain,
! [SV450: $i,SV227: $i,SV664: $i] :
( ( ( ~ ( in @ SV664 @ SV227 )
| ~ ( in @ SV664 @ ( setminus @ SV227 @ ( setminus @ SV227 @ SV450 ) ) )
| ( in @ SV664 @ SV450 ) )
= $true )
| ( ( in @ SV450 @ ( powerset @ SV227 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(1974,plain,
! [SV618: $i,SV586: $i,SV451: $i,SV228: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV228 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV228 @ ( setadjoin @ SV451 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV586 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV586 @ ( setadjoin @ SV618 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV228 = SV586 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1756]) ).
thf(1975,plain,
! [SV452: $i,SV229: $i,SV665: $i] :
( ( ( ~ ( in @ SV665 @ ( powerset @ SV229 ) )
| ! [SY3122: $i] :
( ~ ( in @ SY3122 @ ( powerset @ SV229 ) )
| ( in @ ( binintersect @ SV452 @ SV665 ) @ ( powerset @ ( binintersect @ ( binunion @ SV452 @ SY3122 ) @ ( binunion @ SV665 @ SY3122 ) ) ) ) ) )
= $true )
| ( ( in @ SV452 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(1976,plain,
! [SV230: $i] :
( ( ( ! [SY2440: $i] :
~ ~ ( ~ ( in @ SY2440 @ SV230 )
| ~ $true ) )
= $false )
| ( ( SV230 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1977,plain,
! [SV453: $o,SV231: $i,SV587: $i] :
( ( ( in @ SV587 @ SV231 )
= $false )
| ( ( ! [SY3030: $i] :
( ~ ( in @ SY3030 @ SV231 )
| ~ SV453
| ( ( dsetconstr @ SV231
@ ^ [SY3031: $i] :
( ~ ( ~ SV453
| ( SY3031 != SV587 ) )
| ~ ( ~ ~ SV453
| ( SY3031 != SY3030 ) ) ) )
= ( setadjoin @ SV587 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1759]) ).
thf(1978,plain,
! [SV231: $i,SV588: $i] :
( ( ( in @ SV588 @ SV231 )
= $false )
| ( ( ! [SY3032: $i] :
( ~ ( in @ SY3032 @ SV231 )
| ~ $true
| ( ( dsetconstr @ SV231
@ ^ [SY3033: $i] :
( ~ ( ~ $true
| ( SY3033 != SV588 ) )
| ~ ( ~ ~ $true
| ( SY3033 != SY3032 ) ) ) )
= ( setadjoin @ SV588 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1760]) ).
thf(1979,plain,
! [SV231: $i,SV589: $i] :
( ( ( in @ SV589 @ SV231 )
= $false )
| ( ( ! [SY3034: $i] :
( ~ ( in @ SY3034 @ SV231 )
| ~ $false
| ( ( dsetconstr @ SV231
@ ^ [SY3035: $i] :
( ~ ( ~ $false
| ( SY3035 != SV589 ) )
| ~ ( ~ ~ $false
| ( SY3035 != SY3034 ) ) ) )
= ( setadjoin @ SV589 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1761]) ).
thf(1980,plain,
! [SV590: $i,SV232: $i,SV454: $i] :
( ( ( in @ SV454 @ ( powerset @ SV232 ) )
= $false )
| ( ( ~ ( in @ SV590 @ SV454 )
| ( in @ SV590 @ SV232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1762]) ).
thf(1981,plain,
! [SV455: $i,SV233: $i,SV666: $i] :
( ( ( ~ ( in @ SV666 @ SV233 )
| ~ ( in @ SV666 @ SV455 )
| ~ ( in @ SV666 @ ( setminus @ SV233 @ SV455 ) ) )
= $true )
| ( ( in @ SV455 @ ( powerset @ SV233 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(1982,plain,
! [SV456: $i,SV591: $i > $i,SV234: $i] :
( ( ( ! [SY3036: $i] :
( ~ ( in @ SY3036 @ SV234 )
| ( in @ ( SV591 @ SY3036 ) @ SV456 ) ) )
= $false )
| ( ( ! [SY3037: $i] :
( ~ ( in @ SY3037 @ SV234 )
| ( ( ap @ SV234 @ SV456
@ ( lam @ SV234 @ SV456
@ ^ [SY3038: $i] : ( SV591 @ SY3038 ) )
@ SY3037 )
= ( SV591 @ SY3037 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1764]) ).
thf(1983,plain,
! [SV457: $i,SV235: $i] :
( ( ( ~ ! [SY2850: $i] :
~ ~ ( ~ ( in @ SY2850 @ SV235 )
| ~ ( in @ SY2850 @ SV457 ) ) )
= $true )
| ( ( ( binintersect @ SV235 @ SV457 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1765]) ).
thf(1984,plain,
! [SV619: $i,SV592: $i,SV458: $i,SV236: $i] :
( ( ( ( kpair @ SV236 @ SV458 )
!= ( kpair @ SV592 @ SV619 ) )
= $true )
| ( ( SV236 = SV592 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1766]) ).
thf(1985,plain,
! [SV459: $i,SV593: $i,SV237: $i] :
( ( ( subset @ SV237 @ SV593 )
= $false )
| ( ( subset @ SV237 @ ( setadjoin @ SV459 @ SV593 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1767]) ).
thf(1986,plain,
! [SV460: $i,SV238: $i,SV594: $i] :
( ( ( in @ SV594 @ ( setadjoin @ SV238 @ ( setadjoin @ SV460 @ emptyset ) ) )
= $false )
| ( ( ( SV594 = SV238 )
| ( SV594 = SV460 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1768]) ).
thf(1987,plain,
! [SV620: $i,SV595: $i,SV461: $i,SV239: $i] :
( ( ( ( kpair @ SV239 @ SV461 )
!= ( kpair @ SV595 @ SV620 ) )
= $true )
| ( ( SV461 = SV620 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1769]) ).
thf(1988,plain,
! [SV464: $i,SV596: $i > $i,SV242: $i] :
( ( ( ! [SY3041: $i] :
( ~ ( in @ SY3041 @ SV242 )
| ( in @ ( SV596 @ SY3041 ) @ SV464 ) ) )
= $false )
| ( ( func @ SV242 @ SV464
@ ( lam @ SV242 @ SV464
@ ^ [SY3042: $i] : ( SV596 @ SY3042 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1772]) ).
thf(1989,plain,
! [SV465: $i,SV243: $i,SV667: $i] :
( ( ( ~ ( in @ SV667 @ ( powerset @ SV243 ) )
| ! [SY3123: $i] :
( ~ ( in @ SY3123 @ SV243 )
| ~ ( in @ SV465 @ ( powerset @ SV667 ) )
| ~ ( in @ SY3123 @ SV465 )
| ( in @ SY3123 @ SV667 ) ) )
= $true )
| ( ( in @ SV465 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(1990,plain,
! [SV466: $o,SV244: $i,SV597: $i] :
( ( ( in @ SV597 @ SV244 )
= $false )
| ( ( ! [SY3043: $i] :
( ~ ( in @ SY3043 @ SV244 )
| ~ ~ SV466
| ( in @ SY3043
@ ( dsetconstr @ SV244
@ ^ [SY3044: $i] :
( ~ ( ~ SV466
| ( SY3044 != SV597 ) )
| ~ ( ~ ~ SV466
| ( SY3044 != SY3043 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1774]) ).
thf(1991,plain,
! [SV244: $i,SV598: $i] :
( ( ( in @ SV598 @ SV244 )
= $false )
| ( ( ! [SY3045: $i] :
( ~ ( in @ SY3045 @ SV244 )
| ~ ~ $true
| ( in @ SY3045
@ ( dsetconstr @ SV244
@ ^ [SY3046: $i] :
( ~ ( ~ $true
| ( SY3046 != SV598 ) )
| ~ ( ~ ~ $true
| ( SY3046 != SY3045 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1775]) ).
thf(1992,plain,
! [SV244: $i,SV599: $i] :
( ( ( in @ SV599 @ SV244 )
= $false )
| ( ( ! [SY3047: $i] :
( ~ ( in @ SY3047 @ SV244 )
| ~ ~ $false
| ( in @ SY3047
@ ( dsetconstr @ SV244
@ ^ [SY3048: $i] :
( ~ ( ~ $false
| ( SY3048 != SV599 ) )
| ~ ( ~ ~ $false
| ( SY3048 != SY3047 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(1993,plain,
! [SV600: $i,SV469: $i,SV247: $i] :
( ( ( func @ SV247 @ SV469 @ SV600 )
= $false )
| ( ( ! [SY3049: $i] :
( ~ ( func @ SV247 @ SV469 @ SY3049 )
| ~ ! [SY3050: $i] :
( ~ ( in @ SY3050 @ SV247 )
| ( ( ap @ SV247 @ SV469 @ SV600 @ SY3050 )
= ( ap @ SV247 @ SV469 @ SY3049 @ SY3050 ) ) )
| ! [SY3051: $i] :
( ~ ( in @ SY3051 @ SV247 )
| ! [SY3052: $i] :
( ~ ( in @ SY3052 @ SV469 )
| ~ ( in @ ( kpair @ SY3051 @ SY3052 ) @ SY3049 )
| ( in @ ( kpair @ SY3051 @ SY3052 ) @ SV600 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1779]) ).
thf(1994,plain,
! [SV470: $i,SV248: $i,SV668: $i] :
( ( ( ~ ( in @ SV668 @ ( powerset @ SV248 ) )
| ( subset @ ( setminus @ SV248 @ SV470 ) @ ( setminus @ SV248 @ ( binintersect @ SV470 @ SV668 ) ) ) )
= $true )
| ( ( in @ SV470 @ ( powerset @ SV248 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(1995,plain,
! [SV471: $i,SV249: $i > $i > $o] :
( ( ( ~ ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
| ~ ! [SY3124: $i] :
~ ~ ( ~ ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SY3124 )
| ~ ! [SY3125: $i] :
( ~ ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SY3125 )
| ( SY3124 = SY3125 ) ) ) )
= $false )
| ( ( ~ ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1781]) ).
thf(1996,plain,
! [SV474: $o,SV252: $i,SV601: $i] :
( ( ( in @ SV601 @ SV252 )
= $false )
| ( ( ! [SY3053: $i] :
( ~ ( in @ SY3053 @ SV252 )
| ~ ~ SV474
| ( ( if @ SV252 @ SV474 @ SV601 @ SY3053 )
= SY3053 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1784]) ).
thf(1997,plain,
! [SV252: $i,SV602: $i] :
( ( ( in @ SV602 @ SV252 )
= $false )
| ( ( ! [SY3054: $i] :
( ~ ( in @ SY3054 @ SV252 )
| ~ ~ $true
| ( ( if @ SV252 @ $true @ SV602 @ SY3054 )
= SY3054 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1785]) ).
thf(1998,plain,
! [SV252: $i,SV603: $i] :
( ( ( in @ SV603 @ SV252 )
= $false )
| ( ( ! [SY3055: $i] :
( ~ ( in @ SY3055 @ SV252 )
| ~ ~ $false
| ( ( if @ SV252 @ $false @ SV603 @ SY3055 )
= SY3055 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1786]) ).
thf(1999,plain,
! [SV475: $i,SV253: $i,SV604: $i] :
( ( ( in @ SV604 @ SV253 )
= $false )
| ( ( ! [SY3056: $i] :
( ~ ( in @ SY3056 @ SV475 )
| ( in @ ( setadjoin @ ( setadjoin @ SV604 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV604 @ ( setadjoin @ SY3056 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV253 @ SV475 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(2000,plain,
! [SV476: $i,SV254: $i,SV669: $i] :
( ( ( ! [SY3126: $i] :
( ( SV669 != SY3126 )
| ~ ( ~ ( ~ ( in @ SV669 @ SV254 )
| ( in @ SY3126 @ SV476 ) )
| ~ ( ~ ( in @ SY3126 @ SV476 )
| ( in @ SV669 @ SV254 ) ) ) ) )
= $true )
| ( ( SV254 = SV476 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(2001,plain,
! [SV255: $i,SV477: $i] :
( ( ( ~ ( subset @ SV477 @ SV255 ) )
= $true )
| ( ( SV255 = SV477 )
= $true )
| ( ( subset @ SV255 @ SV477 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1789]) ).
thf(2002,plain,
! [SV670: $i,SV256: $i > $o] :
( ( ( ~ ~ ( ~ ( SV256 @ SV670 )
| ~ ! [SY3127: $i] :
( ~ ( SV256 @ SY3127 )
| ( SV670 = SY3127 ) ) ) )
= $true )
| ( ( ~ ! [SY2511: $i] :
~ ! [SY2512: $i] :
~ ( ~ ( ~ ( SV256 @ SY2512 )
| ( SY2512 = SY2511 ) )
| ~ ( ( SY2512 != SY2511 )
| ( SV256 @ SY2512 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(2003,plain,
! [SV478: $i,SV257: $i,SV671: $i] :
( ( ( ~ ( in @ SV671 @ ( powerset @ SV257 ) )
| ( in @ ( binunion @ SV478 @ SV671 ) @ ( powerset @ SV257 ) ) )
= $true )
| ( ( in @ SV478 @ ( powerset @ SV257 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(2004,plain,
! [SV479: $i,SV258: $i,SV605: $i] :
( ( ( in @ SV605 @ SV258 )
= $false )
| ( ( ! [SY3057: $i] :
( ~ ( in @ SY3057 @ SV479 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV605 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV605 @ ( setadjoin @ SY3057 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV258 @ SV479 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1792]) ).
thf(2005,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ~ ( ~ ( SV35 @ SV621 )
| ~ ! [SY3073: $i] :
( ~ ( SV35 @ SY3073 )
| ( SV621 = SY3073 ) ) ) )
= $false )
| ( ( ~ ! [SY1902: $i] :
~ ~ ( ~ ( SV35 @ SY1902 )
| ~ ! [SY1903: $i] :
( ~ ( SV35 @ SY1903 )
| ( SY1902 = SY1903 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1794]) ).
thf(2006,plain,
! [SV282: $i,SV36: $i,SV622: $i] :
( ( ( ~ ( in @ SV622 @ ( powerset @ SV36 ) ) )
= $true )
| ( ( ~ ( subset @ ( setminus @ SV36 @ SV622 ) @ ( setminus @ SV36 @ SV282 ) )
| ( subset @ SV282 @ SV622 ) )
= $true )
| ( ( in @ SV282 @ ( powerset @ SV36 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1795]) ).
thf(2007,plain,
! [SV484: $i,SV284: $i,SV38: $i,SV672: $i] :
( ( ( ~ ( in @ SV672 @ SV38 )
| ! [SY3128: $i] :
( ~ ( in @ SY3128 @ SV284 )
| ~ ( in @ ( kpair @ SV672 @ SY3128 ) @ SV484 )
| ( ( ap @ SV38 @ SV284 @ SV484 @ SV672 )
= SY3128 ) ) )
= $true )
| ( ( func @ SV38 @ SV284 @ SV484 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2008,plain,
! [SV485: $i,SV285: $o,SV39: $i,SV673: $i] :
( ( ( ~ ( in @ SV673 @ SV39 )
| ~ SV285
| ( in @ SV485
@ ( dsetconstr @ SV39
@ ^ [SY3129: $i] :
( ~ ( ~ SV285
| ( SY3129 != SV485 ) )
| ~ ( ~ ~ SV285
| ( SY3129 != SV673 ) ) ) ) ) )
= $true )
| ( ( in @ SV485 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2009,plain,
! [SV486: $i,SV39: $i,SV674: $i] :
( ( ( ~ ( in @ SV674 @ SV39 )
| ~ $true
| ( in @ SV486
@ ( dsetconstr @ SV39
@ ^ [SY3130: $i] :
( ~ ( ~ $true
| ( SY3130 != SV486 ) )
| ~ ( ~ ~ $true
| ( SY3130 != SV674 ) ) ) ) ) )
= $true )
| ( ( in @ SV486 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2010,plain,
! [SV487: $i,SV39: $i,SV675: $i] :
( ( ( ~ ( in @ SV675 @ SV39 )
| ~ $false
| ( in @ SV487
@ ( dsetconstr @ SV39
@ ^ [SY3131: $i] :
( ~ ( ~ $false
| ( SY3131 != SV487 ) )
| ~ ( ~ ~ $false
| ( SY3131 != SV675 ) ) ) ) ) )
= $true )
| ( ( in @ SV487 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2011,plain,
! [SV676: $i > $o,SV623: $i > $o,SV286: $i,SV40: $i] :
( ( ( ~ ! [SY3132: $i] :
( ~ ( in @ SY3132 @ SV40 )
| ! [SY3133: $i] :
( ~ ( in @ SY3133 @ SV286 )
| ( SY3132 != SY3133 )
| ~ ( ~ ( ~ ( SV623 @ SY3132 )
| ( SV676 @ SY3133 ) )
| ~ ( ~ ( SV676 @ SY3133 )
| ( SV623 @ SY3132 ) ) ) ) )
| ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(2012,plain,
! [SV287: $i > $o,SV41: $i] :
( ( ( ! [SY2541: $i] :
~ ~ ( ~ ( in @ SY2541 @ SV41 )
| ~ ( SV287 @ SY2541 ) ) )
= $false )
| ( ( ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV41 )
| ~ ( SV287 @ SY2542 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1801]) ).
thf(2013,plain,
! [SV288: $i,SV43: $i,SV488: $i] :
( ( ( in @ SV488 @ SV43 )
= $true )
| ( ( ~ ( in @ SV488 @ ( setminus @ SV43 @ SV288 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1802]) ).
thf(2014,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ! [SY3079: $i] :
~ ( ~ ( ~ ( SV44 @ SY3079 )
| ( SY3079 = SV624 ) )
| ~ ( ( SY3079 != SV624 )
| ( SV44 @ SY3079 ) ) ) )
= $false )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(2015,plain,
! [SV45: $i,SV289: $i,SV489: $i] :
( ( ( in @ SV489 @ SV289 )
= $false )
| ( ( in @ SV489 @ ( setminus @ SV45 @ SV289 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(2016,plain,
! [SV46: $i,SV490: $i,SV290: $i,SV677: $i] :
( ( ( ~ ( in @ SV677 @ SV290 )
| ( in @ ( kpair @ SV490 @ SV677 ) @ ( cartprod @ SV46 @ SV290 ) ) )
= $true )
| ( ( in @ SV490 @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2017,plain,
! [SV291: $i,SV47: $i,SV491: $i] :
( ( ~ ( in @ SV491 @ ( setadjoin @ SV47 @ SV291 ) )
| ( SV491 = SV47 )
| ( in @ SV491 @ SV291 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1806]) ).
thf(2018,plain,
! [SV291: $i,SV47: $i,SV491: $i] :
( ( ~ ( ( SV491 = SV47 )
| ( in @ SV491 @ SV291 ) )
| ( in @ SV491 @ ( setadjoin @ SV47 @ SV291 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1807]) ).
thf(2019,plain,
! [SV493: $i,SV294: $i,SV51: $i,SV678: $i] :
( ( ( ~ ( in @ SV678 @ SV51 )
| ( singleton
@ ( dsetconstr @ SV294
@ ^ [SY3136: $i] : ( in @ ( kpair @ SV678 @ SY3136 ) @ SV493 ) ) ) )
= $true )
| ( ( func @ SV51 @ SV294 @ SV493 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2020,plain,
! [SV55: $i,SV494: $i,SV296: $i,SV679: $i] :
( ( ( ~ ( in @ SV679 @ SV296 )
| ( ( kpair @ SV494 @ SV679 )
= ( kpair @ SV494 @ SV679 ) ) )
= $true )
| ( ( in @ SV494 @ SV55 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2021,plain,
! [SV56: $i,SV495: $i,SV297: $i,SV680: $i] :
( ( ( ~ ( in @ SV680 @ SV297 )
| ( ( ksnd @ ( kpair @ SV495 @ SV680 ) )
= SV680 ) )
= $true )
| ( ( in @ SV495 @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2022,plain,
! [SV496: $i,SV298: $i,SV57: $i,SV681: $i] :
( ( ( ~ ( in @ SV681 @ SV57 )
| ( in @ ( kpair @ SV681 @ ( ap @ SV57 @ SV298 @ SV496 @ SV681 ) ) @ SV496 ) )
= $true )
| ( ( func @ SV57 @ SV298 @ SV496 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2023,plain,
! [SV499: $i,SV301: $o,SV60: $i,SV682: $i] :
( ( ( ~ ( in @ SV682 @ SV60 )
| ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY3137: $i] :
( ~ ( ~ SV301
| ( SY3137 != SV499 ) )
| ~ ( ~ ~ SV301
| ( SY3137 != SV682 ) ) ) ) ) )
= $true )
| ( ( in @ SV499 @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2024,plain,
! [SV500: $i,SV60: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV60 )
| ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY3138: $i] :
( ~ ( ~ $true
| ( SY3138 != SV500 ) )
| ~ ( ~ ~ $true
| ( SY3138 != SV683 ) ) ) ) ) )
= $true )
| ( ( in @ SV500 @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2025,plain,
! [SV501: $i,SV60: $i,SV684: $i] :
( ( ( ~ ( in @ SV684 @ SV60 )
| ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY3139: $i] :
( ~ ( ~ $false
| ( SY3139 != SV501 ) )
| ~ ( ~ ~ $false
| ( SY3139 != SV684 ) ) ) ) ) )
= $true )
| ( ( in @ SV501 @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2026,plain,
! [SV62: $i,SV303: $i,SV503: $i] :
( ( ( ~ ( in @ SV503 @ SV303 ) )
= $true )
| ( ( in @ SV503 @ ( binintersect @ SV62 @ SV303 ) )
= $true )
| ( ( in @ SV503 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1819]) ).
thf(2027,plain,
! [SV63: $i,SV304: $i,SV504: $i] :
( ( ( ~ ( subset @ SV504 @ SV304 ) )
= $true )
| ( ( subset @ SV504 @ ( binintersect @ SV63 @ SV304 ) )
= $true )
| ( ( subset @ SV504 @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(2028,plain,
! [SV305: $i,SV64: $i,SV625: $i] :
( ( ( ~ ( in @ SV625 @ ( powerset @ SV64 ) ) )
= $true )
| ( ( ! [SY3080: $i] :
( ~ ( in @ SY3080 @ SV64 )
| ~ ( in @ SY3080 @ ( setminus @ SV64 @ SV305 ) )
| ~ ( in @ SY3080 @ ( binintersect @ SV305 @ SV625 ) ) ) )
= $true )
| ( ( in @ SV305 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(2029,plain,
! [SV307: $i,SV66: $i,SV626: $i] :
( ( ( ~ ( in @ SV626 @ ( powerset @ SV66 ) ) )
= $true )
| ( ( ! [SY3081: $i] :
( ~ ( in @ SY3081 @ SV66 )
| ~ ~ ( in @ SY3081 @ ( binunion @ SV307 @ SV626 ) )
| ~ ( in @ SY3081 @ SV626 ) ) )
= $true )
| ( ( in @ SV307 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1823]) ).
thf(2030,plain,
! [SV506: $i,SV308: $i,SV67: $i,SV685: $i] :
( ( ( ~ ( in @ SV685 @ SV67 )
| ( ( ap @ SV67 @ SV308 @ SV506 @ SV685 )
= ( ap @ SV67 @ SV308 @ SV506 @ SV685 ) ) )
= $true )
| ( ( func @ SV67 @ SV308 @ SV506 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2031,plain,
! [SV309: $i,SV68: $i,SV507: $i] :
( ( ( in @ SV507 @ ( setminus @ SV68 @ SV309 ) )
= $false )
| ( ( in @ SV507 @ SV309 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1825]) ).
thf(2032,plain,
! [SV69: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ ( setunion @ SV69 ) ) )
= $true )
| ( ( ~ ! [SY2574: $i] :
~ ~ ( ~ ( in @ SV310 @ SY2574 )
| ~ ( in @ SY2574 @ SV69 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1826]) ).
thf(2033,plain,
! [SV69: $i,SV310: $i] :
( ( ( ~ ~ ! [SY2575: $i] :
~ ~ ( ~ ( in @ SV310 @ SY2575 )
| ~ ( in @ SY2575 @ SV69 ) ) )
= $true )
| ( ( in @ SV310 @ ( setunion @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1827]) ).
thf(2034,plain,
! [SV311: $i,SV70: $i,SV627: $i] :
( ( ( ~ ( in @ SV627 @ ( powerset @ SV70 ) ) )
= $true )
| ( ( ! [SY3082: $i] :
( ~ ( in @ SY3082 @ SV70 )
| ~ ( in @ SY3082 @ ( setminus @ SV70 @ ( binunion @ SV311 @ SV627 ) ) )
| ~ ( in @ SY3082 @ SV311 ) ) )
= $true )
| ( ( in @ SV311 @ ( powerset @ SV70 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(2035,plain,
! [SV71: $i,SV312: $i] :
( ( ( ~ ( in @ ( sK6_SY2578 @ SV312 @ SV71 ) @ SV71 ) )
= $false )
| ( ( subset @ SV71 @ SV312 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1829]) ).
thf(2036,plain,
! [SV71: $i,SV312: $i] :
( ( ( in @ ( sK6_SY2578 @ SV312 @ SV71 ) @ SV312 )
= $false )
| ( ( subset @ SV71 @ SV312 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1829]) ).
thf(2037,plain,
! [SV314: $i,SV73: $i,SV628: $i] :
( ( ( ~ ( in @ SV628 @ ( powerset @ SV73 ) ) )
= $true )
| ( ( ~ ! [SY3083: $i] :
( ~ ( in @ SY3083 @ SV73 )
| ~ ( in @ SY3083 @ SV314 )
| ( in @ SY3083 @ SV628 ) )
| ( in @ SV314 @ ( powerset @ SV628 ) ) )
= $true )
| ( ( in @ SV314 @ ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1831]) ).
thf(2038,plain,
! [SV686: $o,SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( ~ ( in @ SV509 @ SV74 )
| ~ ~ ( in @ SV509 @ SV315 )
| SV686 )
| ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SV686 )
| SV686 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1832]) ).
thf(2039,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( ~ ( in @ SV509 @ SV74 )
| ~ ~ ( in @ SV509 @ SV315 )
| $true )
| ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $true )
| $true )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1832]) ).
thf(2040,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( ~ ( in @ SV509 @ SV74 )
| ~ ~ ( in @ SV509 @ SV315 )
| $false )
| ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $false )
| $false )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1832]) ).
thf(2041,plain,
! [SV76: $i,SV316: $i,SV510: $i] :
( ( ( ~ ~ ( in @ SV510 @ SV316 ) )
= $true )
| ( ( ~ ( in @ SV510 @ SV76 ) )
= $true )
| ( ( subset @ SV76 @ SV316 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1834]) ).
thf(2042,plain,
! [SV511: $i > $i > $o,SV317: $i,SV77: $i,SV629: $i,SV606: $i] :
( ( ( ~ ( in @ ( kpair @ SV606 @ SV629 )
@ ( dpsetconstr @ SV77 @ SV317
@ ^ [SY2916: $i,SY2917: $i] : ( SV511 @ SY2916 @ SY2917 ) ) ) )
= $true )
| ( ( in @ SV629 @ SV317 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(2043,plain,
! [SV78: $i] :
( ( ( ~ ( in @ ( sK18_SY2009 @ SV78 ) @ SV78 ) )
= $false )
| ( ( SV78 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1836]) ).
thf(2044,plain,
! [SV318: $i > $o,SV79: $i] :
( ( ( ! [SY2591: $i] :
~ ~ ( ~ ( in @ SY2591 @ SV79 )
| ~ ( SV318 @ SY2591 ) ) )
= $false )
| ( ( ! [SY2592: $i] :
( ~ ( in @ SY2592 @ SV79 )
| ~ ( SV318 @ SY2592 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(2045,plain,
! [SV82: $i,SV630: $i] :
( ( ( in @ SV630 @ SV82 )
= $false )
| ( ( ~ ! [SY2017: $i] :
~ ~ ( ~ ( in @ SY2017 @ SV82 )
| ~ ~ ~ ! [SY2018: $i] :
~ ~ ( ~ ( in @ SY2018 @ SY2017 )
| ~ ( in @ SY2018 @ SV82 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1839]) ).
thf(2046,plain,
! [SV607: $o,SV322: $i,SV84: $i,SV513: $i] :
( ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV513 @ SV84 )
| SV607 )
| ~ ( ~ ( in @ SV513 @ SV322 )
| SV607 )
| SV607 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1840]) ).
thf(2047,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV513 @ SV84 )
| $true )
| ~ ( ~ ( in @ SV513 @ SV322 )
| $true )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1841]) ).
thf(2048,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV513 @ SV84 )
| $false )
| ~ ( ~ ( in @ SV513 @ SV322 )
| $false )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1842]) ).
thf(2049,plain,
! [SV323: $i,SV85: $i,SV631: $i] :
( ( ( ~ ( in @ SV631 @ ( powerset @ SV85 ) ) )
= $true )
| ( ( ! [SY3086: $i] :
( ~ ( in @ SY3086 @ SV85 )
| ~ ~ ( in @ SY3086 @ ( binunion @ SV323 @ SV631 ) )
| ~ ( in @ SY3086 @ SV323 ) ) )
= $true )
| ( ( in @ SV323 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1843]) ).
thf(2050,plain,
! [SV325: $i > $o,SV87: $i,SV687: $i] :
( ( ( ~ ( in @ SV687 @ SV87 )
| ( SV325 @ SV687 ) )
= $true )
| ( ( ~ ! [SY2599: $i] :
~ ~ ( ~ ( in @ SY2599 @ SV87 )
| ~ ~ ( SV325 @ SY2599 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2051,plain,
! [SV88: $i,SV326: $i] :
( ( ( ~ ( in @ ( sK7_SY2600 @ SV326 @ SV88 ) @ SV88 ) )
= $false )
| ( ( ~ ! [SY2601: $i] :
( ~ ( in @ SY2601 @ SV326 )
| ( in @ SY2601 @ SV88 ) )
| ( SV88 = SV326 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1845]) ).
thf(2052,plain,
! [SV88: $i,SV326: $i] :
( ( ( in @ ( sK7_SY2600 @ SV326 @ SV88 ) @ SV326 )
= $false )
| ( ( ~ ! [SY2601: $i] :
( ~ ( in @ SY2601 @ SV326 )
| ( in @ SY2601 @ SV88 ) )
| ( SV88 = SV326 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1845]) ).
thf(2053,plain,
! [SV632: $i,SV91: $i > $o] :
( ( ( ~ ( ~ ( SV91 @ SV632 )
| ~ ! [SY3087: $i] :
( ~ ( SV91 @ SY3087 )
| ( SV632 = SY3087 ) ) ) )
= $false )
| ( ( ! [SY2037: $i,SY2038: $i] :
( ~ ( SV91 @ SY2037 )
| ~ ( SV91 @ SY2038 )
| ( SY2037 = SY2038 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(2054,plain,
! [SV514: $i,SV329: $i,SV92: $i,SV688: $i] :
( ( ( ~ ( in @ SV688 @ SV92 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV329
@ ^ [SY3140: $i] : ( in @ ( kpair @ SV688 @ SY3140 ) @ SV514 ) ) )
@ SV329 ) )
= $true )
| ( ( func @ SV92 @ SV329 @ SV514 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2055,plain,
! [SV94: $i,SV331: $i,SV515: $i] :
( ( ( ~ ~ ( in @ SV515 @ SV331 ) )
= $true )
| ( ( ~ ( subset @ SV94 @ SV331 ) )
= $true )
| ( ( in @ SV515 @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(2056,plain,
! [SV516: $i,SV332: $i,SV95: $i,SV689: $i] :
( ( ( ~ ( subset @ SV689 @ ( cartprod @ SV95 @ SV332 ) )
| ~ ! [SY3141: $i] :
( ~ ( in @ SY3141 @ SV95 )
| ! [SY3142: $i] :
( ~ ( in @ SY3142 @ SV332 )
| ~ ( in @ ( kpair @ SY3141 @ SY3142 ) @ SV516 )
| ( in @ ( kpair @ SY3141 @ SY3142 ) @ SV689 ) ) )
| ( subset @ SV516 @ SV689 ) )
= $true )
| ( ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2057,plain,
! [SV96: $i,SV333: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY2610 @ SV333 @ SV96 ) @ SV96 )
| ~ ( in @ SV333 @ ( sK19_SY2610 @ SV333 @ SV96 ) ) ) )
= $false )
| ( ( in @ SV333 @ ( setunion @ SV96 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1850]) ).
thf(2058,plain,
! [SV334: $i,SV97: $i,SV633: $i] :
( ( ( ~ ( in @ SV633 @ SV97 ) )
= $true )
| ( ( ~ ~ ( in @ SV633 @ ( setminus @ SV97 @ SV334 ) )
| ( in @ SV633 @ SV334 ) )
= $true )
| ( ( in @ SV334 @ ( powerset @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1851]) ).
thf(2059,plain,
! [SV335: $i > $o,SV98: $i,SV517: $i] :
( ( ( ~ ( ~ ( in @ SV517
@ ( dsetconstr @ SV98
@ ^ [SY2613: $i] : ( SV335 @ SY2613 ) ) )
| ( SV335 @ SV517 ) )
| ~ ( ~ ( SV335 @ SV517 )
| ( in @ SV517
@ ( dsetconstr @ SV98
@ ^ [SY2614: $i] : ( SV335 @ SY2614 ) ) ) ) )
= $false )
| ( ( in @ SV517 @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1852]) ).
thf(2060,plain,
! [SV336: $i,SV99: $i] :
( ( ( ~ ( in @ ( sK8_SY2615 @ SV99 @ SV336 ) @ SV336 ) )
= $false )
| ( ( in @ SV336 @ ( powerset @ SV99 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1853]) ).
thf(2061,plain,
! [SV336: $i,SV99: $i] :
( ( ( in @ ( sK8_SY2615 @ SV99 @ SV336 ) @ SV99 )
= $false )
| ( ( in @ SV336 @ ( powerset @ SV99 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1853]) ).
thf(2062,plain,
! [SV100: $i,SV518: $i,SV337: $i > $o] :
( ( ( ~ ( SV337 @ SV518 ) )
= $true )
| ( ( ~ ! [SY2926: $i] :
( ~ ( in @ SY2926 @ SV100 )
| ~ ( SV337 @ SY2926 )
| ( SY2926 = SV518 ) )
| ( singleton
@ ( dsetconstr @ SV100
@ ^ [SY2618: $i] : ( SV337 @ SY2618 ) ) ) )
= $true )
| ( ( in @ SV518 @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1854]) ).
thf(2063,plain,
! [SV519: $i > $i > $o,SV338: $i,SV101: $i,SV634: $i,SV608: $i] :
( ( ( ~ ( in @ ( kpair @ SV608 @ SV634 )
@ ( dpsetconstr @ SV101 @ SV338
@ ^ [SY2930: $i,SY2931: $i] : ( SV519 @ SY2930 @ SY2931 ) ) ) )
= $true )
| ( ( SV519 @ SV608 @ SV634 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(2064,plain,
( ( ~ ( in @ sK9_SY2932 @ ( powerset @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1857]) ).
thf(2065,plain,
( ( ! [SY3090: $o,SY3091: $i] :
( ~ ( in @ SY3091 @ sK1_SX0 )
| ~ ( in @ SY3091 @ ( binunion @ sK2_SY2624 @ sK9_SY2932 ) )
| ~ ( ~ ( in @ SY3091 @ sK2_SY2624 )
| SY3090 )
| ~ ( ~ ( in @ SY3091 @ sK9_SY2932 )
| SY3090 )
| SY3090 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1857]) ).
thf(2066,plain,
! [SV104: $i,SV521: $i,SV341: $i,SV690: $i] :
( ( ( ~ ( in @ SV690 @ SV341 )
| ( subset @ ( setadjoin @ SV521 @ ( setadjoin @ SV690 @ emptyset ) ) @ ( binunion @ SV104 @ SV341 ) ) )
= $true )
| ( ( in @ SV521 @ SV104 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2067,plain,
! [SV691: $i > $o,SV522: $i,SV342: $i,SV105: $i] :
( ( ( ~ ! [SY3143: $i] :
( ~ ( in @ SY3143 @ SV105 )
| ! [SY3144: $i] :
( ~ ( in @ SY3144 @ SV342 )
| ~ ( in @ ( kpair @ SY3143 @ SY3144 ) @ SV522 )
| ( SV691 @ ( kpair @ SY3143 @ SY3144 ) ) ) )
| ! [SY3145: $i] :
( ~ ( in @ SY3145 @ SV522 )
| ( SV691 @ SY3145 ) ) )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2068,plain,
! [SV635: $i,SV106: $i > $o] :
( ( ( ~ ( ~ ( SV106 @ SV635 )
| ~ ! [SY3092: $i] :
( ~ ( SV106 @ SY3092 )
| ( SV635 = SY3092 ) ) ) )
= $false )
| ( ( ! [SY2086: $i,SY2087: $i] :
( ~ ( SV106 @ SY2086 )
| ~ ( SV106 @ SY2087 )
| ( SY2086 = SY2087 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(2069,plain,
! [SV107: $i,SV523: $i,SV343: $i > $o] :
( ( ( ~ ( SV343 @ SV523 ) )
= $true )
| ( ( in @ SV523
@ ( dsetconstr @ SV107
@ ^ [SY2638: $i] : ( SV343 @ SY2638 ) ) )
= $true )
| ( ( in @ SV523 @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1862]) ).
thf(2070,plain,
! [SV636: $i,SV108: $i > $o] :
( ( ( ~ ( ~ ( SV108 @ SV636 )
| ~ ! [SY3093: $i] :
( ~ ( SV108 @ SY3093 )
| ( SV636 = SY3093 ) ) ) )
= $false )
| ( ( SV108
@ ( descr
@ ^ [SY2093: $i] : ( SV108 @ SY2093 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1863]) ).
thf(2071,plain,
! [SV524: $i > $i > $o,SV344: $i,SV109: $i,SV637: $i,SV609: $i] :
( ( ( ~ ( in @ ( kpair @ SV609 @ SV637 )
@ ( dpsetconstr @ SV109 @ SV344
@ ^ [SY2944: $i,SY2945: $i] : ( SV524 @ SY2944 @ SY2945 ) ) ) )
= $true )
| ( ( in @ SV609 @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1864]) ).
thf(2072,plain,
! [SV347: $i,SV113: $i,SV525: $i] :
( ( ( in @ SV525 @ ( setminus @ SV113 @ SV347 ) )
= $true )
| ( ( ~ ~ ( in @ SV525 @ SV347 )
| ~ ( in @ SV525 @ SV113 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1866]) ).
thf(2073,plain,
! [SV638: $i,SV114: $i > $o] :
( ( ( ~ ( ~ ( SV114 @ SV638 )
| ~ ! [SY3096: $i] :
( ~ ( SV114 @ SY3096 )
| ( SV638 = SY3096 ) ) ) )
= $false )
| ( ( ~ ! [SY2107: $i] :
~ ( SV114 @ SY2107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(2074,plain,
! [SV348: $i,SV115: $i,SV639: $i] :
( ( ( ~ ( in @ SV639 @ ( powerset @ SV115 ) ) )
= $true )
| ( ( ! [SY3097: $i] :
( ~ ( in @ SY3097 @ ( powerset @ SV115 ) )
| ! [SY3098: $i] :
( ~ ( in @ SY3098 @ SV115 )
| ~ ( in @ SY3098 @ ( binintersect @ SV348 @ SV639 ) )
| ( in @ SY3098 @ ( binunion @ SV348 @ SY3097 ) ) ) ) )
= $true )
| ( ( in @ SV348 @ ( powerset @ SV115 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1868]) ).
thf(2075,plain,
! [SV349: $i,SV117: $i,SV640: $i] :
( ( ( ~ ( in @ SV640 @ ( powerset @ SV117 ) ) )
= $true )
| ( ( in @ ( binintersect @ SV349 @ SV640 ) @ ( powerset @ SV117 ) )
= $true )
| ( ( in @ SV349 @ ( powerset @ SV117 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1869]) ).
thf(2076,plain,
! [SV118: $i,SV350: $i > $o] :
( ( ( ~ ( in @ ( sK10_SY2649 @ SV350 @ SV118 ) @ SV118 ) )
= $false )
| ( ( ~ ~ ! [SY2650: $i] :
~ ~ ( ~ ( in @ SY2650 @ SV118 )
| ~ ( SV350 @ SY2650 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1870]) ).
thf(2077,plain,
! [SV118: $i,SV350: $i > $o] :
( ( ( ~ ( SV350 @ ( sK10_SY2649 @ SV350 @ SV118 ) ) )
= $false )
| ( ( ~ ~ ! [SY2650: $i] :
~ ~ ( ~ ( in @ SY2650 @ SV118 )
| ~ ( SV350 @ SY2650 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1870]) ).
thf(2078,plain,
! [SV351: $i > $o,SV119: $i,SV692: $i] :
( ( ( ~ ( in @ SV692 @ SV119 )
| ( SV351 @ SV692 ) )
= $true )
| ( ( ~ ! [SY2652: $i] :
~ ~ ( ~ ( in @ SY2652 @ SV119 )
| ~ ~ ( SV351 @ SY2652 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2079,plain,
! [SV352: $i,SV120: $i,SV641: $i] :
( ( ( ~ ( in @ SV641 @ ( powerset @ SV120 ) ) )
= $true )
| ( ( ! [SY3099: $i] :
( ~ ( in @ SY3099 @ SV120 )
| ~ ~ ( in @ SY3099 @ SV641 )
| ~ ( in @ SY3099 @ ( binintersect @ SV352 @ SV641 ) ) ) )
= $true )
| ( ( in @ SV352 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1872]) ).
thf(2080,plain,
! [SV353: $i,SV121: $i,SV642: $i] :
( ( ( ~ ( in @ SV642 @ ( powerset @ SV121 ) ) )
= $true )
| ( ( ~ ( subset @ SV353 @ ( setminus @ SV121 @ SV642 ) )
| ! [SY3100: $i] :
( ~ ( in @ SY3100 @ SV121 )
| ~ ( in @ SY3100 @ SV642 )
| ( in @ SY3100 @ ( setminus @ SV121 @ SV353 ) ) ) )
= $true )
| ( ( in @ SV353 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1873]) ).
thf(2081,plain,
! [SV354: $i,SV122: $i] :
( ( ( SV122 = SV354 )
= $false )
| ( ( subset @ SV122 @ SV354 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1874]) ).
thf(2082,plain,
! [SV123: $i,SV526: $i > $i,SV355: $i] :
( ( ( ~ ( in @ ( sK20_SY2946 @ SV355 @ SV526 @ SV123 ) @ SV123 )
| ( in @ ( SV526 @ ( sK20_SY2946 @ SV355 @ SV526 @ SV123 ) ) @ SV355 ) )
= $false )
| ( ( in
@ ( lam @ SV123 @ SV355
@ ^ [SY2947: $i] : ( SV526 @ SY2947 ) )
@ ( funcSet @ SV123 @ SV355 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1875]) ).
thf(2083,plain,
! [SV356: $i,SV124: $i,SV527: $i] :
( ( ( ~ ( in @ SV527 @ SV124 ) )
= $true )
| ( ( in @ SV356 @ ( setunion @ SV124 ) )
= $true )
| ( ( in @ SV356 @ SV527 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(2084,plain,
! [SV358: $i,SV693: $o,SV126: $i,SV529: $i] :
( ( ( ~ ( ( SV529 != SV126 )
| SV693 )
| ~ ( ~ ( in @ SV529 @ SV358 )
| SV693 )
| SV693 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1878]) ).
thf(2085,plain,
! [SV358: $i,SV126: $i,SV529: $i] :
( ( ( ~ ( ( SV529 != SV126 )
| $true )
| ~ ( ~ ( in @ SV529 @ SV358 )
| $true )
| $true )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1878]) ).
thf(2086,plain,
! [SV358: $i,SV126: $i,SV529: $i] :
( ( ( ~ ( ( SV529 != SV126 )
| $false )
| ~ ( ~ ( in @ SV529 @ SV358 )
| $false )
| $false )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1878]) ).
thf(2087,plain,
! [SV359: $i,SV127: $i,SV530: $i] :
( ( ( in @ SV530 @ SV127 )
= $true )
| ( ( ~ ~ ( in @ SV530 @ SV359 )
| ~ ( in @ SV530 @ ( symdiff @ SV127 @ SV359 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1879]) ).
thf(2088,plain,
! [SV128: $i,SV531: $i,SV360: $i,SV694: $i] :
( ( ( ~ ( in @ SV694 @ SV360 )
| ( in @ ( setadjoin @ SV531 @ ( setadjoin @ SV694 @ emptyset ) ) @ ( powerset @ ( binunion @ SV128 @ SV360 ) ) ) )
= $true )
| ( ( in @ SV531 @ SV128 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2089,plain,
! [SV361: $i,SV129: $i,SV643: $i] :
( ( ( ~ ( in @ SV643 @ ( powerset @ SV129 ) ) )
= $true )
| ( ( ~ ( subset @ SV361 @ ( setminus @ SV129 @ SV643 ) )
| ( subset @ SV643 @ ( setminus @ SV129 @ SV361 ) ) )
= $true )
| ( ( in @ SV361 @ ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1881]) ).
thf(2090,plain,
! [SV362: $i,SV130: $i,SV644: $i] :
( ( ( ~ ( in @ SV644 @ ( powerset @ SV130 ) ) )
= $true )
| ( ( ! [SY3101: $i] :
( ~ ( in @ SY3101 @ SV130 )
| ~ ~ ( in @ SY3101 @ SV362 )
| ~ ( in @ SY3101 @ ( binintersect @ SV362 @ SV644 ) ) ) )
= $true )
| ( ( in @ SV362 @ ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1882]) ).
thf(2091,plain,
! [SV363: $i,SV131: $i,SV645: $i] :
( ( ( ~ ( in @ SV645 @ ( powerset @ SV131 ) ) )
= $true )
| ( ( ! [SY3102: $i] :
( ~ ( in @ SY3102 @ SV131 )
| ~ ( in @ SY3102 @ ( setminus @ SV131 @ SV363 ) )
| ( in @ SY3102 @ ( setminus @ SV131 @ ( binintersect @ SV363 @ SV645 ) ) ) ) )
= $true )
| ( ( in @ SV363 @ ( powerset @ SV131 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1883]) ).
thf(2092,plain,
! [SV365: $i,SV133: $i,SV646: $i] :
( ( ( ~ ( in @ SV646 @ SV133 ) )
= $true )
| ( ( ~ ( in @ SV646 @ SV365 )
| ( in @ SV646 @ ( setminus @ SV133 @ ( setminus @ SV133 @ SV365 ) ) ) )
= $true )
| ( ( in @ SV365 @ ( powerset @ SV133 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1885]) ).
thf(2093,plain,
! [SV367: $i > $o,SV135: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV135 ) )
= $true )
| ( ( ! [SY3103: $i] :
( ~ ( in @ SY3103 @ SV135 )
| ~ ( SV367 @ SV647 )
| ~ ( SV367 @ SY3103 )
| ( SV647 = SY3103 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV135
@ ^ [SY2676: $i] : ( SV367 @ SY2676 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1887]) ).
thf(2094,plain,
! [SV648: $o,SV136: $i,SV368: $i] :
( ( ( ~ ! [SY3104: $i] :
( ~ ( in @ SV368 @ SY3104 )
| ~ ( in @ SY3104 @ SV136 )
| SV648 ) )
= $true )
| ( SV648 = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1888]) ).
thf(2095,plain,
! [SV136: $i,SV368: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV368 @ SX0 )
| ~ ( in @ SX0 @ SV136 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1889]) ).
thf(2096,plain,
! [SV136: $i,SV368: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV368 @ SX0 )
| ~ ( in @ SX0 @ SV136 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1890]) ).
thf(2097,plain,
! [SV369: $i,SV137: $i,SV649: $i] :
( ( ( ~ ( in @ SV649 @ ( powerset @ SV137 ) ) )
= $true )
| ( ( ! [SY3105: $i] :
( ~ ( in @ SY3105 @ SV137 )
| ~ ( subset @ SV369 @ SV649 )
| ~ ~ ( in @ SY3105 @ SV649 )
| ~ ( in @ SY3105 @ SV369 ) ) )
= $true )
| ( ( in @ SV369 @ ( powerset @ SV137 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1891]) ).
thf(2098,plain,
! [SV370: $i,SV138: $i,SV534: $i] :
( ( ( SV534 = SV138 )
= $true )
| ( ( SV534 = SV370 )
= $true )
| ( ( in @ SV534 @ ( setadjoin @ SV138 @ ( setadjoin @ SV370 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(2099,plain,
! [SV373: $i,SV142: $i,SV610: $i,SV537: $i] :
( ( ( in @ ( kpair @ SV537 @ SV610 ) @ ( cartprod @ SV142 @ SV373 ) )
= $false )
| ( ( in @ SV610 @ SV373 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(2100,plain,
! [SV538: $i,SV374: $i,SV143: $i,SV695: $i] :
( ( ( ~ ( in @ SV695 @ SV143 )
| ( in @ ( kpair @ SV695 @ ( ap @ SV143 @ SV374 @ SV538 @ SV695 ) ) @ SV538 ) )
= $true )
| ( ( in @ SV538 @ ( funcSet @ SV143 @ SV374 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2101,plain,
! [SV377: $i,SV146: $i,SV650: $i] :
( ( ( ~ ( in @ SV650 @ ( powerset @ SV146 ) ) )
= $true )
| ( ( ~ ! [SY3106: $i] :
( ~ ( in @ SY3106 @ SV146 )
| ~ ( in @ SY3106 @ SV377 )
| ( in @ SY3106 @ SV650 ) )
| ( subset @ SV377 @ SV650 ) )
= $true )
| ( ( in @ SV377 @ ( powerset @ SV146 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1898]) ).
thf(2102,plain,
! [SV147: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY2953: $i] :
( ~ ( in @ SY2953 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY2188: $i] :
( ~ ( in @ SY2188 @ SY2953 )
| ( in @ SY2188 @ SV147 ) ) )
| ~ ! [SY2955: $i,SY2956: $i] :
( ~ ~ ( ~ ( in @ SY2955 @ SV147 )
| ~ ( in @ SY2956 @ SV147 ) )
| ~ ! [SY2957: $i] :
( ~ ( in @ SY2957 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SY2955 @ SY2957 )
| ( in @ SY2956 @ SY2957 ) )
| ~ ( ~ ( in @ SY2956 @ SY2957 )
| ( in @ SY2955 @ SY2957 ) ) ) )
| ( SY2955 = SY2956 ) ) )
| ~ ! [SY2958: $i,SY2959: $i] :
( ~ ~ ( ~ ( in @ SY2958 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY2959 @ ( sK3_SY2186 @ SV147 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2958 )
| ( in @ SX4 @ SY2959 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2959 )
| ( in @ SX4 @ SY2958 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1899]) ).
thf(2103,plain,
! [SV147: $i] :
( ( ~ ! [SY2962: $i] :
( ~ ~ ( ~ ! [SY2197: $i] :
( ~ ( in @ SY2197 @ SY2962 )
| ( in @ SY2197 @ SV147 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY2962 ) )
| ~ ! [SY2965: $i] :
~ ~ ! [SY2966: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY2965 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY2966 @ SY2962 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY2965 )
| ~ ( in @ SX5 @ SY2962 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY2965 ) )
| ( in @ SY2966 @ SY2968 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1899]) ).
thf(2104,plain,
! [SV378: $i,SV148: $i,SV540: $i] :
( ( ( ~ ( in @ SV540 @ SV148 ) )
= $true )
| ( ( in @ SV540 @ SV378 )
= $true )
| ( ( subset @ SV148 @ SV378 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1900]) ).
thf(2105,plain,
! [SV381: $i,SV151: $i,SV651: $i] :
( ( ( ~ ( in @ SV651 @ ( powerset @ SV151 ) ) )
= $true )
| ( ( ! [SY3107: $i] :
( ~ ( in @ SY3107 @ ( powerset @ SV151 ) )
| ! [SY3108: $i] :
( ~ ( in @ SY3108 @ SV151 )
| ~ ( in @ SY3108 @ ( binintersect @ SV381 @ SV651 ) )
| ( in @ SY3108 @ ( binunion @ SV651 @ SY3107 ) ) ) ) )
= $true )
| ( ( in @ SV381 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1902]) ).
thf(2106,plain,
! [SV383: $i,SV153: $i,SV611: $i,SV542: $i] :
( ( ( in @ ( kpair @ SV542 @ SV611 ) @ ( cartprod @ SV153 @ SV383 ) )
= $false )
| ( ( in @ SV542 @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(2107,plain,
! [SV384: $i,SV154: $i,SV543: $i] :
( ( ( in @ SV543 @ SV154 )
= $true )
| ( ( in @ SV543 @ SV384 )
= $true )
| ( ( in @ SV543 @ ( binunion @ SV154 @ SV384 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1904]) ).
thf(2108,plain,
! [SV155: $i,SV385: $i] :
( ( ( ~ ( in @ ( sK11_SY2701 @ SV385 @ SV155 ) @ SV155 ) )
= $false )
| ( ( subset @ SV155 @ SV385 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1905]) ).
thf(2109,plain,
! [SV155: $i,SV385: $i] :
( ( ( in @ ( sK11_SY2701 @ SV385 @ SV155 ) @ SV385 )
= $false )
| ( ( subset @ SV155 @ SV385 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1905]) ).
thf(2110,plain,
! [SV386: $i,SV156: $i,SV652: $i] :
( ( ( ~ ( in @ SV652 @ ( powerset @ SV156 ) ) )
= $true )
| ( ( ! [SY3109: $i] :
( ~ ( in @ SY3109 @ SV156 )
| ~ ( subset @ SV386 @ ( setminus @ SV156 @ SV652 ) )
| ~ ( in @ SY3109 @ SV652 )
| ~ ( in @ SY3109 @ SV386 ) ) )
= $true )
| ( ( in @ SV386 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1906]) ).
thf(2111,plain,
! [SV388: $i,SV158: $i,SV545: $i] :
( ( ( in @ SV545 @ ( setminus @ SV158 @ SV388 ) )
= $true )
| ( ( ~ ( in @ SV545 @ SV158 )
| ( in @ SV545 @ SV388 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1908]) ).
thf(2112,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( SV160 @ SV653 )
= $false )
| ( ( ~ ! [SY2231: $i,SY2232: $i] :
( ~ ( SV160 @ SY2231 )
| ~ ( SV160 @ SY2232 )
| ( SY2231 = SY2232 ) )
| ~ ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1909]) ).
thf(2113,plain,
! [SV390: $i,SV161: $i,SV654: $i] :
( ( ( ~ ( in @ SV654 @ ( powerset @ SV161 ) ) )
= $true )
| ( ( in @ ( setminus @ SV161 @ SV390 ) @ ( powerset @ ( setminus @ SV161 @ ( binintersect @ SV390 @ SV654 ) ) ) )
= $true )
| ( ( in @ SV390 @ ( powerset @ SV161 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1910]) ).
thf(2114,plain,
! [SV391: $i,SV162: $i,SV655: $i] :
( ( ( ~ ( in @ SV655 @ ( powerset @ SV162 ) ) )
= $true )
| ( ( in @ ( setminus @ SV391 @ SV655 ) @ ( powerset @ SV162 ) )
= $true )
| ( ( in @ SV391 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(2115,plain,
! [SV164: $i,SV392: $i,SV546: $i] :
( ( ( ~ ~ ( in @ SV546 @ SV392 ) )
= $true )
| ( ( in @ SV546 @ ( symdiff @ SV164 @ SV392 ) )
= $true )
| ( ( in @ SV546 @ SV164 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1912]) ).
thf(2116,plain,
! [SV393: $i,SV165: $i,SV696: $i,SV656: $i] :
( ( ( ( SV656 != SV696 )
| ~ ( in @ SV656 @ SV165 )
| ( in @ SV696 @ SV393 ) )
= $true )
| ( ( SV165 = SV393 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2117,plain,
! [SV166: $i,SV394: $i,SV547: $i] :
( ( ( ~ ~ ( in @ SV547 @ SV394 ) )
= $true )
| ( ( SV166 != SV394 )
= $true )
| ( ( in @ SV547 @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1914]) ).
thf(2118,plain,
! [SV395: $i,SV167: $i,SV657: $i] :
( ( ( ~ ( in @ SV657 @ ( powerset @ SV167 ) ) )
= $true )
| ( ( ! [SY3111: $i] :
( ~ ( in @ SY3111 @ SV167 )
| ~ ( in @ SY3111 @ ( setminus @ SV167 @ ( binunion @ SV395 @ SV657 ) ) )
| ( in @ SY3111 @ ( setminus @ SV167 @ SV395 ) ) ) )
= $true )
| ( ( in @ SV395 @ ( powerset @ SV167 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1915]) ).
thf(2119,plain,
! [SV548: $i,SV697: $i,SV396: $i,SV168: $i] :
( ( ( ~ ( func @ SV168 @ SV396 @ SV697 )
| ~ ! [SY3146: $i] :
( ~ ( in @ SY3146 @ SV168 )
| ( ( ap @ SV168 @ SV396 @ SV548 @ SY3146 )
= ( ap @ SV168 @ SV396 @ SV697 @ SY3146 ) ) )
| ( SV548 = SV697 ) )
= $true )
| ( ( func @ SV168 @ SV396 @ SV548 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2120,plain,
! [SV549: $i,SV397: $o,SV169: $i,SV698: $i] :
( ( ( ~ ( in @ SV698 @ SV169 )
| ( in @ ( if @ SV169 @ SV397 @ SV549 @ SV698 ) @ ( setadjoin @ SV549 @ ( setadjoin @ SV698 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV549 @ SV169 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2121,plain,
! [SV550: $i,SV169: $i,SV699: $i] :
( ( ( ~ ( in @ SV699 @ SV169 )
| ( in @ ( if @ SV169 @ $true @ SV550 @ SV699 ) @ ( setadjoin @ SV550 @ ( setadjoin @ SV699 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV550 @ SV169 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2122,plain,
! [SV551: $i,SV169: $i,SV700: $i] :
( ( ( ~ ( in @ SV700 @ SV169 )
| ( in @ ( if @ SV169 @ $false @ SV551 @ SV700 ) @ ( setadjoin @ SV551 @ ( setadjoin @ SV700 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV551 @ SV169 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2123,plain,
! [SV170: $i,SV552: $i > $i,SV398: $i] :
( ( ( ~ ( in @ ( sK21_SY2977 @ SV398 @ SV552 @ SV170 ) @ SV170 )
| ( in @ ( SV552 @ ( sK21_SY2977 @ SV398 @ SV552 @ SV170 ) ) @ SV398 ) )
= $false )
| ( ( ( lam @ SV170 @ SV398
@ ^ [SY2978: $i] : ( SV552 @ SY2978 ) )
= ( lam @ SV170 @ SV398
@ ^ [SY2979: $i] : ( SV552 @ SY2979 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1920]) ).
thf(2124,plain,
! [SV553: $i,SV399: $o,SV171: $i,SV701: $i] :
( ( ( ~ ( in @ SV701 @ SV171 )
| ~ ~ SV399
| ( ( dsetconstr @ SV171
@ ^ [SY3147: $i] :
( ~ ( ~ SV399
| ( SY3147 != SV553 ) )
| ~ ( ~ ~ SV399
| ( SY3147 != SV701 ) ) ) )
= ( setadjoin @ SV701 @ emptyset ) ) )
= $true )
| ( ( in @ SV553 @ SV171 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2125,plain,
! [SV554: $i,SV171: $i,SV702: $i] :
( ( ( ~ ( in @ SV702 @ SV171 )
| ~ ~ $true
| ( ( dsetconstr @ SV171
@ ^ [SY3148: $i] :
( ~ ( ~ $true
| ( SY3148 != SV554 ) )
| ~ ( ~ ~ $true
| ( SY3148 != SV702 ) ) ) )
= ( setadjoin @ SV702 @ emptyset ) ) )
= $true )
| ( ( in @ SV554 @ SV171 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2126,plain,
! [SV555: $i,SV171: $i,SV703: $i] :
( ( ( ~ ( in @ SV703 @ SV171 )
| ~ ~ $false
| ( ( dsetconstr @ SV171
@ ^ [SY3149: $i] :
( ~ ( ~ $false
| ( SY3149 != SV555 ) )
| ~ ( ~ ~ $false
| ( SY3149 != SV703 ) ) ) )
= ( setadjoin @ SV703 @ emptyset ) ) )
= $true )
| ( ( in @ SV555 @ SV171 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2127,plain,
! [SV172: $i,SV400: $i] :
( ( ( ~ ( in @ SV400 @ ( powerset @ SV172 ) ) )
= $true )
| ( ( ! [SY2727: $i] :
( ~ ( in @ SY2727 @ SV400 )
| ( in @ SY2727 @ SV172 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1924]) ).
thf(2128,plain,
! [SV172: $i,SV400: $i] :
( ( ( ~ ! [SY2728: $i] :
( ~ ( in @ SY2728 @ SV400 )
| ( in @ SY2728 @ SV172 ) ) )
= $true )
| ( ( in @ SV400 @ ( powerset @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1925]) ).
thf(2129,plain,
! [SV612: $i,SV556: $i,SV401: $i,SV173: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV173 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV173 @ ( setadjoin @ SV401 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV556 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV556 @ ( setadjoin @ SV612 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV401 = SV612 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(2130,plain,
! [SV174: $i,SV557: $i,SV402: $i,SV704: $i] :
( ( ( ~ ( in @ SV704 @ SV402 )
| ( ( kfst @ ( kpair @ SV557 @ SV704 ) )
= SV557 ) )
= $true )
| ( ( in @ SV557 @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2131,plain,
! [SV558: $i,SV403: $i,SV175: $i,SV705: $i] :
( ( ( ~ ( in @ SV705 @ SV175 )
| ( in @ ( ap @ SV175 @ SV403 @ SV558 @ SV705 ) @ SV403 ) )
= $true )
| ( ( in @ SV558 @ ( funcSet @ SV175 @ SV403 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2132,plain,
! [SV404: $i,SV176: $i,SV658: $i] :
( ( ( ~ ( in @ SV658 @ ( powerset @ SV176 ) ) )
= $true )
| ( ( ~ ( subset @ SV404 @ SV658 )
| ( subset @ ( setminus @ SV176 @ SV658 ) @ ( setminus @ SV176 @ SV404 ) ) )
= $true )
| ( ( in @ SV404 @ ( powerset @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1929]) ).
thf(2133,plain,
! [SV177: $i,SV559: $i,SV405: $i] :
( ( ( ~ ( subset @ SV405 @ SV559 ) )
= $true )
| ( ( subset @ SV177 @ SV559 )
= $true )
| ( ( subset @ SV177 @ SV405 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1930]) ).
thf(2134,plain,
! [SV408: $i > $o,SV180: $i,SV706: $i] :
( ( ( ~ ~ ( ~ ( in @ SV706 @ SV180 )
| ~ ( SV408 @ SV706 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV180
@ ^ [SY2739: $i] : ( SV408 @ SY2739 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2135,plain,
! [SV181: $i,SV409: $i > $o] :
( ( ( ~ ( in @ ( sK12_SY2740 @ SV409 @ SV181 ) @ SV181 ) )
= $false )
| ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) )
| ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1933]) ).
thf(2136,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ( ! [SY3112: $i] :
( ~ ( in @ SY3112 @ SV181 )
| ~ ( SV409 @ ( sK12_SY2740 @ SV409 @ SV181 ) )
| ~ ( SV409 @ SY3112 )
| ( ( sK12_SY2740 @ SV409 @ SV181 )
= SY3112 ) ) )
= $false )
| ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) )
| ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1933]) ).
thf(2137,plain,
! [SV183: $i > $o,SV411: $i > $o] :
( ( ( ( ( sK13_SY2744 @ SV411 @ SV183 )
!= ( sK22_SY3113 @ SV183 @ SV411 ) )
| ~ ( ~ ( ~ ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
| ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) ) )
| ~ ( ~ ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
| ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1934]) ).
thf(2138,plain,
! [SV561: $i,SV413: $i,SV185: $i,SV707: $i] :
( ( ( ~ ( in @ SV707 @ SV185 )
| ! [SY3150: $i] :
( ~ ( in @ SY3150 @ SV413 )
| ~ ( in @ ( kpair @ SV707 @ SY3150 ) @ SV561 )
| ( ( ap @ SV185 @ SV413 @ SV561 @ SV707 )
= SY3150 ) ) )
= $true )
| ( ( in @ SV561 @ ( funcSet @ SV185 @ SV413 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2139,plain,
! [SV414: $i,SV186: $i,SV659: $i] :
( ( ( ~ ( in @ SV659 @ ( powerset @ SV186 ) ) )
= $true )
| ( ( ~ ! [SY3114: $i] :
( ~ ( in @ SY3114 @ SV186 )
| ~ ( in @ SY3114 @ SV414 )
| ( in @ SY3114 @ SV659 ) )
| ~ ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV186 )
| ~ ( in @ SY3115 @ SV659 )
| ( in @ SY3115 @ SV414 ) )
| ( SV414 = SV659 ) )
= $true )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1936]) ).
thf(2140,plain,
! [SV187: $i,SV562: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV562 ) )
= $true )
| ( ( ( dsetconstr @ SV187
@ ^ [SY2759: $i] : ( SV415 @ SY2759 ) )
!= emptyset )
= $true )
| ( ( in @ SV562 @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1937]) ).
thf(2141,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ SV660 )
| ~ ! [SY3116: $i] :
( ~ ( SV188 @ SY3116 )
| ( SV660 = SY3116 ) ) ) )
= $false )
| ( ( ~ ! [SY2316: $i] :
~ ~ ( ~ ( SV188 @ SY2316 )
| ~ ! [SY2317: $i] :
( ~ ( SV188 @ SY2317 )
| ( SY2316 = SY2317 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(2142,plain,
! [SV416: $i,SV189: $i,SV563: $i] :
( ( ( SV563 = SV189 )
= $true )
| ( ( in @ SV563 @ SV416 )
= $true )
| ( ( in @ SV563 @ ( setadjoin @ SV189 @ SV416 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1939]) ).
thf(2143,plain,
! [SV564: $i,SV417: $i,SV190: $i,SV708: $i] :
( ( ( ~ ( in @ SV708 @ SV190 )
| ( ( ap @ SV190 @ SV417 @ SV564 @ SV708 )
= ( ap @ SV190 @ SV417 @ SV564 @ SV708 ) ) )
= $true )
| ( ( in @ SV564 @ ( funcSet @ SV190 @ SV417 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2144,plain,
! [SV418: $i,SV191: $i,SV661: $i] :
( ( ( ~ ( in @ SV661 @ ( powerset @ SV191 ) ) )
= $true )
| ( ( ! [SY3117: $i] :
( ~ ( in @ SY3117 @ ( powerset @ SV191 ) )
| ! [SY3118: $i] :
( ~ ( in @ SY3118 @ SV191 )
| ~ ( in @ SY3118 @ ( binintersect @ SV418 @ SV661 ) )
| ( in @ SY3118 @ ( binintersect @ ( binunion @ SV418 @ SY3117 ) @ ( binunion @ SV661 @ SY3117 ) ) ) ) ) )
= $true )
| ( ( in @ SV418 @ ( powerset @ SV191 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1941]) ).
thf(2145,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ( ( sK14_SY2766 @ SV422 @ SV193 )
!= ( sK23_SY3119 @ SV193 @ SV422 ) )
| ~ ( ~ ( ~ ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
| ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) ) )
| ~ ( ~ ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
| ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1942]) ).
thf(2146,plain,
! [SV194: $i,SV613: $i] :
( ( ( in @ SV613 @ SV194 )
= $false )
| ( ( ( setunion @ SV194 )
= SV613 )
= $true )
| ( ( singleton @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1943]) ).
thf(2147,plain,
! [SV195: $i,SV423: $i,SV565: $i] :
( ( ( ~ ~ ( in @ SV565 @ SV423 ) )
= $true )
| ( ( in @ SV565 @ ( setminus @ SV195 @ SV423 ) )
= $true )
| ( ( in @ SV565 @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1944]) ).
thf(2148,plain,
! [SV566: $i,SV424: $i,SV196: $i] :
( ( ( ! [SY2993: $i] :
~ ~ ( ~ ( in @ SY2993 @ SV196 )
| ~ ~ ! [SY2994: $i] :
~ ~ ( ~ ( in @ SY2994 @ SV424 )
| ( SV566
!= ( kpair @ SY2993 @ SY2994 ) ) ) ) )
= $false )
| ( ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1945]) ).
thf(2149,plain,
! [SV567: $i,SV425: $o,SV197: $i,SV709: $i] :
( ( ( ~ ( in @ SV709 @ SV197 )
| ~ SV425
| ( ( if @ SV197 @ SV425 @ SV567 @ SV709 )
= SV567 ) )
= $true )
| ( ( in @ SV567 @ SV197 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2150,plain,
! [SV568: $i,SV197: $i,SV710: $i] :
( ( ( ~ ( in @ SV710 @ SV197 )
| ~ $true
| ( ( if @ SV197 @ $true @ SV568 @ SV710 )
= SV568 ) )
= $true )
| ( ( in @ SV568 @ SV197 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2151,plain,
! [SV569: $i,SV197: $i,SV711: $i] :
( ( ( ~ ( in @ SV711 @ SV197 )
| ~ $false
| ( ( if @ SV197 @ $false @ SV569 @ SV711 )
= SV569 ) )
= $true )
| ( ( in @ SV569 @ SV197 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2152,plain,
! [SV570: $i,SV426: $i,SV198: $i,SV712: $i] :
( ( ( ~ ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
| ~ ! [SY3151: $i] :
( ~ ( in @ SY3151 @ SV198 )
| ! [SY3152: $i] :
( ~ ( in @ SY3152 @ SV426 )
| ~ ( in @ ( kpair @ SY3151 @ SY3152 ) @ SV570 )
| ( in @ ( kpair @ SY3151 @ SY3152 ) @ SV712 ) ) )
| ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) )
| ( SV570 = SV712 ) )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2153,plain,
! [SV713: $i > $o,SV571: $i,SV428: $i,SV200: $i] :
( ( ( ~ ! [SY3155: $i] :
( ~ ( in @ SY3155 @ SV200 )
| ! [SY3156: $i] :
( ~ ( in @ SY3156 @ SV428 )
| ~ ( in @ ( kpair @ SY3155 @ SY3156 ) @ SV571 )
| ( SV713 @ ( kpair @ SY3155 @ SY3156 ) ) ) )
| ! [SY3157: $i] :
( ~ ( in @ SY3157 @ SV571 )
| ( SV713 @ SY3157 ) ) )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2154,plain,
! [SV429: $i > $o,SV201: $i,SV714: $i] :
( ( ( ~ ~ ( ~ ( in @ SV714 @ SV201 )
| ~ ~ ( SV429 @ SV714 ) ) )
= $true )
| ( ( ~ ! [SY2794: $i] :
( ~ ( in @ SY2794 @ SV201 )
| ( SV429 @ SY2794 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2155,plain,
! [SV203: $i,SV572: $i > $i,SV430: $i] :
( ( ( ~ ( in @ ( sK24_SY3007 @ SV430 @ SV572 @ SV203 ) @ SV203 )
| ( in @ ( SV572 @ ( sK24_SY3007 @ SV430 @ SV572 @ SV203 ) ) @ SV430 ) )
= $false )
| ( ( func @ SV203 @ SV430
@ ( dpsetconstr @ SV203 @ SV430
@ ^ [SY3008: $i,SY3009: $i] :
( ( SV572 @ SY3008 )
= SY3009 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1952]) ).
thf(2156,plain,
! [SV204: $i,SV662: $i] :
( ( ( in @ SV662 @ SV204 )
= $false )
| ( ( SV204 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1953]) ).
thf(2157,plain,
! [SV431: $i,SV206: $i,SV573: $i] :
( ( ( in @ SV573 @ SV206 )
= $true )
| ( ( ~ ( in @ SV573 @ SV431 )
| ( in @ SV573 @ ( symdiff @ SV206 @ SV431 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1954]) ).
thf(2158,plain,
! [SV209: $i,SV574: $i > $i,SV433: $i] :
( ( ( ~ ( in @ ( sK25_SY3010 @ SV433 @ SV574 @ SV209 ) @ SV209 )
| ( in @ ( SV574 @ ( sK25_SY3010 @ SV433 @ SV574 @ SV209 ) ) @ SV433 ) )
= $false )
| ( ( ! [SY3011: $i] :
( ~ ( in @ SY3011 @ SV209 )
| ( ( ap @ SV209 @ SV433
@ ( lam @ SV209 @ SV433
@ ^ [SY3012: $i] : ( SV574 @ SY3012 ) )
@ SY3011 )
= ( SV574 @ SY3011 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1955]) ).
thf(2159,plain,
! [SV435: $i,SV211: $i,SV715: $i,SV663: $i] :
( ( ( ( SV663 != SV715 )
| ( ( setadjoin @ SV211 @ SV663 )
= ( setadjoin @ SV435 @ SV715 ) ) )
= $true )
| ( ( SV211 = SV435 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2160,plain,
! [SV212: $i,SV436: $i > $o] :
( ( ( ~ ( in @ ( sK15_SY2806 @ SV436 @ SV212 ) @ SV212 ) )
= $false )
| ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) )
| ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1957]) ).
thf(2161,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ( ! [SY3121: $i] :
( ~ ( in @ SY3121 @ SV212 )
| ~ ( SV436 @ ( sK15_SY2806 @ SV436 @ SV212 ) )
| ~ ( SV436 @ SY3121 )
| ( ( sK15_SY2806 @ SV436 @ SV212 )
= SY3121 ) ) )
= $false )
| ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) )
| ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1957]) ).
thf(2162,plain,
! [SV615: $i,SV575: $i,SV438: $i,SV214: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV214 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV214 @ ( setadjoin @ SV438 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV575 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV575 @ ( setadjoin @ SV615 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( ( SV575 != SV615 )
| ( SV438 = SV615 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2163,plain,
! [SV215: $i] :
( ( ( in @ emptyset @ SV215 )
= $false )
| ( ( ~ ! [SY2395: $i] :
( ~ ~ ( ~ ( in @ SY2395 @ omega )
| ~ ( in @ SY2395 @ SV215 ) )
| ( in @ ( setadjoin @ SY2395 @ SY2395 ) @ SV215 ) ) )
= $true )
| ( ( ! [SY2396: $i] :
( ~ ( in @ SY2396 @ omega )
| ( in @ SY2396 @ SV215 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1959]) ).
thf(2164,plain,
! [SV216: $i,SV576: $i,SV439: $i,SV716: $i] :
( ( ( ~ ( in @ SV716 @ SV439 )
| ( in @ ( kpair @ SV576 @ SV716 ) @ ( powerset @ ( powerset @ ( binunion @ SV216 @ SV439 ) ) ) ) )
= $true )
| ( ( in @ SV576 @ SV216 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2165,plain,
! [SV577: $i > $i > $o,SV440: $i,SV217: $i,SV616: $i] :
( ( ( in @ SV616 @ SV217 )
= $false )
| ( ( ! [SY3067: $i] :
( ~ ( in @ SY3067 @ SV440 )
| ~ ( SV577 @ SV616 @ SY3067 )
| ( in @ ( kpair @ SV616 @ SY3067 )
@ ( dpsetconstr @ SV217 @ SV440
@ ^ [SY3017: $i,SY3018: $i] : ( SV577 @ SY3017 @ SY3018 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1961]) ).
thf(2166,plain,
! [SV578: $i,SV441: $o,SV218: $i,SV717: $i] :
( ( ( ~ ( in @ SV717 @ SV218 )
| ( in @ ( if @ SV218 @ SV441 @ SV578 @ SV717 ) @ SV218 ) )
= $true )
| ( ( in @ SV578 @ SV218 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2167,plain,
! [SV579: $i,SV218: $i,SV718: $i] :
( ( ( ~ ( in @ SV718 @ SV218 )
| ( in @ ( if @ SV218 @ $true @ SV579 @ SV718 ) @ SV218 ) )
= $true )
| ( ( in @ SV579 @ SV218 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2168,plain,
! [SV580: $i,SV218: $i,SV719: $i] :
( ( ( ~ ( in @ SV719 @ SV218 )
| ( in @ ( if @ SV218 @ $false @ SV580 @ SV719 ) @ SV218 ) )
= $true )
| ( ( in @ SV580 @ SV218 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2169,plain,
! [SV581: $i,SV442: $i,SV219: $i,SV720: $i] :
( ( ( ~ ( in @ SV720 @ ( funcSet @ SV219 @ SV442 ) )
| ~ ! [SY3158: $i] :
( ~ ( in @ SY3158 @ SV219 )
| ( ( ap @ SV219 @ SV442 @ SV581 @ SY3158 )
= ( ap @ SV219 @ SV442 @ SV720 @ SY3158 ) ) )
| ( SV581 = SV720 ) )
= $true )
| ( ( in @ SV581 @ ( funcSet @ SV219 @ SV442 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2170,plain,
! [SV582: $i > $i > $o,SV443: $i,SV220: $i,SV617: $i] :
( ( ( in @ SV617 @ SV220 )
= $false )
| ( ( ! [SY3070: $i] :
( ~ ( in @ SY3070 @ SV443 )
| ~ ( in @ ( kpair @ SV617 @ SY3070 )
@ ( dpsetconstr @ SV220 @ SV443
@ ^ [SY3026: $i,SY3027: $i] : ( SV582 @ SY3026 @ SY3027 ) ) )
| ( SV582 @ SV617 @ SY3070 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(2171,plain,
! [SV583: $i,SV444: $i,SV221: $i,SV721: $i] :
( ( ( ~ ( in @ SV721 @ SV221 )
| ( in @ ( ap @ SV221 @ SV444 @ SV583 @ SV721 ) @ SV444 ) )
= $true )
| ( ( func @ SV221 @ SV444 @ SV583 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2172,plain,
! [SV223: $i,SV446: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK26_SY2833 @ SV446 @ SV223 ) @ SV223 )
| ~ ( SV446 @ ( sK26_SY2833 @ SV446 @ SV223 ) ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY2832: $i] : ( SV446 @ SY2832 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1969]) ).
thf(2173,plain,
! [SV224: $i,SV447: $i] :
( ( ( in @ SV447 @ ( setadjoin @ SV224 @ emptyset ) )
= $false )
| ( ( SV224 = SV447 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1970]) ).
thf(2174,plain,
! [SV225: $i,SV448: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 )
| ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 ) )
| ~ ( ~ ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 )
| ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 ) ) )
= $true )
| ( ( SV225 = SV448 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1971]) ).
thf(2175,plain,
! [SV226: $i,SV449: $i,SV585: $i] :
( ( ( ~ ( in @ SV585 @ SV449 ) )
= $true )
| ( ( ~ ( in @ SV585 @ ( symdiff @ SV226 @ SV449 ) ) )
= $true )
| ( ( in @ SV585 @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1972]) ).
thf(2176,plain,
! [SV450: $i,SV227: $i,SV664: $i] :
( ( ( ~ ( in @ SV664 @ SV227 ) )
= $true )
| ( ( ~ ( in @ SV664 @ ( setminus @ SV227 @ ( setminus @ SV227 @ SV450 ) ) )
| ( in @ SV664 @ SV450 ) )
= $true )
| ( ( in @ SV450 @ ( powerset @ SV227 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1973]) ).
thf(2177,plain,
! [SV618: $i,SV586: $i,SV451: $i,SV228: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV228 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV228 @ ( setadjoin @ SV451 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV586 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV586 @ ( setadjoin @ SV618 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV228 = SV586 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1974]) ).
thf(2178,plain,
! [SV452: $i,SV229: $i,SV665: $i] :
( ( ( ~ ( in @ SV665 @ ( powerset @ SV229 ) ) )
= $true )
| ( ( ! [SY3122: $i] :
( ~ ( in @ SY3122 @ ( powerset @ SV229 ) )
| ( in @ ( binintersect @ SV452 @ SV665 ) @ ( powerset @ ( binintersect @ ( binunion @ SV452 @ SY3122 ) @ ( binunion @ SV665 @ SY3122 ) ) ) ) ) )
= $true )
| ( ( in @ SV452 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1975]) ).
thf(2179,plain,
! [SV230: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK27_SY2440 @ SV230 ) @ SV230 )
| ~ $true ) )
= $false )
| ( ( SV230 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1976]) ).
thf(2180,plain,
! [SV587: $i,SV453: $o,SV231: $i,SV722: $i] :
( ( ( ~ ( in @ SV722 @ SV231 )
| ~ SV453
| ( ( dsetconstr @ SV231
@ ^ [SY3159: $i] :
( ~ ( ~ SV453
| ( SY3159 != SV587 ) )
| ~ ( ~ ~ SV453
| ( SY3159 != SV722 ) ) ) )
= ( setadjoin @ SV587 @ emptyset ) ) )
= $true )
| ( ( in @ SV587 @ SV231 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2181,plain,
! [SV588: $i,SV231: $i,SV723: $i] :
( ( ( ~ ( in @ SV723 @ SV231 )
| ~ $true
| ( ( dsetconstr @ SV231
@ ^ [SY3160: $i] :
( ~ ( ~ $true
| ( SY3160 != SV588 ) )
| ~ ( ~ ~ $true
| ( SY3160 != SV723 ) ) ) )
= ( setadjoin @ SV588 @ emptyset ) ) )
= $true )
| ( ( in @ SV588 @ SV231 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2182,plain,
! [SV589: $i,SV231: $i,SV724: $i] :
( ( ( ~ ( in @ SV724 @ SV231 )
| ~ $false
| ( ( dsetconstr @ SV231
@ ^ [SY3161: $i] :
( ~ ( ~ $false
| ( SY3161 != SV589 ) )
| ~ ( ~ ~ $false
| ( SY3161 != SV724 ) ) ) )
= ( setadjoin @ SV589 @ emptyset ) ) )
= $true )
| ( ( in @ SV589 @ SV231 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2183,plain,
! [SV232: $i,SV454: $i,SV590: $i] :
( ( ( ~ ( in @ SV590 @ SV454 ) )
= $true )
| ( ( in @ SV590 @ SV232 )
= $true )
| ( ( in @ SV454 @ ( powerset @ SV232 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1980]) ).
thf(2184,plain,
! [SV455: $i,SV233: $i,SV666: $i] :
( ( ( ~ ( in @ SV666 @ SV233 ) )
= $true )
| ( ( ~ ( in @ SV666 @ SV455 )
| ~ ( in @ SV666 @ ( setminus @ SV233 @ SV455 ) ) )
= $true )
| ( ( in @ SV455 @ ( powerset @ SV233 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1981]) ).
thf(2185,plain,
! [SV234: $i,SV591: $i > $i,SV456: $i] :
( ( ( ~ ( in @ ( sK28_SY3036 @ SV456 @ SV591 @ SV234 ) @ SV234 )
| ( in @ ( SV591 @ ( sK28_SY3036 @ SV456 @ SV591 @ SV234 ) ) @ SV456 ) )
= $false )
| ( ( ! [SY3037: $i] :
( ~ ( in @ SY3037 @ SV234 )
| ( ( ap @ SV234 @ SV456
@ ( lam @ SV234 @ SV456
@ ^ [SY3038: $i] : ( SV591 @ SY3038 ) )
@ SY3037 )
= ( SV591 @ SY3037 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1982]) ).
thf(2186,plain,
! [SV457: $i,SV235: $i] :
( ( ( ! [SY2850: $i] :
~ ~ ( ~ ( in @ SY2850 @ SV235 )
| ~ ( in @ SY2850 @ SV457 ) ) )
= $false )
| ( ( ( binintersect @ SV235 @ SV457 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2187,plain,
! [SV619: $i,SV592: $i,SV458: $i,SV236: $i] :
( ( ( ( kpair @ SV236 @ SV458 )
= ( kpair @ SV592 @ SV619 ) )
= $false )
| ( ( SV236 = SV592 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2188,plain,
! [SV460: $i,SV238: $i,SV594: $i] :
( ( ( SV594 = SV238 )
= $true )
| ( ( SV594 = SV460 )
= $true )
| ( ( in @ SV594 @ ( setadjoin @ SV238 @ ( setadjoin @ SV460 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1986]) ).
thf(2189,plain,
! [SV620: $i,SV595: $i,SV461: $i,SV239: $i] :
( ( ( ( kpair @ SV239 @ SV461 )
= ( kpair @ SV595 @ SV620 ) )
= $false )
| ( ( SV461 = SV620 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1987]) ).
thf(2190,plain,
! [SV242: $i,SV596: $i > $i,SV464: $i] :
( ( ( ~ ( in @ ( sK29_SY3041 @ SV464 @ SV596 @ SV242 ) @ SV242 )
| ( in @ ( SV596 @ ( sK29_SY3041 @ SV464 @ SV596 @ SV242 ) ) @ SV464 ) )
= $false )
| ( ( func @ SV242 @ SV464
@ ( lam @ SV242 @ SV464
@ ^ [SY3042: $i] : ( SV596 @ SY3042 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1988]) ).
thf(2191,plain,
! [SV465: $i,SV243: $i,SV667: $i] :
( ( ( ~ ( in @ SV667 @ ( powerset @ SV243 ) ) )
= $true )
| ( ( ! [SY3123: $i] :
( ~ ( in @ SY3123 @ SV243 )
| ~ ( in @ SV465 @ ( powerset @ SV667 ) )
| ~ ( in @ SY3123 @ SV465 )
| ( in @ SY3123 @ SV667 ) ) )
= $true )
| ( ( in @ SV465 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1989]) ).
thf(2192,plain,
! [SV597: $i,SV466: $o,SV244: $i,SV725: $i] :
( ( ( ~ ( in @ SV725 @ SV244 )
| ~ ~ SV466
| ( in @ SV725
@ ( dsetconstr @ SV244
@ ^ [SY3162: $i] :
( ~ ( ~ SV466
| ( SY3162 != SV597 ) )
| ~ ( ~ ~ SV466
| ( SY3162 != SV725 ) ) ) ) ) )
= $true )
| ( ( in @ SV597 @ SV244 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2193,plain,
! [SV598: $i,SV244: $i,SV726: $i] :
( ( ( ~ ( in @ SV726 @ SV244 )
| ~ ~ $true
| ( in @ SV726
@ ( dsetconstr @ SV244
@ ^ [SY3163: $i] :
( ~ ( ~ $true
| ( SY3163 != SV598 ) )
| ~ ( ~ ~ $true
| ( SY3163 != SV726 ) ) ) ) ) )
= $true )
| ( ( in @ SV598 @ SV244 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2194,plain,
! [SV599: $i,SV244: $i,SV727: $i] :
( ( ( ~ ( in @ SV727 @ SV244 )
| ~ ~ $false
| ( in @ SV727
@ ( dsetconstr @ SV244
@ ^ [SY3164: $i] :
( ~ ( ~ $false
| ( SY3164 != SV599 ) )
| ~ ( ~ ~ $false
| ( SY3164 != SV727 ) ) ) ) ) )
= $true )
| ( ( in @ SV599 @ SV244 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2195,plain,
! [SV600: $i,SV728: $i,SV469: $i,SV247: $i] :
( ( ( ~ ( func @ SV247 @ SV469 @ SV728 )
| ~ ! [SY3165: $i] :
( ~ ( in @ SY3165 @ SV247 )
| ( ( ap @ SV247 @ SV469 @ SV600 @ SY3165 )
= ( ap @ SV247 @ SV469 @ SV728 @ SY3165 ) ) )
| ! [SY3166: $i] :
( ~ ( in @ SY3166 @ SV247 )
| ! [SY3167: $i] :
( ~ ( in @ SY3167 @ SV469 )
| ~ ( in @ ( kpair @ SY3166 @ SY3167 ) @ SV728 )
| ( in @ ( kpair @ SY3166 @ SY3167 ) @ SV600 ) ) ) )
= $true )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2196,plain,
! [SV470: $i,SV248: $i,SV668: $i] :
( ( ( ~ ( in @ SV668 @ ( powerset @ SV248 ) ) )
= $true )
| ( ( subset @ ( setminus @ SV248 @ SV470 ) @ ( setminus @ SV248 @ ( binintersect @ SV470 @ SV668 ) ) )
= $true )
| ( ( in @ SV470 @ ( powerset @ SV248 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1994]) ).
thf(2197,plain,
! [SV471: $i,SV249: $i > $i > $o] :
( ( ( ~ ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 ) )
= $false )
| ( ( ~ ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1995]) ).
thf(2198,plain,
! [SV471: $i,SV249: $i > $i > $o] :
( ( ( ~ ! [SY3124: $i] :
~ ~ ( ~ ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SY3124 )
| ~ ! [SY3125: $i] :
( ~ ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SY3125 )
| ( SY3124 = SY3125 ) ) ) )
= $false )
| ( ( ~ ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1995]) ).
thf(2199,plain,
! [SV601: $i,SV474: $o,SV252: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV252 )
| ~ ~ SV474
| ( ( if @ SV252 @ SV474 @ SV601 @ SV729 )
= SV729 ) )
= $true )
| ( ( in @ SV601 @ SV252 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2200,plain,
! [SV602: $i,SV252: $i,SV730: $i] :
( ( ( ~ ( in @ SV730 @ SV252 )
| ~ ~ $true
| ( ( if @ SV252 @ $true @ SV602 @ SV730 )
= SV730 ) )
= $true )
| ( ( in @ SV602 @ SV252 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2201,plain,
! [SV603: $i,SV252: $i,SV731: $i] :
( ( ( ~ ( in @ SV731 @ SV252 )
| ~ ~ $false
| ( ( if @ SV252 @ $false @ SV603 @ SV731 )
= SV731 ) )
= $true )
| ( ( in @ SV603 @ SV252 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2202,plain,
! [SV253: $i,SV604: $i,SV475: $i,SV732: $i] :
( ( ( ~ ( in @ SV732 @ SV475 )
| ( in @ ( setadjoin @ ( setadjoin @ SV604 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV604 @ ( setadjoin @ SV732 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV253 @ SV475 ) ) ) ) )
= $true )
| ( ( in @ SV604 @ SV253 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2203,plain,
! [SV476: $i,SV254: $i,SV733: $i,SV669: $i] :
( ( ( ( SV669 != SV733 )
| ~ ( ~ ( ~ ( in @ SV669 @ SV254 )
| ( in @ SV733 @ SV476 ) )
| ~ ( ~ ( in @ SV733 @ SV476 )
| ( in @ SV669 @ SV254 ) ) ) )
= $true )
| ( ( SV254 = SV476 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2204,plain,
! [SV255: $i,SV477: $i] :
( ( ( subset @ SV477 @ SV255 )
= $false )
| ( ( SV255 = SV477 )
= $true )
| ( ( subset @ SV255 @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2001]) ).
thf(2205,plain,
! [SV670: $i,SV256: $i > $o] :
( ( ( ~ ( ~ ( SV256 @ SV670 )
| ~ ! [SY3127: $i] :
( ~ ( SV256 @ SY3127 )
| ( SV670 = SY3127 ) ) ) )
= $false )
| ( ( ~ ! [SY2511: $i] :
~ ! [SY2512: $i] :
~ ( ~ ( ~ ( SV256 @ SY2512 )
| ( SY2512 = SY2511 ) )
| ~ ( ( SY2512 != SY2511 )
| ( SV256 @ SY2512 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2002]) ).
thf(2206,plain,
! [SV478: $i,SV257: $i,SV671: $i] :
( ( ( ~ ( in @ SV671 @ ( powerset @ SV257 ) ) )
= $true )
| ( ( in @ ( binunion @ SV478 @ SV671 ) @ ( powerset @ SV257 ) )
= $true )
| ( ( in @ SV478 @ ( powerset @ SV257 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2003]) ).
thf(2207,plain,
! [SV258: $i,SV605: $i,SV479: $i,SV734: $i] :
( ( ( ~ ( in @ SV734 @ SV479 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV605 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV605 @ ( setadjoin @ SV734 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV258 @ SV479 ) ) ) )
= $true )
| ( ( in @ SV605 @ SV258 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2208,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ~ ( SV35 @ SV621 )
| ~ ! [SY3073: $i] :
( ~ ( SV35 @ SY3073 )
| ( SV621 = SY3073 ) ) )
= $true )
| ( ( ~ ! [SY1902: $i] :
~ ~ ( ~ ( SV35 @ SY1902 )
| ~ ! [SY1903: $i] :
( ~ ( SV35 @ SY1903 )
| ( SY1902 = SY1903 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2005]) ).
thf(2209,plain,
! [SV282: $i,SV36: $i,SV622: $i] :
( ( ( in @ SV622 @ ( powerset @ SV36 ) )
= $false )
| ( ( ~ ( subset @ ( setminus @ SV36 @ SV622 ) @ ( setminus @ SV36 @ SV282 ) )
| ( subset @ SV282 @ SV622 ) )
= $true )
| ( ( in @ SV282 @ ( powerset @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2006]) ).
thf(2210,plain,
! [SV484: $i,SV284: $i,SV38: $i,SV672: $i] :
( ( ( ~ ( in @ SV672 @ SV38 ) )
= $true )
| ( ( ! [SY3128: $i] :
( ~ ( in @ SY3128 @ SV284 )
| ~ ( in @ ( kpair @ SV672 @ SY3128 ) @ SV484 )
| ( ( ap @ SV38 @ SV284 @ SV484 @ SV672 )
= SY3128 ) ) )
= $true )
| ( ( func @ SV38 @ SV284 @ SV484 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2007]) ).
thf(2211,plain,
! [SV485: $i,SV285: $o,SV39: $i,SV673: $i] :
( ( ( ~ ( in @ SV673 @ SV39 ) )
= $true )
| ( ( ~ SV285
| ( in @ SV485
@ ( dsetconstr @ SV39
@ ^ [SY3129: $i] :
( ~ ( ~ SV285
| ( SY3129 != SV485 ) )
| ~ ( ~ ~ SV285
| ( SY3129 != SV673 ) ) ) ) ) )
= $true )
| ( ( in @ SV485 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2008]) ).
thf(2212,plain,
! [SV486: $i,SV39: $i,SV674: $i] :
( ( ( ~ ( in @ SV674 @ SV39 ) )
= $true )
| ( ( ~ $true
| ( in @ SV486
@ ( dsetconstr @ SV39
@ ^ [SY3130: $i] :
( ~ ( ~ $true
| ( SY3130 != SV486 ) )
| ~ ( ~ ~ $true
| ( SY3130 != SV674 ) ) ) ) ) )
= $true )
| ( ( in @ SV486 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2009]) ).
thf(2213,plain,
! [SV487: $i,SV39: $i,SV675: $i] :
( ( ( ~ ( in @ SV675 @ SV39 ) )
= $true )
| ( ( ~ $false
| ( in @ SV487
@ ( dsetconstr @ SV39
@ ^ [SY3131: $i] :
( ~ ( ~ $false
| ( SY3131 != SV487 ) )
| ~ ( ~ ~ $false
| ( SY3131 != SV675 ) ) ) ) ) )
= $true )
| ( ( in @ SV487 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2010]) ).
thf(2214,plain,
! [SV676: $i > $o,SV623: $i > $o,SV286: $i,SV40: $i] :
( ( ( ~ ! [SY3132: $i] :
( ~ ( in @ SY3132 @ SV40 )
| ! [SY3133: $i] :
( ~ ( in @ SY3133 @ SV286 )
| ( SY3132 != SY3133 )
| ~ ( ~ ( ~ ( SV623 @ SY3132 )
| ( SV676 @ SY3133 ) )
| ~ ( ~ ( SV676 @ SY3133 )
| ( SV623 @ SY3132 ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2011]) ).
thf(2215,plain,
! [SV41: $i,SV287: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK30_SY2541 @ SV287 @ SV41 ) @ SV41 )
| ~ ( SV287 @ ( sK30_SY2541 @ SV287 @ SV41 ) ) ) )
= $false )
| ( ( ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV41 )
| ~ ( SV287 @ SY2542 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2012]) ).
thf(2216,plain,
! [SV288: $i,SV43: $i,SV488: $i] :
( ( ( in @ SV488 @ ( setminus @ SV43 @ SV288 ) )
= $false )
| ( ( in @ SV488 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2217,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
| ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 ) )
| ~ ( ( ( sK31_SY3079 @ SV624 @ SV44 )
!= SV624 )
| ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) ) ) ) )
= $false )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2014]) ).
thf(2218,plain,
! [SV46: $i,SV490: $i,SV290: $i,SV677: $i] :
( ( ( ~ ( in @ SV677 @ SV290 ) )
= $true )
| ( ( in @ ( kpair @ SV490 @ SV677 ) @ ( cartprod @ SV46 @ SV290 ) )
= $true )
| ( ( in @ SV490 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2016]) ).
thf(2219,plain,
! [SV291: $i,SV47: $i,SV491: $i] :
( ( ( ~ ( in @ SV491 @ ( setadjoin @ SV47 @ SV291 ) ) )
= $true )
| ( ( ( SV491 = SV47 )
| ( in @ SV491 @ SV291 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2017]) ).
thf(2220,plain,
! [SV291: $i,SV47: $i,SV491: $i] :
( ( ( ~ ( ( SV491 = SV47 )
| ( in @ SV491 @ SV291 ) ) )
= $true )
| ( ( in @ SV491 @ ( setadjoin @ SV47 @ SV291 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2018]) ).
thf(2221,plain,
! [SV493: $i,SV294: $i,SV51: $i,SV678: $i] :
( ( ( ~ ( in @ SV678 @ SV51 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV294
@ ^ [SY3136: $i] : ( in @ ( kpair @ SV678 @ SY3136 ) @ SV493 ) ) )
= $true )
| ( ( func @ SV51 @ SV294 @ SV493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2019]) ).
thf(2222,plain,
! [SV55: $i,SV494: $i,SV296: $i,SV679: $i] :
( ( ( ~ ( in @ SV679 @ SV296 ) )
= $true )
| ( ( ( kpair @ SV494 @ SV679 )
= ( kpair @ SV494 @ SV679 ) )
= $true )
| ( ( in @ SV494 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2020]) ).
thf(2223,plain,
! [SV56: $i,SV495: $i,SV297: $i,SV680: $i] :
( ( ( ~ ( in @ SV680 @ SV297 ) )
= $true )
| ( ( ( ksnd @ ( kpair @ SV495 @ SV680 ) )
= SV680 )
= $true )
| ( ( in @ SV495 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2021]) ).
thf(2224,plain,
! [SV496: $i,SV298: $i,SV57: $i,SV681: $i] :
( ( ( ~ ( in @ SV681 @ SV57 ) )
= $true )
| ( ( in @ ( kpair @ SV681 @ ( ap @ SV57 @ SV298 @ SV496 @ SV681 ) ) @ SV496 )
= $true )
| ( ( func @ SV57 @ SV298 @ SV496 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2022]) ).
thf(2225,plain,
! [SV499: $i,SV301: $o,SV60: $i,SV682: $i] :
( ( ( ~ ( in @ SV682 @ SV60 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY3137: $i] :
( ~ ( ~ SV301
| ( SY3137 != SV499 ) )
| ~ ( ~ ~ SV301
| ( SY3137 != SV682 ) ) ) ) )
= $true )
| ( ( in @ SV499 @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2023]) ).
thf(2226,plain,
! [SV500: $i,SV60: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV60 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY3138: $i] :
( ~ ( ~ $true
| ( SY3138 != SV500 ) )
| ~ ( ~ ~ $true
| ( SY3138 != SV683 ) ) ) ) )
= $true )
| ( ( in @ SV500 @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2024]) ).
thf(2227,plain,
! [SV501: $i,SV60: $i,SV684: $i] :
( ( ( ~ ( in @ SV684 @ SV60 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY3139: $i] :
( ~ ( ~ $false
| ( SY3139 != SV501 ) )
| ~ ( ~ ~ $false
| ( SY3139 != SV684 ) ) ) ) )
= $true )
| ( ( in @ SV501 @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2025]) ).
thf(2228,plain,
! [SV62: $i,SV303: $i,SV503: $i] :
( ( ( in @ SV503 @ SV303 )
= $false )
| ( ( in @ SV503 @ ( binintersect @ SV62 @ SV303 ) )
= $true )
| ( ( in @ SV503 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2026]) ).
thf(2229,plain,
! [SV63: $i,SV304: $i,SV504: $i] :
( ( ( subset @ SV504 @ SV304 )
= $false )
| ( ( subset @ SV504 @ ( binintersect @ SV63 @ SV304 ) )
= $true )
| ( ( subset @ SV504 @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2230,plain,
! [SV305: $i,SV64: $i,SV625: $i] :
( ( ( in @ SV625 @ ( powerset @ SV64 ) )
= $false )
| ( ( ! [SY3080: $i] :
( ~ ( in @ SY3080 @ SV64 )
| ~ ( in @ SY3080 @ ( setminus @ SV64 @ SV305 ) )
| ~ ( in @ SY3080 @ ( binintersect @ SV305 @ SV625 ) ) ) )
= $true )
| ( ( in @ SV305 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2231,plain,
! [SV307: $i,SV66: $i,SV626: $i] :
( ( ( in @ SV626 @ ( powerset @ SV66 ) )
= $false )
| ( ( ! [SY3081: $i] :
( ~ ( in @ SY3081 @ SV66 )
| ~ ~ ( in @ SY3081 @ ( binunion @ SV307 @ SV626 ) )
| ~ ( in @ SY3081 @ SV626 ) ) )
= $true )
| ( ( in @ SV307 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2029]) ).
thf(2232,plain,
! [SV506: $i,SV308: $i,SV67: $i,SV685: $i] :
( ( ( ~ ( in @ SV685 @ SV67 ) )
= $true )
| ( ( ( ap @ SV67 @ SV308 @ SV506 @ SV685 )
= ( ap @ SV67 @ SV308 @ SV506 @ SV685 ) )
= $true )
| ( ( func @ SV67 @ SV308 @ SV506 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2030]) ).
thf(2233,plain,
! [SV69: $i,SV310: $i] :
( ( ( in @ SV310 @ ( setunion @ SV69 ) )
= $false )
| ( ( ~ ! [SY2574: $i] :
~ ~ ( ~ ( in @ SV310 @ SY2574 )
| ~ ( in @ SY2574 @ SV69 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2032]) ).
thf(2234,plain,
! [SV69: $i,SV310: $i] :
( ( ( ~ ! [SY2575: $i] :
~ ~ ( ~ ( in @ SV310 @ SY2575 )
| ~ ( in @ SY2575 @ SV69 ) ) )
= $false )
| ( ( in @ SV310 @ ( setunion @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2235,plain,
! [SV311: $i,SV70: $i,SV627: $i] :
( ( ( in @ SV627 @ ( powerset @ SV70 ) )
= $false )
| ( ( ! [SY3082: $i] :
( ~ ( in @ SY3082 @ SV70 )
| ~ ( in @ SY3082 @ ( setminus @ SV70 @ ( binunion @ SV311 @ SV627 ) ) )
| ~ ( in @ SY3082 @ SV311 ) ) )
= $true )
| ( ( in @ SV311 @ ( powerset @ SV70 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2034]) ).
thf(2236,plain,
! [SV71: $i,SV312: $i] :
( ( ( in @ ( sK6_SY2578 @ SV312 @ SV71 ) @ SV71 )
= $true )
| ( ( subset @ SV71 @ SV312 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2035]) ).
thf(2237,plain,
! [SV314: $i,SV73: $i,SV628: $i] :
( ( ( in @ SV628 @ ( powerset @ SV73 ) )
= $false )
| ( ( ~ ! [SY3083: $i] :
( ~ ( in @ SY3083 @ SV73 )
| ~ ( in @ SY3083 @ SV314 )
| ( in @ SY3083 @ SV628 ) )
| ( in @ SV314 @ ( powerset @ SV628 ) ) )
= $true )
| ( ( in @ SV314 @ ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2037]) ).
thf(2238,plain,
! [SV686: $o,SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( ~ ( in @ SV509 @ SV74 )
| ~ ~ ( in @ SV509 @ SV315 )
| SV686 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SV686 )
| SV686 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2038]) ).
thf(2239,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( ~ ( in @ SV509 @ SV74 )
| ~ ~ ( in @ SV509 @ SV315 )
| $true ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $true )
| $true )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2039]) ).
thf(2240,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( ~ ( in @ SV509 @ SV74 )
| ~ ~ ( in @ SV509 @ SV315 )
| $false ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $false )
| $false )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2040]) ).
thf(2241,plain,
! [SV76: $i,SV316: $i,SV510: $i] :
( ( ( ~ ( in @ SV510 @ SV316 ) )
= $false )
| ( ( ~ ( in @ SV510 @ SV76 ) )
= $true )
| ( ( subset @ SV76 @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2041]) ).
thf(2242,plain,
! [SV511: $i > $i > $o,SV317: $i,SV77: $i,SV629: $i,SV606: $i] :
( ( ( in @ ( kpair @ SV606 @ SV629 )
@ ( dpsetconstr @ SV77 @ SV317
@ ^ [SY2916: $i,SY2917: $i] : ( SV511 @ SY2916 @ SY2917 ) ) )
= $false )
| ( ( in @ SV629 @ SV317 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2042]) ).
thf(2243,plain,
! [SV78: $i] :
( ( ( in @ ( sK18_SY2009 @ SV78 ) @ SV78 )
= $true )
| ( ( SV78 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2043]) ).
thf(2244,plain,
! [SV79: $i,SV318: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK32_SY2591 @ SV318 @ SV79 ) @ SV79 )
| ~ ( SV318 @ ( sK32_SY2591 @ SV318 @ SV79 ) ) ) )
= $false )
| ( ( ! [SY2592: $i] :
( ~ ( in @ SY2592 @ SV79 )
| ~ ( SV318 @ SY2592 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2044]) ).
thf(2245,plain,
! [SV630: $i,SV82: $i] :
( ( ( ! [SY2017: $i] :
~ ~ ( ~ ( in @ SY2017 @ SV82 )
| ~ ~ ~ ! [SY2018: $i] :
~ ~ ( ~ ( in @ SY2018 @ SY2017 )
| ~ ( in @ SY2018 @ SV82 ) ) ) )
= $false )
| ( ( in @ SV630 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2045]) ).
thf(2246,plain,
! [SV322: $i,SV607: $o,SV84: $i,SV513: $i] :
( ( ( ~ ( ~ ( in @ SV513 @ SV84 )
| SV607 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| SV607 )
| SV607 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2247,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( ( ~ ( ~ ( in @ SV513 @ SV84 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| $true )
| $true )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2047]) ).
thf(2248,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( ( ~ ( ~ ( in @ SV513 @ SV84 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| $false )
| $false )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2048]) ).
thf(2249,plain,
! [SV323: $i,SV85: $i,SV631: $i] :
( ( ( in @ SV631 @ ( powerset @ SV85 ) )
= $false )
| ( ( ! [SY3086: $i] :
( ~ ( in @ SY3086 @ SV85 )
| ~ ~ ( in @ SY3086 @ ( binunion @ SV323 @ SV631 ) )
| ~ ( in @ SY3086 @ SV323 ) ) )
= $true )
| ( ( in @ SV323 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2250,plain,
! [SV325: $i > $o,SV87: $i,SV687: $i] :
( ( ( ~ ( in @ SV687 @ SV87 ) )
= $true )
| ( ( SV325 @ SV687 )
= $true )
| ( ( ~ ! [SY2599: $i] :
~ ~ ( ~ ( in @ SY2599 @ SV87 )
| ~ ~ ( SV325 @ SY2599 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2050]) ).
thf(2251,plain,
! [SV88: $i,SV326: $i] :
( ( ( in @ ( sK7_SY2600 @ SV326 @ SV88 ) @ SV88 )
= $true )
| ( ( ~ ! [SY2601: $i] :
( ~ ( in @ SY2601 @ SV326 )
| ( in @ SY2601 @ SV88 ) )
| ( SV88 = SV326 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2051]) ).
thf(2252,plain,
! [SV88: $i,SV326: $i] :
( ( ( ~ ! [SY2601: $i] :
( ~ ( in @ SY2601 @ SV326 )
| ( in @ SY2601 @ SV88 ) ) )
= $true )
| ( ( SV88 = SV326 )
= $true )
| ( ( in @ ( sK7_SY2600 @ SV326 @ SV88 ) @ SV326 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2052]) ).
thf(2253,plain,
! [SV632: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV632 )
| ~ ! [SY3087: $i] :
( ~ ( SV91 @ SY3087 )
| ( SV632 = SY3087 ) ) )
= $true )
| ( ( ! [SY2037: $i,SY2038: $i] :
( ~ ( SV91 @ SY2037 )
| ~ ( SV91 @ SY2038 )
| ( SY2037 = SY2038 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2053]) ).
thf(2254,plain,
! [SV514: $i,SV329: $i,SV92: $i,SV688: $i] :
( ( ( ~ ( in @ SV688 @ SV92 ) )
= $true )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV329
@ ^ [SY3140: $i] : ( in @ ( kpair @ SV688 @ SY3140 ) @ SV514 ) ) )
@ SV329 )
= $true )
| ( ( func @ SV92 @ SV329 @ SV514 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2054]) ).
thf(2255,plain,
! [SV94: $i,SV331: $i,SV515: $i] :
( ( ( ~ ( in @ SV515 @ SV331 ) )
= $false )
| ( ( ~ ( subset @ SV94 @ SV331 ) )
= $true )
| ( ( in @ SV515 @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2055]) ).
thf(2256,plain,
! [SV516: $i,SV332: $i,SV95: $i,SV689: $i] :
( ( ( ~ ( subset @ SV689 @ ( cartprod @ SV95 @ SV332 ) ) )
= $true )
| ( ( ~ ! [SY3141: $i] :
( ~ ( in @ SY3141 @ SV95 )
| ! [SY3142: $i] :
( ~ ( in @ SY3142 @ SV332 )
| ~ ( in @ ( kpair @ SY3141 @ SY3142 ) @ SV516 )
| ( in @ ( kpair @ SY3141 @ SY3142 ) @ SV689 ) ) )
| ( subset @ SV516 @ SV689 ) )
= $true )
| ( ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2056]) ).
thf(2257,plain,
! [SV96: $i,SV333: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY2610 @ SV333 @ SV96 ) @ SV96 )
| ~ ( in @ SV333 @ ( sK19_SY2610 @ SV333 @ SV96 ) ) ) )
= $true )
| ( ( in @ SV333 @ ( setunion @ SV96 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2057]) ).
thf(2258,plain,
! [SV334: $i,SV97: $i,SV633: $i] :
( ( ( in @ SV633 @ SV97 )
= $false )
| ( ( ~ ~ ( in @ SV633 @ ( setminus @ SV97 @ SV334 ) )
| ( in @ SV633 @ SV334 ) )
= $true )
| ( ( in @ SV334 @ ( powerset @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2058]) ).
thf(2259,plain,
! [SV335: $i > $o,SV98: $i,SV517: $i] :
( ( ( ~ ( ~ ( in @ SV517
@ ( dsetconstr @ SV98
@ ^ [SY2613: $i] : ( SV335 @ SY2613 ) ) )
| ( SV335 @ SV517 ) ) )
= $false )
| ( ( in @ SV517 @ SV98 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2059]) ).
thf(2260,plain,
! [SV98: $i,SV517: $i,SV335: $i > $o] :
( ( ( ~ ( ~ ( SV335 @ SV517 )
| ( in @ SV517
@ ( dsetconstr @ SV98
@ ^ [SY2614: $i] : ( SV335 @ SY2614 ) ) ) ) )
= $false )
| ( ( in @ SV517 @ SV98 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2059]) ).
thf(2261,plain,
! [SV336: $i,SV99: $i] :
( ( ( in @ ( sK8_SY2615 @ SV99 @ SV336 ) @ SV336 )
= $true )
| ( ( in @ SV336 @ ( powerset @ SV99 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2060]) ).
thf(2262,plain,
! [SV100: $i,SV518: $i,SV337: $i > $o] :
( ( ( SV337 @ SV518 )
= $false )
| ( ( ~ ! [SY2926: $i] :
( ~ ( in @ SY2926 @ SV100 )
| ~ ( SV337 @ SY2926 )
| ( SY2926 = SV518 ) )
| ( singleton
@ ( dsetconstr @ SV100
@ ^ [SY2618: $i] : ( SV337 @ SY2618 ) ) ) )
= $true )
| ( ( in @ SV518 @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2062]) ).
thf(2263,plain,
! [SV519: $i > $i > $o,SV338: $i,SV101: $i,SV634: $i,SV608: $i] :
( ( ( in @ ( kpair @ SV608 @ SV634 )
@ ( dpsetconstr @ SV101 @ SV338
@ ^ [SY2930: $i,SY2931: $i] : ( SV519 @ SY2930 @ SY2931 ) ) )
= $false )
| ( ( SV519 @ SV608 @ SV634 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2264,plain,
( ( in @ sK9_SY2932 @ ( powerset @ sK1_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2064]) ).
thf(2265,plain,
( ( ! [SY3168: $i] :
( ~ ( in @ SY3168 @ sK1_SX0 )
| ~ ( in @ SY3168 @ ( binunion @ sK2_SY2624 @ sK9_SY2932 ) )
| ~ ( ~ ( in @ SY3168 @ sK2_SY2624 )
| sK33_SY3090 )
| ~ ( ~ ( in @ SY3168 @ sK9_SY2932 )
| sK33_SY3090 )
| sK33_SY3090 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[2065]) ).
thf(2266,plain,
! [SV104: $i,SV521: $i,SV341: $i,SV690: $i] :
( ( ( ~ ( in @ SV690 @ SV341 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV521 @ ( setadjoin @ SV690 @ emptyset ) ) @ ( binunion @ SV104 @ SV341 ) )
= $true )
| ( ( in @ SV521 @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2066]) ).
thf(2267,plain,
! [SV691: $i > $o,SV522: $i,SV342: $i,SV105: $i] :
( ( ( ~ ! [SY3143: $i] :
( ~ ( in @ SY3143 @ SV105 )
| ! [SY3144: $i] :
( ~ ( in @ SY3144 @ SV342 )
| ~ ( in @ ( kpair @ SY3143 @ SY3144 ) @ SV522 )
| ( SV691 @ ( kpair @ SY3143 @ SY3144 ) ) ) ) )
= $true )
| ( ( ! [SY3145: $i] :
( ~ ( in @ SY3145 @ SV522 )
| ( SV691 @ SY3145 ) ) )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2067]) ).
thf(2268,plain,
! [SV635: $i,SV106: $i > $o] :
( ( ( ~ ( SV106 @ SV635 )
| ~ ! [SY3092: $i] :
( ~ ( SV106 @ SY3092 )
| ( SV635 = SY3092 ) ) )
= $true )
| ( ( ! [SY2086: $i,SY2087: $i] :
( ~ ( SV106 @ SY2086 )
| ~ ( SV106 @ SY2087 )
| ( SY2086 = SY2087 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2068]) ).
thf(2269,plain,
! [SV107: $i,SV523: $i,SV343: $i > $o] :
( ( ( SV343 @ SV523 )
= $false )
| ( ( in @ SV523
@ ( dsetconstr @ SV107
@ ^ [SY2638: $i] : ( SV343 @ SY2638 ) ) )
= $true )
| ( ( in @ SV523 @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2069]) ).
thf(2270,plain,
! [SV636: $i,SV108: $i > $o] :
( ( ( ~ ( SV108 @ SV636 )
| ~ ! [SY3093: $i] :
( ~ ( SV108 @ SY3093 )
| ( SV636 = SY3093 ) ) )
= $true )
| ( ( SV108
@ ( descr
@ ^ [SY2093: $i] : ( SV108 @ SY2093 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2070]) ).
thf(2271,plain,
! [SV524: $i > $i > $o,SV344: $i,SV109: $i,SV637: $i,SV609: $i] :
( ( ( in @ ( kpair @ SV609 @ SV637 )
@ ( dpsetconstr @ SV109 @ SV344
@ ^ [SY2944: $i,SY2945: $i] : ( SV524 @ SY2944 @ SY2945 ) ) )
= $false )
| ( ( in @ SV609 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2071]) ).
thf(2272,plain,
! [SV113: $i,SV347: $i,SV525: $i] :
( ( ( ~ ~ ( in @ SV525 @ SV347 ) )
= $true )
| ( ( ~ ( in @ SV525 @ SV113 ) )
= $true )
| ( ( in @ SV525 @ ( setminus @ SV113 @ SV347 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2072]) ).
thf(2273,plain,
! [SV638: $i,SV114: $i > $o] :
( ( ( ~ ( SV114 @ SV638 )
| ~ ! [SY3096: $i] :
( ~ ( SV114 @ SY3096 )
| ( SV638 = SY3096 ) ) )
= $true )
| ( ( ~ ! [SY2107: $i] :
~ ( SV114 @ SY2107 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2073]) ).
thf(2274,plain,
! [SV348: $i,SV115: $i,SV639: $i] :
( ( ( in @ SV639 @ ( powerset @ SV115 ) )
= $false )
| ( ( ! [SY3097: $i] :
( ~ ( in @ SY3097 @ ( powerset @ SV115 ) )
| ! [SY3098: $i] :
( ~ ( in @ SY3098 @ SV115 )
| ~ ( in @ SY3098 @ ( binintersect @ SV348 @ SV639 ) )
| ( in @ SY3098 @ ( binunion @ SV348 @ SY3097 ) ) ) ) )
= $true )
| ( ( in @ SV348 @ ( powerset @ SV115 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2074]) ).
thf(2275,plain,
! [SV349: $i,SV117: $i,SV640: $i] :
( ( ( in @ SV640 @ ( powerset @ SV117 ) )
= $false )
| ( ( in @ ( binintersect @ SV349 @ SV640 ) @ ( powerset @ SV117 ) )
= $true )
| ( ( in @ SV349 @ ( powerset @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2075]) ).
thf(2276,plain,
! [SV118: $i,SV350: $i > $o] :
( ( ( in @ ( sK10_SY2649 @ SV350 @ SV118 ) @ SV118 )
= $true )
| ( ( ~ ~ ! [SY2650: $i] :
~ ~ ( ~ ( in @ SY2650 @ SV118 )
| ~ ( SV350 @ SY2650 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2076]) ).
thf(2277,plain,
! [SV118: $i,SV350: $i > $o] :
( ( ( SV350 @ ( sK10_SY2649 @ SV350 @ SV118 ) )
= $true )
| ( ( ~ ~ ! [SY2650: $i] :
~ ~ ( ~ ( in @ SY2650 @ SV118 )
| ~ ( SV350 @ SY2650 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2077]) ).
thf(2278,plain,
! [SV351: $i > $o,SV119: $i,SV692: $i] :
( ( ( ~ ( in @ SV692 @ SV119 ) )
= $true )
| ( ( SV351 @ SV692 )
= $true )
| ( ( ~ ! [SY2652: $i] :
~ ~ ( ~ ( in @ SY2652 @ SV119 )
| ~ ~ ( SV351 @ SY2652 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2078]) ).
thf(2279,plain,
! [SV352: $i,SV120: $i,SV641: $i] :
( ( ( in @ SV641 @ ( powerset @ SV120 ) )
= $false )
| ( ( ! [SY3099: $i] :
( ~ ( in @ SY3099 @ SV120 )
| ~ ~ ( in @ SY3099 @ SV641 )
| ~ ( in @ SY3099 @ ( binintersect @ SV352 @ SV641 ) ) ) )
= $true )
| ( ( in @ SV352 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2079]) ).
thf(2280,plain,
! [SV353: $i,SV121: $i,SV642: $i] :
( ( ( in @ SV642 @ ( powerset @ SV121 ) )
= $false )
| ( ( ~ ( subset @ SV353 @ ( setminus @ SV121 @ SV642 ) )
| ! [SY3100: $i] :
( ~ ( in @ SY3100 @ SV121 )
| ~ ( in @ SY3100 @ SV642 )
| ( in @ SY3100 @ ( setminus @ SV121 @ SV353 ) ) ) )
= $true )
| ( ( in @ SV353 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2281,plain,
! [SV123: $i,SV526: $i > $i,SV355: $i] :
( ( ( ~ ( in @ ( sK20_SY2946 @ SV355 @ SV526 @ SV123 ) @ SV123 ) )
= $false )
| ( ( in
@ ( lam @ SV123 @ SV355
@ ^ [SY2947: $i] : ( SV526 @ SY2947 ) )
@ ( funcSet @ SV123 @ SV355 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2082]) ).
thf(2282,plain,
! [SV123: $i,SV355: $i,SV526: $i > $i] :
( ( ( in @ ( SV526 @ ( sK20_SY2946 @ SV355 @ SV526 @ SV123 ) ) @ SV355 )
= $false )
| ( ( in
@ ( lam @ SV123 @ SV355
@ ^ [SY2947: $i] : ( SV526 @ SY2947 ) )
@ ( funcSet @ SV123 @ SV355 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2082]) ).
thf(2283,plain,
! [SV356: $i,SV124: $i,SV527: $i] :
( ( ( in @ SV527 @ SV124 )
= $false )
| ( ( in @ SV356 @ ( setunion @ SV124 ) )
= $true )
| ( ( in @ SV356 @ SV527 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2083]) ).
thf(2284,plain,
! [SV358: $i,SV693: $o,SV126: $i,SV529: $i] :
( ( ( ~ ( ( SV529 != SV126 )
| SV693 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| SV693 )
| SV693 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2084]) ).
thf(2285,plain,
! [SV358: $i,SV126: $i,SV529: $i] :
( ( ( ~ ( ( SV529 != SV126 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| $true )
| $true )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2085]) ).
thf(2286,plain,
! [SV358: $i,SV126: $i,SV529: $i] :
( ( ( ~ ( ( SV529 != SV126 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| $false )
| $false )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2086]) ).
thf(2287,plain,
! [SV127: $i,SV359: $i,SV530: $i] :
( ( ( ~ ~ ( in @ SV530 @ SV359 ) )
= $true )
| ( ( ~ ( in @ SV530 @ ( symdiff @ SV127 @ SV359 ) ) )
= $true )
| ( ( in @ SV530 @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2087]) ).
thf(2288,plain,
! [SV128: $i,SV531: $i,SV360: $i,SV694: $i] :
( ( ( ~ ( in @ SV694 @ SV360 ) )
= $true )
| ( ( in @ ( setadjoin @ SV531 @ ( setadjoin @ SV694 @ emptyset ) ) @ ( powerset @ ( binunion @ SV128 @ SV360 ) ) )
= $true )
| ( ( in @ SV531 @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2088]) ).
thf(2289,plain,
! [SV361: $i,SV129: $i,SV643: $i] :
( ( ( in @ SV643 @ ( powerset @ SV129 ) )
= $false )
| ( ( ~ ( subset @ SV361 @ ( setminus @ SV129 @ SV643 ) )
| ( subset @ SV643 @ ( setminus @ SV129 @ SV361 ) ) )
= $true )
| ( ( in @ SV361 @ ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2089]) ).
thf(2290,plain,
! [SV362: $i,SV130: $i,SV644: $i] :
( ( ( in @ SV644 @ ( powerset @ SV130 ) )
= $false )
| ( ( ! [SY3101: $i] :
( ~ ( in @ SY3101 @ SV130 )
| ~ ~ ( in @ SY3101 @ SV362 )
| ~ ( in @ SY3101 @ ( binintersect @ SV362 @ SV644 ) ) ) )
= $true )
| ( ( in @ SV362 @ ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2090]) ).
thf(2291,plain,
! [SV363: $i,SV131: $i,SV645: $i] :
( ( ( in @ SV645 @ ( powerset @ SV131 ) )
= $false )
| ( ( ! [SY3102: $i] :
( ~ ( in @ SY3102 @ SV131 )
| ~ ( in @ SY3102 @ ( setminus @ SV131 @ SV363 ) )
| ( in @ SY3102 @ ( setminus @ SV131 @ ( binintersect @ SV363 @ SV645 ) ) ) ) )
= $true )
| ( ( in @ SV363 @ ( powerset @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2091]) ).
thf(2292,plain,
! [SV365: $i,SV133: $i,SV646: $i] :
( ( ( in @ SV646 @ SV133 )
= $false )
| ( ( ~ ( in @ SV646 @ SV365 )
| ( in @ SV646 @ ( setminus @ SV133 @ ( setminus @ SV133 @ SV365 ) ) ) )
= $true )
| ( ( in @ SV365 @ ( powerset @ SV133 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2092]) ).
thf(2293,plain,
! [SV367: $i > $o,SV135: $i,SV647: $i] :
( ( ( in @ SV647 @ SV135 )
= $false )
| ( ( ! [SY3103: $i] :
( ~ ( in @ SY3103 @ SV135 )
| ~ ( SV367 @ SV647 )
| ~ ( SV367 @ SY3103 )
| ( SV647 = SY3103 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV135
@ ^ [SY2676: $i] : ( SV367 @ SY2676 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2093]) ).
thf(2294,plain,
! [SV648: $o,SV136: $i,SV368: $i] :
( ( ( ! [SY3104: $i] :
( ~ ( in @ SV368 @ SY3104 )
| ~ ( in @ SY3104 @ SV136 )
| SV648 ) )
= $false )
| ( SV648 = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2094]) ).
thf(2295,plain,
! [SV136: $i,SV368: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV368 @ SX0 )
| ~ ( in @ SX0 @ SV136 )
| $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2095]) ).
thf(2296,plain,
! [SV136: $i,SV368: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV368 @ SX0 )
| ~ ( in @ SX0 @ SV136 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2096]) ).
thf(2297,plain,
! [SV369: $i,SV137: $i,SV649: $i] :
( ( ( in @ SV649 @ ( powerset @ SV137 ) )
= $false )
| ( ( ! [SY3105: $i] :
( ~ ( in @ SY3105 @ SV137 )
| ~ ( subset @ SV369 @ SV649 )
| ~ ~ ( in @ SY3105 @ SV649 )
| ~ ( in @ SY3105 @ SV369 ) ) )
= $true )
| ( ( in @ SV369 @ ( powerset @ SV137 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2298,plain,
! [SV538: $i,SV374: $i,SV143: $i,SV695: $i] :
( ( ( ~ ( in @ SV695 @ SV143 ) )
= $true )
| ( ( in @ ( kpair @ SV695 @ ( ap @ SV143 @ SV374 @ SV538 @ SV695 ) ) @ SV538 )
= $true )
| ( ( in @ SV538 @ ( funcSet @ SV143 @ SV374 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2100]) ).
thf(2299,plain,
! [SV377: $i,SV146: $i,SV650: $i] :
( ( ( in @ SV650 @ ( powerset @ SV146 ) )
= $false )
| ( ( ~ ! [SY3106: $i] :
( ~ ( in @ SY3106 @ SV146 )
| ~ ( in @ SY3106 @ SV377 )
| ( in @ SY3106 @ SV650 ) )
| ( subset @ SV377 @ SV650 ) )
= $true )
| ( ( in @ SV377 @ ( powerset @ SV146 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2101]) ).
thf(2300,plain,
! [SV147: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY2953: $i] :
( ~ ( in @ SY2953 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY2188: $i] :
( ~ ( in @ SY2188 @ SY2953 )
| ( in @ SY2188 @ SV147 ) ) )
| ~ ! [SY2955: $i,SY2956: $i] :
( ~ ~ ( ~ ( in @ SY2955 @ SV147 )
| ~ ( in @ SY2956 @ SV147 ) )
| ~ ! [SY2957: $i] :
( ~ ( in @ SY2957 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SY2955 @ SY2957 )
| ( in @ SY2956 @ SY2957 ) )
| ~ ( ~ ( in @ SY2956 @ SY2957 )
| ( in @ SY2955 @ SY2957 ) ) ) )
| ( SY2955 = SY2956 ) ) )
| ~ ! [SY2958: $i,SY2959: $i] :
( ~ ~ ( ~ ( in @ SY2958 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY2959 @ ( sK3_SY2186 @ SV147 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2958 )
| ( in @ SX4 @ SY2959 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2959 )
| ( in @ SX4 @ SY2958 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2102]) ).
thf(2301,plain,
! [SV147: $i] :
( ( ! [SY2962: $i] :
( ~ ~ ( ~ ! [SY2197: $i] :
( ~ ( in @ SY2197 @ SY2962 )
| ( in @ SY2197 @ SV147 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY2962 ) )
| ~ ! [SY2965: $i] :
~ ~ ! [SY2966: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY2965 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY2966 @ SY2962 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY2965 )
| ~ ( in @ SX5 @ SY2962 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY2965 ) )
| ( in @ SY2966 @ SY2968 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2103]) ).
thf(2302,plain,
! [SV378: $i,SV148: $i,SV540: $i] :
( ( ( in @ SV540 @ SV148 )
= $false )
| ( ( in @ SV540 @ SV378 )
= $true )
| ( ( subset @ SV148 @ SV378 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2104]) ).
thf(2303,plain,
! [SV381: $i,SV151: $i,SV651: $i] :
( ( ( in @ SV651 @ ( powerset @ SV151 ) )
= $false )
| ( ( ! [SY3107: $i] :
( ~ ( in @ SY3107 @ ( powerset @ SV151 ) )
| ! [SY3108: $i] :
( ~ ( in @ SY3108 @ SV151 )
| ~ ( in @ SY3108 @ ( binintersect @ SV381 @ SV651 ) )
| ( in @ SY3108 @ ( binunion @ SV651 @ SY3107 ) ) ) ) )
= $true )
| ( ( in @ SV381 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2105]) ).
thf(2304,plain,
! [SV155: $i,SV385: $i] :
( ( ( in @ ( sK11_SY2701 @ SV385 @ SV155 ) @ SV155 )
= $true )
| ( ( subset @ SV155 @ SV385 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2108]) ).
thf(2305,plain,
! [SV386: $i,SV156: $i,SV652: $i] :
( ( ( in @ SV652 @ ( powerset @ SV156 ) )
= $false )
| ( ( ! [SY3109: $i] :
( ~ ( in @ SY3109 @ SV156 )
| ~ ( subset @ SV386 @ ( setminus @ SV156 @ SV652 ) )
| ~ ( in @ SY3109 @ SV652 )
| ~ ( in @ SY3109 @ SV386 ) ) )
= $true )
| ( ( in @ SV386 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2306,plain,
! [SV388: $i,SV158: $i,SV545: $i] :
( ( ( ~ ( in @ SV545 @ SV158 ) )
= $true )
| ( ( in @ SV545 @ SV388 )
= $true )
| ( ( in @ SV545 @ ( setminus @ SV158 @ SV388 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2111]) ).
thf(2307,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ! [SY2231: $i,SY2232: $i] :
( ~ ( SV160 @ SY2231 )
| ~ ( SV160 @ SY2232 )
| ( SY2231 = SY2232 ) ) )
= $true )
| ( ( ~ ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2112]) ).
thf(2308,plain,
! [SV390: $i,SV161: $i,SV654: $i] :
( ( ( in @ SV654 @ ( powerset @ SV161 ) )
= $false )
| ( ( in @ ( setminus @ SV161 @ SV390 ) @ ( powerset @ ( setminus @ SV161 @ ( binintersect @ SV390 @ SV654 ) ) ) )
= $true )
| ( ( in @ SV390 @ ( powerset @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2113]) ).
thf(2309,plain,
! [SV391: $i,SV162: $i,SV655: $i] :
( ( ( in @ SV655 @ ( powerset @ SV162 ) )
= $false )
| ( ( in @ ( setminus @ SV391 @ SV655 ) @ ( powerset @ SV162 ) )
= $true )
| ( ( in @ SV391 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2310,plain,
! [SV164: $i,SV392: $i,SV546: $i] :
( ( ( ~ ( in @ SV546 @ SV392 ) )
= $false )
| ( ( in @ SV546 @ ( symdiff @ SV164 @ SV392 ) )
= $true )
| ( ( in @ SV546 @ SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2311,plain,
! [SV393: $i,SV165: $i,SV696: $i,SV656: $i] :
( ( ( SV656 != SV696 )
= $true )
| ( ( ~ ( in @ SV656 @ SV165 )
| ( in @ SV696 @ SV393 ) )
= $true )
| ( ( SV165 = SV393 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2116]) ).
thf(2312,plain,
! [SV166: $i,SV394: $i,SV547: $i] :
( ( ( ~ ( in @ SV547 @ SV394 ) )
= $false )
| ( ( SV166 != SV394 )
= $true )
| ( ( in @ SV547 @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2117]) ).
thf(2313,plain,
! [SV395: $i,SV167: $i,SV657: $i] :
( ( ( in @ SV657 @ ( powerset @ SV167 ) )
= $false )
| ( ( ! [SY3111: $i] :
( ~ ( in @ SY3111 @ SV167 )
| ~ ( in @ SY3111 @ ( setminus @ SV167 @ ( binunion @ SV395 @ SV657 ) ) )
| ( in @ SY3111 @ ( setminus @ SV167 @ SV395 ) ) ) )
= $true )
| ( ( in @ SV395 @ ( powerset @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2314,plain,
! [SV548: $i,SV697: $i,SV396: $i,SV168: $i] :
( ( ( ~ ( func @ SV168 @ SV396 @ SV697 ) )
= $true )
| ( ( ~ ! [SY3146: $i] :
( ~ ( in @ SY3146 @ SV168 )
| ( ( ap @ SV168 @ SV396 @ SV548 @ SY3146 )
= ( ap @ SV168 @ SV396 @ SV697 @ SY3146 ) ) )
| ( SV548 = SV697 ) )
= $true )
| ( ( func @ SV168 @ SV396 @ SV548 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2119]) ).
thf(2315,plain,
! [SV549: $i,SV397: $o,SV169: $i,SV698: $i] :
( ( ( ~ ( in @ SV698 @ SV169 ) )
= $true )
| ( ( in @ ( if @ SV169 @ SV397 @ SV549 @ SV698 ) @ ( setadjoin @ SV549 @ ( setadjoin @ SV698 @ emptyset ) ) )
= $true )
| ( ( in @ SV549 @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2120]) ).
thf(2316,plain,
! [SV550: $i,SV169: $i,SV699: $i] :
( ( ( ~ ( in @ SV699 @ SV169 ) )
= $true )
| ( ( in @ ( if @ SV169 @ $true @ SV550 @ SV699 ) @ ( setadjoin @ SV550 @ ( setadjoin @ SV699 @ emptyset ) ) )
= $true )
| ( ( in @ SV550 @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2121]) ).
thf(2317,plain,
! [SV551: $i,SV169: $i,SV700: $i] :
( ( ( ~ ( in @ SV700 @ SV169 ) )
= $true )
| ( ( in @ ( if @ SV169 @ $false @ SV551 @ SV700 ) @ ( setadjoin @ SV551 @ ( setadjoin @ SV700 @ emptyset ) ) )
= $true )
| ( ( in @ SV551 @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2122]) ).
thf(2318,plain,
! [SV170: $i,SV552: $i > $i,SV398: $i] :
( ( ( ~ ( in @ ( sK21_SY2977 @ SV398 @ SV552 @ SV170 ) @ SV170 ) )
= $false )
| ( ( ( lam @ SV170 @ SV398
@ ^ [SY2978: $i] : ( SV552 @ SY2978 ) )
= ( lam @ SV170 @ SV398
@ ^ [SY2979: $i] : ( SV552 @ SY2979 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2123]) ).
thf(2319,plain,
! [SV170: $i,SV398: $i,SV552: $i > $i] :
( ( ( in @ ( SV552 @ ( sK21_SY2977 @ SV398 @ SV552 @ SV170 ) ) @ SV398 )
= $false )
| ( ( ( lam @ SV170 @ SV398
@ ^ [SY2978: $i] : ( SV552 @ SY2978 ) )
= ( lam @ SV170 @ SV398
@ ^ [SY2979: $i] : ( SV552 @ SY2979 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2123]) ).
thf(2320,plain,
! [SV553: $i,SV399: $o,SV171: $i,SV701: $i] :
( ( ( ~ ( in @ SV701 @ SV171 ) )
= $true )
| ( ( ~ ~ SV399
| ( ( dsetconstr @ SV171
@ ^ [SY3147: $i] :
( ~ ( ~ SV399
| ( SY3147 != SV553 ) )
| ~ ( ~ ~ SV399
| ( SY3147 != SV701 ) ) ) )
= ( setadjoin @ SV701 @ emptyset ) ) )
= $true )
| ( ( in @ SV553 @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2124]) ).
thf(2321,plain,
! [SV554: $i,SV171: $i,SV702: $i] :
( ( ( ~ ( in @ SV702 @ SV171 ) )
= $true )
| ( ( ~ ~ $true
| ( ( dsetconstr @ SV171
@ ^ [SY3148: $i] :
( ~ ( ~ $true
| ( SY3148 != SV554 ) )
| ~ ( ~ ~ $true
| ( SY3148 != SV702 ) ) ) )
= ( setadjoin @ SV702 @ emptyset ) ) )
= $true )
| ( ( in @ SV554 @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2125]) ).
thf(2322,plain,
! [SV555: $i,SV171: $i,SV703: $i] :
( ( ( ~ ( in @ SV703 @ SV171 ) )
= $true )
| ( ( ~ ~ $false
| ( ( dsetconstr @ SV171
@ ^ [SY3149: $i] :
( ~ ( ~ $false
| ( SY3149 != SV555 ) )
| ~ ( ~ ~ $false
| ( SY3149 != SV703 ) ) ) )
= ( setadjoin @ SV703 @ emptyset ) ) )
= $true )
| ( ( in @ SV555 @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2126]) ).
thf(2323,plain,
! [SV172: $i,SV400: $i] :
( ( ( in @ SV400 @ ( powerset @ SV172 ) )
= $false )
| ( ( ! [SY2727: $i] :
( ~ ( in @ SY2727 @ SV400 )
| ( in @ SY2727 @ SV172 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2324,plain,
! [SV172: $i,SV400: $i] :
( ( ( ! [SY2728: $i] :
( ~ ( in @ SY2728 @ SV400 )
| ( in @ SY2728 @ SV172 ) ) )
= $false )
| ( ( in @ SV400 @ ( powerset @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2128]) ).
thf(2325,plain,
! [SV174: $i,SV557: $i,SV402: $i,SV704: $i] :
( ( ( ~ ( in @ SV704 @ SV402 ) )
= $true )
| ( ( ( kfst @ ( kpair @ SV557 @ SV704 ) )
= SV557 )
= $true )
| ( ( in @ SV557 @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2130]) ).
thf(2326,plain,
! [SV558: $i,SV403: $i,SV175: $i,SV705: $i] :
( ( ( ~ ( in @ SV705 @ SV175 ) )
= $true )
| ( ( in @ ( ap @ SV175 @ SV403 @ SV558 @ SV705 ) @ SV403 )
= $true )
| ( ( in @ SV558 @ ( funcSet @ SV175 @ SV403 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2131]) ).
thf(2327,plain,
! [SV404: $i,SV176: $i,SV658: $i] :
( ( ( in @ SV658 @ ( powerset @ SV176 ) )
= $false )
| ( ( ~ ( subset @ SV404 @ SV658 )
| ( subset @ ( setminus @ SV176 @ SV658 ) @ ( setminus @ SV176 @ SV404 ) ) )
= $true )
| ( ( in @ SV404 @ ( powerset @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2328,plain,
! [SV177: $i,SV559: $i,SV405: $i] :
( ( ( subset @ SV405 @ SV559 )
= $false )
| ( ( subset @ SV177 @ SV559 )
= $true )
| ( ( subset @ SV177 @ SV405 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2329,plain,
! [SV408: $i > $o,SV180: $i,SV706: $i] :
( ( ( ~ ( ~ ( in @ SV706 @ SV180 )
| ~ ( SV408 @ SV706 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV180
@ ^ [SY2739: $i] : ( SV408 @ SY2739 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2134]) ).
thf(2330,plain,
! [SV181: $i,SV409: $i > $o] :
( ( ( in @ ( sK12_SY2740 @ SV409 @ SV181 ) @ SV181 )
= $true )
| ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) )
| ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2135]) ).
thf(2331,plain,
! [SV181: $i,SV409: $i > $o] :
( ( ( ~ ( in @ ( sK34_SY3112 @ SV409 @ SV181 ) @ SV181 )
| ~ ( SV409 @ ( sK12_SY2740 @ SV409 @ SV181 ) )
| ~ ( SV409 @ ( sK34_SY3112 @ SV409 @ SV181 ) )
| ( ( sK12_SY2740 @ SV409 @ SV181 )
= ( sK34_SY3112 @ SV409 @ SV181 ) ) )
= $false )
| ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) )
| ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2136]) ).
thf(2332,plain,
! [SV183: $i > $o,SV411: $i > $o] :
( ( ( ( sK13_SY2744 @ SV411 @ SV183 )
!= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2137]) ).
thf(2333,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
| ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) ) )
| ~ ( ~ ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
| ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2137]) ).
thf(2334,plain,
! [SV561: $i,SV413: $i,SV185: $i,SV707: $i] :
( ( ( ~ ( in @ SV707 @ SV185 ) )
= $true )
| ( ( ! [SY3150: $i] :
( ~ ( in @ SY3150 @ SV413 )
| ~ ( in @ ( kpair @ SV707 @ SY3150 ) @ SV561 )
| ( ( ap @ SV185 @ SV413 @ SV561 @ SV707 )
= SY3150 ) ) )
= $true )
| ( ( in @ SV561 @ ( funcSet @ SV185 @ SV413 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2138]) ).
thf(2335,plain,
! [SV414: $i,SV186: $i,SV659: $i] :
( ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( ~ ! [SY3114: $i] :
( ~ ( in @ SY3114 @ SV186 )
| ~ ( in @ SY3114 @ SV414 )
| ( in @ SY3114 @ SV659 ) )
| ~ ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV186 )
| ~ ( in @ SY3115 @ SV659 )
| ( in @ SY3115 @ SV414 ) )
| ( SV414 = SV659 ) )
= $true )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2336,plain,
! [SV187: $i,SV562: $i,SV415: $i > $o] :
( ( ( SV415 @ SV562 )
= $false )
| ( ( ( dsetconstr @ SV187
@ ^ [SY2759: $i] : ( SV415 @ SY2759 ) )
!= emptyset )
= $true )
| ( ( in @ SV562 @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2337,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV660 )
| ~ ! [SY3116: $i] :
( ~ ( SV188 @ SY3116 )
| ( SV660 = SY3116 ) ) )
= $true )
| ( ( ~ ! [SY2316: $i] :
~ ~ ( ~ ( SV188 @ SY2316 )
| ~ ! [SY2317: $i] :
( ~ ( SV188 @ SY2317 )
| ( SY2316 = SY2317 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2141]) ).
thf(2338,plain,
! [SV564: $i,SV417: $i,SV190: $i,SV708: $i] :
( ( ( ~ ( in @ SV708 @ SV190 ) )
= $true )
| ( ( ( ap @ SV190 @ SV417 @ SV564 @ SV708 )
= ( ap @ SV190 @ SV417 @ SV564 @ SV708 ) )
= $true )
| ( ( in @ SV564 @ ( funcSet @ SV190 @ SV417 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2143]) ).
thf(2339,plain,
! [SV418: $i,SV191: $i,SV661: $i] :
( ( ( in @ SV661 @ ( powerset @ SV191 ) )
= $false )
| ( ( ! [SY3117: $i] :
( ~ ( in @ SY3117 @ ( powerset @ SV191 ) )
| ! [SY3118: $i] :
( ~ ( in @ SY3118 @ SV191 )
| ~ ( in @ SY3118 @ ( binintersect @ SV418 @ SV661 ) )
| ( in @ SY3118 @ ( binintersect @ ( binunion @ SV418 @ SY3117 ) @ ( binunion @ SV661 @ SY3117 ) ) ) ) ) )
= $true )
| ( ( in @ SV418 @ ( powerset @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2144]) ).
thf(2340,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ( sK14_SY2766 @ SV422 @ SV193 )
!= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2145]) ).
thf(2341,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
| ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) ) )
| ~ ( ~ ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
| ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2145]) ).
thf(2342,plain,
! [SV195: $i,SV423: $i,SV565: $i] :
( ( ( ~ ( in @ SV565 @ SV423 ) )
= $false )
| ( ( in @ SV565 @ ( setminus @ SV195 @ SV423 ) )
= $true )
| ( ( in @ SV565 @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2147]) ).
thf(2343,plain,
! [SV196: $i,SV424: $i,SV566: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK35_SY2993 @ SV566 @ SV424 @ SV196 ) @ SV196 )
| ~ ~ ! [SY3169: $i] :
~ ~ ( ~ ( in @ SY3169 @ SV424 )
| ( SV566
!= ( kpair @ ( sK35_SY2993 @ SV566 @ SV424 @ SV196 ) @ SY3169 ) ) ) ) )
= $false )
| ( ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2148]) ).
thf(2344,plain,
! [SV567: $i,SV425: $o,SV197: $i,SV709: $i] :
( ( ( ~ ( in @ SV709 @ SV197 ) )
= $true )
| ( ( ~ SV425
| ( ( if @ SV197 @ SV425 @ SV567 @ SV709 )
= SV567 ) )
= $true )
| ( ( in @ SV567 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2149]) ).
thf(2345,plain,
! [SV568: $i,SV197: $i,SV710: $i] :
( ( ( ~ ( in @ SV710 @ SV197 ) )
= $true )
| ( ( ~ $true
| ( ( if @ SV197 @ $true @ SV568 @ SV710 )
= SV568 ) )
= $true )
| ( ( in @ SV568 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2150]) ).
thf(2346,plain,
! [SV569: $i,SV197: $i,SV711: $i] :
( ( ( ~ ( in @ SV711 @ SV197 ) )
= $true )
| ( ( ~ $false
| ( ( if @ SV197 @ $false @ SV569 @ SV711 )
= SV569 ) )
= $true )
| ( ( in @ SV569 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2347,plain,
! [SV570: $i,SV426: $i,SV198: $i,SV712: $i] :
( ( ( ~ ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) ) )
= $true )
| ( ( ~ ! [SY3151: $i] :
( ~ ( in @ SY3151 @ SV198 )
| ! [SY3152: $i] :
( ~ ( in @ SY3152 @ SV426 )
| ~ ( in @ ( kpair @ SY3151 @ SY3152 ) @ SV570 )
| ( in @ ( kpair @ SY3151 @ SY3152 ) @ SV712 ) ) )
| ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) )
| ( SV570 = SV712 ) )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2152]) ).
thf(2348,plain,
! [SV713: $i > $o,SV571: $i,SV428: $i,SV200: $i] :
( ( ( ~ ! [SY3155: $i] :
( ~ ( in @ SY3155 @ SV200 )
| ! [SY3156: $i] :
( ~ ( in @ SY3156 @ SV428 )
| ~ ( in @ ( kpair @ SY3155 @ SY3156 ) @ SV571 )
| ( SV713 @ ( kpair @ SY3155 @ SY3156 ) ) ) ) )
= $true )
| ( ( ! [SY3157: $i] :
( ~ ( in @ SY3157 @ SV571 )
| ( SV713 @ SY3157 ) ) )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2349,plain,
! [SV429: $i > $o,SV201: $i,SV714: $i] :
( ( ( ~ ( ~ ( in @ SV714 @ SV201 )
| ~ ~ ( SV429 @ SV714 ) ) )
= $false )
| ( ( ~ ! [SY2794: $i] :
( ~ ( in @ SY2794 @ SV201 )
| ( SV429 @ SY2794 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2154]) ).
thf(2350,plain,
! [SV203: $i,SV572: $i > $i,SV430: $i] :
( ( ( ~ ( in @ ( sK24_SY3007 @ SV430 @ SV572 @ SV203 ) @ SV203 ) )
= $false )
| ( ( func @ SV203 @ SV430
@ ( dpsetconstr @ SV203 @ SV430
@ ^ [SY3008: $i,SY3009: $i] :
( ( SV572 @ SY3008 )
= SY3009 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2155]) ).
thf(2351,plain,
! [SV203: $i,SV430: $i,SV572: $i > $i] :
( ( ( in @ ( SV572 @ ( sK24_SY3007 @ SV430 @ SV572 @ SV203 ) ) @ SV430 )
= $false )
| ( ( func @ SV203 @ SV430
@ ( dpsetconstr @ SV203 @ SV430
@ ^ [SY3008: $i,SY3009: $i] :
( ( SV572 @ SY3008 )
= SY3009 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2155]) ).
thf(2352,plain,
! [SV662: $i,SV204: $i] :
( ( ( SV204 = emptyset )
= $false )
| ( ( in @ SV662 @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2353,plain,
! [SV206: $i,SV431: $i,SV573: $i] :
( ( ( ~ ( in @ SV573 @ SV431 ) )
= $true )
| ( ( in @ SV573 @ ( symdiff @ SV206 @ SV431 ) )
= $true )
| ( ( in @ SV573 @ SV206 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2157]) ).
thf(2354,plain,
! [SV209: $i,SV574: $i > $i,SV433: $i] :
( ( ( ~ ( in @ ( sK25_SY3010 @ SV433 @ SV574 @ SV209 ) @ SV209 ) )
= $false )
| ( ( ! [SY3011: $i] :
( ~ ( in @ SY3011 @ SV209 )
| ( ( ap @ SV209 @ SV433
@ ( lam @ SV209 @ SV433
@ ^ [SY3012: $i] : ( SV574 @ SY3012 ) )
@ SY3011 )
= ( SV574 @ SY3011 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2158]) ).
thf(2355,plain,
! [SV209: $i,SV433: $i,SV574: $i > $i] :
( ( ( in @ ( SV574 @ ( sK25_SY3010 @ SV433 @ SV574 @ SV209 ) ) @ SV433 )
= $false )
| ( ( ! [SY3011: $i] :
( ~ ( in @ SY3011 @ SV209 )
| ( ( ap @ SV209 @ SV433
@ ( lam @ SV209 @ SV433
@ ^ [SY3012: $i] : ( SV574 @ SY3012 ) )
@ SY3011 )
= ( SV574 @ SY3011 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2158]) ).
thf(2356,plain,
! [SV435: $i,SV211: $i,SV715: $i,SV663: $i] :
( ( ( SV663 != SV715 )
= $true )
| ( ( ( setadjoin @ SV211 @ SV663 )
= ( setadjoin @ SV435 @ SV715 ) )
= $true )
| ( ( SV211 = SV435 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2159]) ).
thf(2357,plain,
! [SV212: $i,SV436: $i > $o] :
( ( ( in @ ( sK15_SY2806 @ SV436 @ SV212 ) @ SV212 )
= $true )
| ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) )
| ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2160]) ).
thf(2358,plain,
! [SV212: $i,SV436: $i > $o] :
( ( ( ~ ( in @ ( sK36_SY3121 @ SV436 @ SV212 ) @ SV212 )
| ~ ( SV436 @ ( sK15_SY2806 @ SV436 @ SV212 ) )
| ~ ( SV436 @ ( sK36_SY3121 @ SV436 @ SV212 ) )
| ( ( sK15_SY2806 @ SV436 @ SV212 )
= ( sK36_SY3121 @ SV436 @ SV212 ) ) )
= $false )
| ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) )
| ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2161]) ).
thf(2359,plain,
! [SV214: $i,SV438: $i,SV615: $i,SV575: $i] :
( ( ( SV575 != SV615 )
= $true )
| ( ( SV438 = SV615 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV214 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV214 @ ( setadjoin @ SV438 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV575 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV575 @ ( setadjoin @ SV615 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2162]) ).
thf(2360,plain,
! [SV215: $i] :
( ( ( ! [SY2395: $i] :
( ~ ~ ( ~ ( in @ SY2395 @ omega )
| ~ ( in @ SY2395 @ SV215 ) )
| ( in @ ( setadjoin @ SY2395 @ SY2395 ) @ SV215 ) ) )
= $false )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( ! [SY2396: $i] :
( ~ ( in @ SY2396 @ omega )
| ( in @ SY2396 @ SV215 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2361,plain,
! [SV216: $i,SV576: $i,SV439: $i,SV716: $i] :
( ( ( ~ ( in @ SV716 @ SV439 ) )
= $true )
| ( ( in @ ( kpair @ SV576 @ SV716 ) @ ( powerset @ ( powerset @ ( binunion @ SV216 @ SV439 ) ) ) )
= $true )
| ( ( in @ SV576 @ SV216 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2164]) ).
thf(2362,plain,
! [SV217: $i,SV616: $i,SV577: $i > $i > $o,SV440: $i,SV735: $i] :
( ( ( ~ ( in @ SV735 @ SV440 )
| ~ ( SV577 @ SV616 @ SV735 )
| ( in @ ( kpair @ SV616 @ SV735 )
@ ( dpsetconstr @ SV217 @ SV440
@ ^ [SY3017: $i,SY3018: $i] : ( SV577 @ SY3017 @ SY3018 ) ) ) )
= $true )
| ( ( in @ SV616 @ SV217 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(2363,plain,
! [SV578: $i,SV441: $o,SV218: $i,SV717: $i] :
( ( ( ~ ( in @ SV717 @ SV218 ) )
= $true )
| ( ( in @ ( if @ SV218 @ SV441 @ SV578 @ SV717 ) @ SV218 )
= $true )
| ( ( in @ SV578 @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2166]) ).
thf(2364,plain,
! [SV579: $i,SV218: $i,SV718: $i] :
( ( ( ~ ( in @ SV718 @ SV218 ) )
= $true )
| ( ( in @ ( if @ SV218 @ $true @ SV579 @ SV718 ) @ SV218 )
= $true )
| ( ( in @ SV579 @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2167]) ).
thf(2365,plain,
! [SV580: $i,SV218: $i,SV719: $i] :
( ( ( ~ ( in @ SV719 @ SV218 ) )
= $true )
| ( ( in @ ( if @ SV218 @ $false @ SV580 @ SV719 ) @ SV218 )
= $true )
| ( ( in @ SV580 @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2168]) ).
thf(2366,plain,
! [SV581: $i,SV442: $i,SV219: $i,SV720: $i] :
( ( ( ~ ( in @ SV720 @ ( funcSet @ SV219 @ SV442 ) ) )
= $true )
| ( ( ~ ! [SY3158: $i] :
( ~ ( in @ SY3158 @ SV219 )
| ( ( ap @ SV219 @ SV442 @ SV581 @ SY3158 )
= ( ap @ SV219 @ SV442 @ SV720 @ SY3158 ) ) )
| ( SV581 = SV720 ) )
= $true )
| ( ( in @ SV581 @ ( funcSet @ SV219 @ SV442 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2169]) ).
thf(2367,plain,
! [SV582: $i > $i > $o,SV220: $i,SV617: $i,SV443: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ SV443 )
| ~ ( in @ ( kpair @ SV617 @ SV736 )
@ ( dpsetconstr @ SV220 @ SV443
@ ^ [SY3026: $i,SY3027: $i] : ( SV582 @ SY3026 @ SY3027 ) ) )
| ( SV582 @ SV617 @ SV736 ) )
= $true )
| ( ( in @ SV617 @ SV220 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2170]) ).
thf(2368,plain,
! [SV583: $i,SV444: $i,SV221: $i,SV721: $i] :
( ( ( ~ ( in @ SV721 @ SV221 ) )
= $true )
| ( ( in @ ( ap @ SV221 @ SV444 @ SV583 @ SV721 ) @ SV444 )
= $true )
| ( ( func @ SV221 @ SV444 @ SV583 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2171]) ).
thf(2369,plain,
! [SV223: $i,SV446: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK26_SY2833 @ SV446 @ SV223 ) @ SV223 )
| ~ ( SV446 @ ( sK26_SY2833 @ SV446 @ SV223 ) ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY2832: $i] : ( SV446 @ SY2832 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2172]) ).
thf(2370,plain,
! [SV225: $i,SV448: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 )
| ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 )
| ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 ) ) )
= $true )
| ( ( SV225 = SV448 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2174]) ).
thf(2371,plain,
! [SV226: $i,SV449: $i,SV585: $i] :
( ( ( in @ SV585 @ SV449 )
= $false )
| ( ( ~ ( in @ SV585 @ ( symdiff @ SV226 @ SV449 ) ) )
= $true )
| ( ( in @ SV585 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2175]) ).
thf(2372,plain,
! [SV450: $i,SV227: $i,SV664: $i] :
( ( ( in @ SV664 @ SV227 )
= $false )
| ( ( ~ ( in @ SV664 @ ( setminus @ SV227 @ ( setminus @ SV227 @ SV450 ) ) )
| ( in @ SV664 @ SV450 ) )
= $true )
| ( ( in @ SV450 @ ( powerset @ SV227 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2176]) ).
thf(2373,plain,
! [SV452: $i,SV229: $i,SV665: $i] :
( ( ( in @ SV665 @ ( powerset @ SV229 ) )
= $false )
| ( ( ! [SY3122: $i] :
( ~ ( in @ SY3122 @ ( powerset @ SV229 ) )
| ( in @ ( binintersect @ SV452 @ SV665 ) @ ( powerset @ ( binintersect @ ( binunion @ SV452 @ SY3122 ) @ ( binunion @ SV665 @ SY3122 ) ) ) ) ) )
= $true )
| ( ( in @ SV452 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2178]) ).
thf(2374,plain,
! [SV230: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_SY2440 @ SV230 ) @ SV230 )
| ~ $true ) )
= $true )
| ( ( SV230 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2179]) ).
thf(2375,plain,
! [SV587: $i,SV453: $o,SV231: $i,SV722: $i] :
( ( ( ~ ( in @ SV722 @ SV231 ) )
= $true )
| ( ( ~ SV453
| ( ( dsetconstr @ SV231
@ ^ [SY3159: $i] :
( ~ ( ~ SV453
| ( SY3159 != SV587 ) )
| ~ ( ~ ~ SV453
| ( SY3159 != SV722 ) ) ) )
= ( setadjoin @ SV587 @ emptyset ) ) )
= $true )
| ( ( in @ SV587 @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2180]) ).
thf(2376,plain,
! [SV588: $i,SV231: $i,SV723: $i] :
( ( ( ~ ( in @ SV723 @ SV231 ) )
= $true )
| ( ( ~ $true
| ( ( dsetconstr @ SV231
@ ^ [SY3160: $i] :
( ~ ( ~ $true
| ( SY3160 != SV588 ) )
| ~ ( ~ ~ $true
| ( SY3160 != SV723 ) ) ) )
= ( setadjoin @ SV588 @ emptyset ) ) )
= $true )
| ( ( in @ SV588 @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2377,plain,
! [SV589: $i,SV231: $i,SV724: $i] :
( ( ( ~ ( in @ SV724 @ SV231 ) )
= $true )
| ( ( ~ $false
| ( ( dsetconstr @ SV231
@ ^ [SY3161: $i] :
( ~ ( ~ $false
| ( SY3161 != SV589 ) )
| ~ ( ~ ~ $false
| ( SY3161 != SV724 ) ) ) )
= ( setadjoin @ SV589 @ emptyset ) ) )
= $true )
| ( ( in @ SV589 @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2182]) ).
thf(2378,plain,
! [SV232: $i,SV454: $i,SV590: $i] :
( ( ( in @ SV590 @ SV454 )
= $false )
| ( ( in @ SV590 @ SV232 )
= $true )
| ( ( in @ SV454 @ ( powerset @ SV232 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2183]) ).
thf(2379,plain,
! [SV455: $i,SV233: $i,SV666: $i] :
( ( ( in @ SV666 @ SV233 )
= $false )
| ( ( ~ ( in @ SV666 @ SV455 )
| ~ ( in @ SV666 @ ( setminus @ SV233 @ SV455 ) ) )
= $true )
| ( ( in @ SV455 @ ( powerset @ SV233 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2184]) ).
thf(2380,plain,
! [SV234: $i,SV591: $i > $i,SV456: $i] :
( ( ( ~ ( in @ ( sK28_SY3036 @ SV456 @ SV591 @ SV234 ) @ SV234 ) )
= $false )
| ( ( ! [SY3037: $i] :
( ~ ( in @ SY3037 @ SV234 )
| ( ( ap @ SV234 @ SV456
@ ( lam @ SV234 @ SV456
@ ^ [SY3038: $i] : ( SV591 @ SY3038 ) )
@ SY3037 )
= ( SV591 @ SY3037 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2185]) ).
thf(2381,plain,
! [SV234: $i,SV456: $i,SV591: $i > $i] :
( ( ( in @ ( SV591 @ ( sK28_SY3036 @ SV456 @ SV591 @ SV234 ) ) @ SV456 )
= $false )
| ( ( ! [SY3037: $i] :
( ~ ( in @ SY3037 @ SV234 )
| ( ( ap @ SV234 @ SV456
@ ( lam @ SV234 @ SV456
@ ^ [SY3038: $i] : ( SV591 @ SY3038 ) )
@ SY3037 )
= ( SV591 @ SY3037 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2185]) ).
thf(2382,plain,
! [SV235: $i,SV457: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK37_SY2850 @ SV457 @ SV235 ) @ SV235 )
| ~ ( in @ ( sK37_SY2850 @ SV457 @ SV235 ) @ SV457 ) ) )
= $false )
| ( ( ( binintersect @ SV235 @ SV457 )
= emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2186]) ).
thf(2383,plain,
! [SV242: $i,SV596: $i > $i,SV464: $i] :
( ( ( ~ ( in @ ( sK29_SY3041 @ SV464 @ SV596 @ SV242 ) @ SV242 ) )
= $false )
| ( ( func @ SV242 @ SV464
@ ( lam @ SV242 @ SV464
@ ^ [SY3042: $i] : ( SV596 @ SY3042 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2190]) ).
thf(2384,plain,
! [SV242: $i,SV464: $i,SV596: $i > $i] :
( ( ( in @ ( SV596 @ ( sK29_SY3041 @ SV464 @ SV596 @ SV242 ) ) @ SV464 )
= $false )
| ( ( func @ SV242 @ SV464
@ ( lam @ SV242 @ SV464
@ ^ [SY3042: $i] : ( SV596 @ SY3042 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2190]) ).
thf(2385,plain,
! [SV465: $i,SV243: $i,SV667: $i] :
( ( ( in @ SV667 @ ( powerset @ SV243 ) )
= $false )
| ( ( ! [SY3123: $i] :
( ~ ( in @ SY3123 @ SV243 )
| ~ ( in @ SV465 @ ( powerset @ SV667 ) )
| ~ ( in @ SY3123 @ SV465 )
| ( in @ SY3123 @ SV667 ) ) )
= $true )
| ( ( in @ SV465 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2386,plain,
! [SV597: $i,SV466: $o,SV244: $i,SV725: $i] :
( ( ( ~ ( in @ SV725 @ SV244 ) )
= $true )
| ( ( ~ ~ SV466
| ( in @ SV725
@ ( dsetconstr @ SV244
@ ^ [SY3162: $i] :
( ~ ( ~ SV466
| ( SY3162 != SV597 ) )
| ~ ( ~ ~ SV466
| ( SY3162 != SV725 ) ) ) ) ) )
= $true )
| ( ( in @ SV597 @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2192]) ).
thf(2387,plain,
! [SV598: $i,SV244: $i,SV726: $i] :
( ( ( ~ ( in @ SV726 @ SV244 ) )
= $true )
| ( ( ~ ~ $true
| ( in @ SV726
@ ( dsetconstr @ SV244
@ ^ [SY3163: $i] :
( ~ ( ~ $true
| ( SY3163 != SV598 ) )
| ~ ( ~ ~ $true
| ( SY3163 != SV726 ) ) ) ) ) )
= $true )
| ( ( in @ SV598 @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2193]) ).
thf(2388,plain,
! [SV599: $i,SV244: $i,SV727: $i] :
( ( ( ~ ( in @ SV727 @ SV244 ) )
= $true )
| ( ( ~ ~ $false
| ( in @ SV727
@ ( dsetconstr @ SV244
@ ^ [SY3164: $i] :
( ~ ( ~ $false
| ( SY3164 != SV599 ) )
| ~ ( ~ ~ $false
| ( SY3164 != SV727 ) ) ) ) ) )
= $true )
| ( ( in @ SV599 @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2194]) ).
thf(2389,plain,
! [SV600: $i,SV728: $i,SV469: $i,SV247: $i] :
( ( ( ~ ( func @ SV247 @ SV469 @ SV728 ) )
= $true )
| ( ( ~ ! [SY3165: $i] :
( ~ ( in @ SY3165 @ SV247 )
| ( ( ap @ SV247 @ SV469 @ SV600 @ SY3165 )
= ( ap @ SV247 @ SV469 @ SV728 @ SY3165 ) ) )
| ! [SY3166: $i] :
( ~ ( in @ SY3166 @ SV247 )
| ! [SY3167: $i] :
( ~ ( in @ SY3167 @ SV469 )
| ~ ( in @ ( kpair @ SY3166 @ SY3167 ) @ SV728 )
| ( in @ ( kpair @ SY3166 @ SY3167 ) @ SV600 ) ) ) )
= $true )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2195]) ).
thf(2390,plain,
! [SV470: $i,SV248: $i,SV668: $i] :
( ( ( in @ SV668 @ ( powerset @ SV248 ) )
= $false )
| ( ( subset @ ( setminus @ SV248 @ SV470 ) @ ( setminus @ SV248 @ ( binintersect @ SV470 @ SV668 ) ) )
= $true )
| ( ( in @ SV470 @ ( powerset @ SV248 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2196]) ).
thf(2391,plain,
! [SV471: $i,SV249: $i > $i > $o] :
( ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true )
| ( ( ~ ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2197]) ).
thf(2392,plain,
! [SV471: $i,SV249: $i > $i > $o] :
( ( ( ! [SY3124: $i] :
~ ~ ( ~ ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SY3124 )
| ~ ! [SY3125: $i] :
( ~ ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SY3125 )
| ( SY3124 = SY3125 ) ) ) )
= $true )
| ( ( ~ ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2198]) ).
thf(2393,plain,
! [SV601: $i,SV474: $o,SV252: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV252 ) )
= $true )
| ( ( ~ ~ SV474
| ( ( if @ SV252 @ SV474 @ SV601 @ SV729 )
= SV729 ) )
= $true )
| ( ( in @ SV601 @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2199]) ).
thf(2394,plain,
! [SV602: $i,SV252: $i,SV730: $i] :
( ( ( ~ ( in @ SV730 @ SV252 ) )
= $true )
| ( ( ~ ~ $true
| ( ( if @ SV252 @ $true @ SV602 @ SV730 )
= SV730 ) )
= $true )
| ( ( in @ SV602 @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2200]) ).
thf(2395,plain,
! [SV603: $i,SV252: $i,SV731: $i] :
( ( ( ~ ( in @ SV731 @ SV252 ) )
= $true )
| ( ( ~ ~ $false
| ( ( if @ SV252 @ $false @ SV603 @ SV731 )
= SV731 ) )
= $true )
| ( ( in @ SV603 @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2201]) ).
thf(2396,plain,
! [SV253: $i,SV604: $i,SV475: $i,SV732: $i] :
( ( ( ~ ( in @ SV732 @ SV475 ) )
= $true )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV604 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV604 @ ( setadjoin @ SV732 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV253 @ SV475 ) ) ) )
= $true )
| ( ( in @ SV604 @ SV253 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2202]) ).
thf(2397,plain,
! [SV476: $i,SV254: $i,SV733: $i,SV669: $i] :
( ( ( SV669 != SV733 )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV669 @ SV254 )
| ( in @ SV733 @ SV476 ) )
| ~ ( ~ ( in @ SV733 @ SV476 )
| ( in @ SV669 @ SV254 ) ) ) )
= $true )
| ( ( SV254 = SV476 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2203]) ).
thf(2398,plain,
! [SV670: $i,SV256: $i > $o] :
( ( ( ~ ( SV256 @ SV670 )
| ~ ! [SY3127: $i] :
( ~ ( SV256 @ SY3127 )
| ( SV670 = SY3127 ) ) )
= $true )
| ( ( ~ ! [SY2511: $i] :
~ ! [SY2512: $i] :
~ ( ~ ( ~ ( SV256 @ SY2512 )
| ( SY2512 = SY2511 ) )
| ~ ( ( SY2512 != SY2511 )
| ( SV256 @ SY2512 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2205]) ).
thf(2399,plain,
! [SV478: $i,SV257: $i,SV671: $i] :
( ( ( in @ SV671 @ ( powerset @ SV257 ) )
= $false )
| ( ( in @ ( binunion @ SV478 @ SV671 ) @ ( powerset @ SV257 ) )
= $true )
| ( ( in @ SV478 @ ( powerset @ SV257 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2206]) ).
thf(2400,plain,
! [SV258: $i,SV605: $i,SV479: $i,SV734: $i] :
( ( ( ~ ( in @ SV734 @ SV479 ) )
= $true )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV605 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV605 @ ( setadjoin @ SV734 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV258 @ SV479 ) ) )
= $true )
| ( ( in @ SV605 @ SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2207]) ).
thf(2401,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ~ ( SV35 @ SV621 ) )
= $true )
| ( ( ~ ! [SY3073: $i] :
( ~ ( SV35 @ SY3073 )
| ( SV621 = SY3073 ) ) )
= $true )
| ( ( ~ ! [SY1902: $i] :
~ ~ ( ~ ( SV35 @ SY1902 )
| ~ ! [SY1903: $i] :
( ~ ( SV35 @ SY1903 )
| ( SY1902 = SY1903 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2208]) ).
thf(2402,plain,
! [SV282: $i,SV622: $i,SV36: $i] :
( ( ( ~ ( subset @ ( setminus @ SV36 @ SV622 ) @ ( setminus @ SV36 @ SV282 ) ) )
= $true )
| ( ( subset @ SV282 @ SV622 )
= $true )
| ( ( in @ SV622 @ ( powerset @ SV36 ) )
= $false )
| ( ( in @ SV282 @ ( powerset @ SV36 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2209]) ).
thf(2403,plain,
! [SV484: $i,SV284: $i,SV38: $i,SV672: $i] :
( ( ( in @ SV672 @ SV38 )
= $false )
| ( ( ! [SY3128: $i] :
( ~ ( in @ SY3128 @ SV284 )
| ~ ( in @ ( kpair @ SV672 @ SY3128 ) @ SV484 )
| ( ( ap @ SV38 @ SV284 @ SV484 @ SV672 )
= SY3128 ) ) )
= $true )
| ( ( func @ SV38 @ SV284 @ SV484 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2210]) ).
thf(2404,plain,
! [SV485: $i,SV285: $o,SV39: $i,SV673: $i] :
( ( ( in @ SV673 @ SV39 )
= $false )
| ( ( ~ SV285
| ( in @ SV485
@ ( dsetconstr @ SV39
@ ^ [SY3129: $i] :
( ~ ( ~ SV285
| ( SY3129 != SV485 ) )
| ~ ( ~ ~ SV285
| ( SY3129 != SV673 ) ) ) ) ) )
= $true )
| ( ( in @ SV485 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2211]) ).
thf(2405,plain,
! [SV486: $i,SV39: $i,SV674: $i] :
( ( ( in @ SV674 @ SV39 )
= $false )
| ( ( ~ $true
| ( in @ SV486
@ ( dsetconstr @ SV39
@ ^ [SY3130: $i] :
( ~ ( ~ $true
| ( SY3130 != SV486 ) )
| ~ ( ~ ~ $true
| ( SY3130 != SV674 ) ) ) ) ) )
= $true )
| ( ( in @ SV486 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2212]) ).
thf(2406,plain,
! [SV487: $i,SV39: $i,SV675: $i] :
( ( ( in @ SV675 @ SV39 )
= $false )
| ( ( ~ $false
| ( in @ SV487
@ ( dsetconstr @ SV39
@ ^ [SY3131: $i] :
( ~ ( ~ $false
| ( SY3131 != SV487 ) )
| ~ ( ~ ~ $false
| ( SY3131 != SV675 ) ) ) ) ) )
= $true )
| ( ( in @ SV487 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2213]) ).
thf(2407,plain,
! [SV676: $i > $o,SV623: $i > $o,SV286: $i,SV40: $i] :
( ( ( ! [SY3132: $i] :
( ~ ( in @ SY3132 @ SV40 )
| ! [SY3133: $i] :
( ~ ( in @ SY3133 @ SV286 )
| ( SY3132 != SY3133 )
| ~ ( ~ ( ~ ( SV623 @ SY3132 )
| ( SV676 @ SY3133 ) )
| ~ ( ~ ( SV676 @ SY3133 )
| ( SV623 @ SY3132 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2214]) ).
thf(2408,plain,
! [SV41: $i,SV287: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK30_SY2541 @ SV287 @ SV41 ) @ SV41 )
| ~ ( SV287 @ ( sK30_SY2541 @ SV287 @ SV41 ) ) ) )
= $true )
| ( ( ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV41 )
| ~ ( SV287 @ SY2542 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2215]) ).
thf(2409,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ( ~ ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
| ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 ) )
| ~ ( ( ( sK31_SY3079 @ SV624 @ SV44 )
!= SV624 )
| ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) ) ) )
= $true )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2217]) ).
thf(2410,plain,
! [SV46: $i,SV490: $i,SV290: $i,SV677: $i] :
( ( ( in @ SV677 @ SV290 )
= $false )
| ( ( in @ ( kpair @ SV490 @ SV677 ) @ ( cartprod @ SV46 @ SV290 ) )
= $true )
| ( ( in @ SV490 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2218]) ).
thf(2411,plain,
! [SV291: $i,SV47: $i,SV491: $i] :
( ( ( in @ SV491 @ ( setadjoin @ SV47 @ SV291 ) )
= $false )
| ( ( ( SV491 = SV47 )
| ( in @ SV491 @ SV291 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2219]) ).
thf(2412,plain,
! [SV291: $i,SV47: $i,SV491: $i] :
( ( ( ( SV491 = SV47 )
| ( in @ SV491 @ SV291 ) )
= $false )
| ( ( in @ SV491 @ ( setadjoin @ SV47 @ SV291 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2220]) ).
thf(2413,plain,
! [SV493: $i,SV294: $i,SV51: $i,SV678: $i] :
( ( ( in @ SV678 @ SV51 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV294
@ ^ [SY3136: $i] : ( in @ ( kpair @ SV678 @ SY3136 ) @ SV493 ) ) )
= $true )
| ( ( func @ SV51 @ SV294 @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2221]) ).
thf(2414,plain,
! [SV55: $i,SV494: $i,SV296: $i,SV679: $i] :
( ( ( in @ SV679 @ SV296 )
= $false )
| ( ( ( kpair @ SV494 @ SV679 )
= ( kpair @ SV494 @ SV679 ) )
= $true )
| ( ( in @ SV494 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2222]) ).
thf(2415,plain,
! [SV56: $i,SV495: $i,SV297: $i,SV680: $i] :
( ( ( in @ SV680 @ SV297 )
= $false )
| ( ( ( ksnd @ ( kpair @ SV495 @ SV680 ) )
= SV680 )
= $true )
| ( ( in @ SV495 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2223]) ).
thf(2416,plain,
! [SV496: $i,SV298: $i,SV57: $i,SV681: $i] :
( ( ( in @ SV681 @ SV57 )
= $false )
| ( ( in @ ( kpair @ SV681 @ ( ap @ SV57 @ SV298 @ SV496 @ SV681 ) ) @ SV496 )
= $true )
| ( ( func @ SV57 @ SV298 @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2224]) ).
thf(2417,plain,
! [SV499: $i,SV301: $o,SV60: $i,SV682: $i] :
( ( ( in @ SV682 @ SV60 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY3137: $i] :
( ~ ( ~ SV301
| ( SY3137 != SV499 ) )
| ~ ( ~ ~ SV301
| ( SY3137 != SV682 ) ) ) ) )
= $true )
| ( ( in @ SV499 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2225]) ).
thf(2418,plain,
! [SV500: $i,SV60: $i,SV683: $i] :
( ( ( in @ SV683 @ SV60 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY3138: $i] :
( ~ ( ~ $true
| ( SY3138 != SV500 ) )
| ~ ( ~ ~ $true
| ( SY3138 != SV683 ) ) ) ) )
= $true )
| ( ( in @ SV500 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2226]) ).
thf(2419,plain,
! [SV501: $i,SV60: $i,SV684: $i] :
( ( ( in @ SV684 @ SV60 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV60
@ ^ [SY3139: $i] :
( ~ ( ~ $false
| ( SY3139 != SV501 ) )
| ~ ( ~ ~ $false
| ( SY3139 != SV684 ) ) ) ) )
= $true )
| ( ( in @ SV501 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2227]) ).
thf(2420,plain,
! [SV625: $i,SV305: $i,SV64: $i,SV737: $i] :
( ( ( ~ ( in @ SV737 @ SV64 )
| ~ ( in @ SV737 @ ( setminus @ SV64 @ SV305 ) )
| ~ ( in @ SV737 @ ( binintersect @ SV305 @ SV625 ) ) )
= $true )
| ( ( in @ SV625 @ ( powerset @ SV64 ) )
= $false )
| ( ( in @ SV305 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2421,plain,
! [SV626: $i,SV307: $i,SV66: $i,SV738: $i] :
( ( ( ~ ( in @ SV738 @ SV66 )
| ~ ~ ( in @ SV738 @ ( binunion @ SV307 @ SV626 ) )
| ~ ( in @ SV738 @ SV626 ) )
= $true )
| ( ( in @ SV626 @ ( powerset @ SV66 ) )
= $false )
| ( ( in @ SV307 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2422,plain,
! [SV506: $i,SV308: $i,SV67: $i,SV685: $i] :
( ( ( in @ SV685 @ SV67 )
= $false )
| ( ( ( ap @ SV67 @ SV308 @ SV506 @ SV685 )
= ( ap @ SV67 @ SV308 @ SV506 @ SV685 ) )
= $true )
| ( ( func @ SV67 @ SV308 @ SV506 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2232]) ).
thf(2423,plain,
! [SV69: $i,SV310: $i] :
( ( ( ! [SY2574: $i] :
~ ~ ( ~ ( in @ SV310 @ SY2574 )
| ~ ( in @ SY2574 @ SV69 ) ) )
= $false )
| ( ( in @ SV310 @ ( setunion @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2424,plain,
! [SV69: $i,SV310: $i] :
( ( ( ! [SY2575: $i] :
~ ~ ( ~ ( in @ SV310 @ SY2575 )
| ~ ( in @ SY2575 @ SV69 ) ) )
= $true )
| ( ( in @ SV310 @ ( setunion @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2234]) ).
thf(2425,plain,
! [SV627: $i,SV311: $i,SV70: $i,SV739: $i] :
( ( ( ~ ( in @ SV739 @ SV70 )
| ~ ( in @ SV739 @ ( setminus @ SV70 @ ( binunion @ SV311 @ SV627 ) ) )
| ~ ( in @ SV739 @ SV311 ) )
= $true )
| ( ( in @ SV627 @ ( powerset @ SV70 ) )
= $false )
| ( ( in @ SV311 @ ( powerset @ SV70 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2426,plain,
! [SV628: $i,SV314: $i,SV73: $i] :
( ( ( ~ ! [SY3083: $i] :
( ~ ( in @ SY3083 @ SV73 )
| ~ ( in @ SY3083 @ SV314 )
| ( in @ SY3083 @ SV628 ) ) )
= $true )
| ( ( in @ SV314 @ ( powerset @ SV628 ) )
= $true )
| ( ( in @ SV628 @ ( powerset @ SV73 ) )
= $false )
| ( ( in @ SV314 @ ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2237]) ).
thf(2427,plain,
! [SV686: $o,SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV74 )
| ~ ~ ( in @ SV509 @ SV315 )
| SV686 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SV686 )
| SV686 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2238]) ).
thf(2428,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV74 )
| ~ ~ ( in @ SV509 @ SV315 )
| $true )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $true )
| $true )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2239]) ).
thf(2429,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV74 )
| ~ ~ ( in @ SV509 @ SV315 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $false )
| $false )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2240]) ).
thf(2430,plain,
! [SV76: $i,SV316: $i,SV510: $i] :
( ( ( in @ SV510 @ SV316 )
= $true )
| ( ( ~ ( in @ SV510 @ SV76 ) )
= $true )
| ( ( subset @ SV76 @ SV316 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2241]) ).
thf(2431,plain,
! [SV79: $i,SV318: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK32_SY2591 @ SV318 @ SV79 ) @ SV79 )
| ~ ( SV318 @ ( sK32_SY2591 @ SV318 @ SV79 ) ) ) )
= $true )
| ( ( ! [SY2592: $i] :
( ~ ( in @ SY2592 @ SV79 )
| ~ ( SV318 @ SY2592 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2244]) ).
thf(2432,plain,
! [SV82: $i,SV630: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK38_SY2017 @ SV630 @ SV82 ) @ SV82 )
| ~ ~ ~ ! [SY3174: $i] :
~ ~ ( ~ ( in @ SY3174 @ ( sK38_SY2017 @ SV630 @ SV82 ) )
| ~ ( in @ SY3174 @ SV82 ) ) ) )
= $false )
| ( ( in @ SV630 @ SV82 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2245]) ).
thf(2433,plain,
! [SV322: $i,SV607: $o,SV84: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV84 )
| SV607 )
= $false )
| ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| SV607 )
| SV607 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2246]) ).
thf(2434,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV84 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| $true )
| $true )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2247]) ).
thf(2435,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV84 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| $false )
| $false )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2248]) ).
thf(2436,plain,
! [SV631: $i,SV323: $i,SV85: $i,SV740: $i] :
( ( ( ~ ( in @ SV740 @ SV85 )
| ~ ~ ( in @ SV740 @ ( binunion @ SV323 @ SV631 ) )
| ~ ( in @ SV740 @ SV323 ) )
= $true )
| ( ( in @ SV631 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV323 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2437,plain,
! [SV325: $i > $o,SV87: $i,SV687: $i] :
( ( ( in @ SV687 @ SV87 )
= $false )
| ( ( SV325 @ SV687 )
= $true )
| ( ( ~ ! [SY2599: $i] :
~ ~ ( ~ ( in @ SY2599 @ SV87 )
| ~ ~ ( SV325 @ SY2599 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2250]) ).
thf(2438,plain,
! [SV88: $i,SV326: $i] :
( ( ( ~ ! [SY2601: $i] :
( ~ ( in @ SY2601 @ SV326 )
| ( in @ SY2601 @ SV88 ) ) )
= $true )
| ( ( SV88 = SV326 )
= $true )
| ( ( in @ ( sK7_SY2600 @ SV326 @ SV88 ) @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2251]) ).
thf(2439,plain,
! [SV88: $i,SV326: $i] :
( ( ( ! [SY2601: $i] :
( ~ ( in @ SY2601 @ SV326 )
| ( in @ SY2601 @ SV88 ) ) )
= $false )
| ( ( SV88 = SV326 )
= $true )
| ( ( in @ ( sK7_SY2600 @ SV326 @ SV88 ) @ SV326 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2440,plain,
! [SV632: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV632 ) )
= $true )
| ( ( ~ ! [SY3087: $i] :
( ~ ( SV91 @ SY3087 )
| ( SV632 = SY3087 ) ) )
= $true )
| ( ( ! [SY2037: $i,SY2038: $i] :
( ~ ( SV91 @ SY2037 )
| ~ ( SV91 @ SY2038 )
| ( SY2037 = SY2038 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2253]) ).
thf(2441,plain,
! [SV514: $i,SV329: $i,SV92: $i,SV688: $i] :
( ( ( in @ SV688 @ SV92 )
= $false )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV329
@ ^ [SY3140: $i] : ( in @ ( kpair @ SV688 @ SY3140 ) @ SV514 ) ) )
@ SV329 )
= $true )
| ( ( func @ SV92 @ SV329 @ SV514 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2442,plain,
! [SV94: $i,SV331: $i,SV515: $i] :
( ( ( in @ SV515 @ SV331 )
= $true )
| ( ( ~ ( subset @ SV94 @ SV331 ) )
= $true )
| ( ( in @ SV515 @ SV94 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2255]) ).
thf(2443,plain,
! [SV516: $i,SV332: $i,SV95: $i,SV689: $i] :
( ( ( subset @ SV689 @ ( cartprod @ SV95 @ SV332 ) )
= $false )
| ( ( ~ ! [SY3141: $i] :
( ~ ( in @ SY3141 @ SV95 )
| ! [SY3142: $i] :
( ~ ( in @ SY3142 @ SV332 )
| ~ ( in @ ( kpair @ SY3141 @ SY3142 ) @ SV516 )
| ( in @ ( kpair @ SY3141 @ SY3142 ) @ SV689 ) ) )
| ( subset @ SV516 @ SV689 ) )
= $true )
| ( ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2256]) ).
thf(2444,plain,
! [SV96: $i,SV333: $i] :
( ( ( ~ ( in @ ( sK19_SY2610 @ SV333 @ SV96 ) @ SV96 )
| ~ ( in @ SV333 @ ( sK19_SY2610 @ SV333 @ SV96 ) ) )
= $false )
| ( ( in @ SV333 @ ( setunion @ SV96 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2257]) ).
thf(2445,plain,
! [SV334: $i,SV97: $i,SV633: $i] :
( ( ( ~ ~ ( in @ SV633 @ ( setminus @ SV97 @ SV334 ) ) )
= $true )
| ( ( in @ SV633 @ SV334 )
= $true )
| ( ( in @ SV633 @ SV97 )
= $false )
| ( ( in @ SV334 @ ( powerset @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2258]) ).
thf(2446,plain,
! [SV335: $i > $o,SV98: $i,SV517: $i] :
( ( ( ~ ( in @ SV517
@ ( dsetconstr @ SV98
@ ^ [SY2613: $i] : ( SV335 @ SY2613 ) ) )
| ( SV335 @ SV517 ) )
= $true )
| ( ( in @ SV517 @ SV98 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2259]) ).
thf(2447,plain,
! [SV98: $i,SV517: $i,SV335: $i > $o] :
( ( ( ~ ( SV335 @ SV517 )
| ( in @ SV517
@ ( dsetconstr @ SV98
@ ^ [SY2614: $i] : ( SV335 @ SY2614 ) ) ) )
= $true )
| ( ( in @ SV517 @ SV98 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2260]) ).
thf(2448,plain,
! [SV518: $i,SV337: $i > $o,SV100: $i] :
( ( ( ~ ! [SY2926: $i] :
( ~ ( in @ SY2926 @ SV100 )
| ~ ( SV337 @ SY2926 )
| ( SY2926 = SV518 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV100
@ ^ [SY2618: $i] : ( SV337 @ SY2618 ) ) )
= $true )
| ( ( SV337 @ SV518 )
= $false )
| ( ( in @ SV518 @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2262]) ).
thf(2449,plain,
( ( ~ ( in @ sK39_SY3168 @ sK1_SX0 )
| ~ ( in @ sK39_SY3168 @ ( binunion @ sK2_SY2624 @ sK9_SY2932 ) )
| ~ ( ~ ( in @ sK39_SY3168 @ sK2_SY2624 )
| sK33_SY3090 )
| ~ ( ~ ( in @ sK39_SY3168 @ sK9_SY2932 )
| sK33_SY3090 )
| sK33_SY3090 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[2265]) ).
thf(2450,plain,
! [SV104: $i,SV521: $i,SV341: $i,SV690: $i] :
( ( ( in @ SV690 @ SV341 )
= $false )
| ( ( subset @ ( setadjoin @ SV521 @ ( setadjoin @ SV690 @ emptyset ) ) @ ( binunion @ SV104 @ SV341 ) )
= $true )
| ( ( in @ SV521 @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2266]) ).
thf(2451,plain,
! [SV691: $i > $o,SV522: $i,SV342: $i,SV105: $i] :
( ( ( ! [SY3143: $i] :
( ~ ( in @ SY3143 @ SV105 )
| ! [SY3144: $i] :
( ~ ( in @ SY3144 @ SV342 )
| ~ ( in @ ( kpair @ SY3143 @ SY3144 ) @ SV522 )
| ( SV691 @ ( kpair @ SY3143 @ SY3144 ) ) ) ) )
= $false )
| ( ( ! [SY3145: $i] :
( ~ ( in @ SY3145 @ SV522 )
| ( SV691 @ SY3145 ) ) )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2267]) ).
thf(2452,plain,
! [SV635: $i,SV106: $i > $o] :
( ( ( ~ ( SV106 @ SV635 ) )
= $true )
| ( ( ~ ! [SY3092: $i] :
( ~ ( SV106 @ SY3092 )
| ( SV635 = SY3092 ) ) )
= $true )
| ( ( ! [SY2086: $i,SY2087: $i] :
( ~ ( SV106 @ SY2086 )
| ~ ( SV106 @ SY2087 )
| ( SY2086 = SY2087 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2453,plain,
! [SV636: $i,SV108: $i > $o] :
( ( ( ~ ( SV108 @ SV636 ) )
= $true )
| ( ( ~ ! [SY3093: $i] :
( ~ ( SV108 @ SY3093 )
| ( SV636 = SY3093 ) ) )
= $true )
| ( ( SV108
@ ( descr
@ ^ [SY2093: $i] : ( SV108 @ SY2093 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2270]) ).
thf(2454,plain,
! [SV113: $i,SV347: $i,SV525: $i] :
( ( ( ~ ( in @ SV525 @ SV347 ) )
= $false )
| ( ( ~ ( in @ SV525 @ SV113 ) )
= $true )
| ( ( in @ SV525 @ ( setminus @ SV113 @ SV347 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2272]) ).
thf(2455,plain,
! [SV638: $i,SV114: $i > $o] :
( ( ( ~ ( SV114 @ SV638 ) )
= $true )
| ( ( ~ ! [SY3096: $i] :
( ~ ( SV114 @ SY3096 )
| ( SV638 = SY3096 ) ) )
= $true )
| ( ( ~ ! [SY2107: $i] :
~ ( SV114 @ SY2107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2273]) ).
thf(2456,plain,
! [SV639: $i,SV348: $i,SV115: $i,SV741: $i] :
( ( ( ~ ( in @ SV741 @ ( powerset @ SV115 ) )
| ! [SY3175: $i] :
( ~ ( in @ SY3175 @ SV115 )
| ~ ( in @ SY3175 @ ( binintersect @ SV348 @ SV639 ) )
| ( in @ SY3175 @ ( binunion @ SV348 @ SV741 ) ) ) )
= $true )
| ( ( in @ SV639 @ ( powerset @ SV115 ) )
= $false )
| ( ( in @ SV348 @ ( powerset @ SV115 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2274]) ).
thf(2457,plain,
! [SV350: $i > $o,SV118: $i] :
( ( ( ~ ! [SY2650: $i] :
~ ~ ( ~ ( in @ SY2650 @ SV118 )
| ~ ( SV350 @ SY2650 ) ) )
= $false )
| ( ( in @ ( sK10_SY2649 @ SV350 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2276]) ).
thf(2458,plain,
! [SV350: $i > $o,SV118: $i] :
( ( ( ~ ! [SY2650: $i] :
~ ~ ( ~ ( in @ SY2650 @ SV118 )
| ~ ( SV350 @ SY2650 ) ) )
= $false )
| ( ( SV350 @ ( sK10_SY2649 @ SV350 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2459,plain,
! [SV351: $i > $o,SV119: $i,SV692: $i] :
( ( ( in @ SV692 @ SV119 )
= $false )
| ( ( SV351 @ SV692 )
= $true )
| ( ( ~ ! [SY2652: $i] :
~ ~ ( ~ ( in @ SY2652 @ SV119 )
| ~ ~ ( SV351 @ SY2652 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2278]) ).
thf(2460,plain,
! [SV352: $i,SV641: $i,SV120: $i,SV742: $i] :
( ( ( ~ ( in @ SV742 @ SV120 )
| ~ ~ ( in @ SV742 @ SV641 )
| ~ ( in @ SV742 @ ( binintersect @ SV352 @ SV641 ) ) )
= $true )
| ( ( in @ SV641 @ ( powerset @ SV120 ) )
= $false )
| ( ( in @ SV352 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2461,plain,
! [SV642: $i,SV121: $i,SV353: $i] :
( ( ( ~ ( subset @ SV353 @ ( setminus @ SV121 @ SV642 ) ) )
= $true )
| ( ( ! [SY3100: $i] :
( ~ ( in @ SY3100 @ SV121 )
| ~ ( in @ SY3100 @ SV642 )
| ( in @ SY3100 @ ( setminus @ SV121 @ SV353 ) ) ) )
= $true )
| ( ( in @ SV642 @ ( powerset @ SV121 ) )
= $false )
| ( ( in @ SV353 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2280]) ).
thf(2462,plain,
! [SV123: $i,SV526: $i > $i,SV355: $i] :
( ( ( in @ ( sK20_SY2946 @ SV355 @ SV526 @ SV123 ) @ SV123 )
= $true )
| ( ( in
@ ( lam @ SV123 @ SV355
@ ^ [SY2947: $i] : ( SV526 @ SY2947 ) )
@ ( funcSet @ SV123 @ SV355 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2281]) ).
thf(2463,plain,
! [SV358: $i,SV693: $o,SV126: $i,SV529: $i] :
( ( ( ( SV529 != SV126 )
| SV693 )
= $false )
| ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| SV693 )
| SV693 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2284]) ).
thf(2464,plain,
! [SV358: $i,SV126: $i,SV529: $i] :
( ( ( ( SV529 != SV126 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| $true )
| $true )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2285]) ).
thf(2465,plain,
! [SV358: $i,SV126: $i,SV529: $i] :
( ( ( ( SV529 != SV126 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| $false )
| $false )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2286]) ).
thf(2466,plain,
! [SV127: $i,SV359: $i,SV530: $i] :
( ( ( ~ ( in @ SV530 @ SV359 ) )
= $false )
| ( ( ~ ( in @ SV530 @ ( symdiff @ SV127 @ SV359 ) ) )
= $true )
| ( ( in @ SV530 @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2287]) ).
thf(2467,plain,
! [SV128: $i,SV531: $i,SV360: $i,SV694: $i] :
( ( ( in @ SV694 @ SV360 )
= $false )
| ( ( in @ ( setadjoin @ SV531 @ ( setadjoin @ SV694 @ emptyset ) ) @ ( powerset @ ( binunion @ SV128 @ SV360 ) ) )
= $true )
| ( ( in @ SV531 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2468,plain,
! [SV643: $i,SV129: $i,SV361: $i] :
( ( ( ~ ( subset @ SV361 @ ( setminus @ SV129 @ SV643 ) ) )
= $true )
| ( ( subset @ SV643 @ ( setminus @ SV129 @ SV361 ) )
= $true )
| ( ( in @ SV643 @ ( powerset @ SV129 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2289]) ).
thf(2469,plain,
! [SV644: $i,SV362: $i,SV130: $i,SV743: $i] :
( ( ( ~ ( in @ SV743 @ SV130 )
| ~ ~ ( in @ SV743 @ SV362 )
| ~ ( in @ SV743 @ ( binintersect @ SV362 @ SV644 ) ) )
= $true )
| ( ( in @ SV644 @ ( powerset @ SV130 ) )
= $false )
| ( ( in @ SV362 @ ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2470,plain,
! [SV645: $i,SV363: $i,SV131: $i,SV744: $i] :
( ( ( ~ ( in @ SV744 @ SV131 )
| ~ ( in @ SV744 @ ( setminus @ SV131 @ SV363 ) )
| ( in @ SV744 @ ( setminus @ SV131 @ ( binintersect @ SV363 @ SV645 ) ) ) )
= $true )
| ( ( in @ SV645 @ ( powerset @ SV131 ) )
= $false )
| ( ( in @ SV363 @ ( powerset @ SV131 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(2471,plain,
! [SV133: $i,SV365: $i,SV646: $i] :
( ( ( ~ ( in @ SV646 @ SV365 ) )
= $true )
| ( ( in @ SV646 @ ( setminus @ SV133 @ ( setminus @ SV133 @ SV365 ) ) )
= $true )
| ( ( in @ SV646 @ SV133 )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV133 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2292]) ).
thf(2472,plain,
! [SV647: $i,SV367: $i > $o,SV135: $i,SV745: $i] :
( ( ( ~ ( in @ SV745 @ SV135 )
| ~ ( SV367 @ SV647 )
| ~ ( SV367 @ SV745 )
| ( SV647 = SV745 ) )
= $true )
| ( ( in @ SV647 @ SV135 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV135
@ ^ [SY2676: $i] : ( SV367 @ SY2676 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(2473,plain,
! [SV136: $i,SV648: $o,SV368: $i] :
( ( ( ~ ( in @ SV368 @ ( sK40_SY3104 @ SV648 @ SV136 @ SV368 ) )
| ~ ( in @ ( sK40_SY3104 @ SV648 @ SV136 @ SV368 ) @ SV136 )
| SV648 )
= $false )
| ( SV648 = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2294]) ).
thf(2474,plain,
! [SV136: $i,SV368: $i] :
( ( ( ~ ( in @ SV368 @ ( sK41_SX0 @ SV136 @ SV368 ) )
| ~ ( in @ ( sK41_SX0 @ SV136 @ SV368 ) @ SV136 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2295]) ).
thf(2475,plain,
! [SV136: $i,SV368: $i] :
( ( ( ~ ( in @ SV368 @ ( sK42_SX0 @ SV136 @ SV368 ) )
| ~ ( in @ ( sK42_SX0 @ SV136 @ SV368 ) @ SV136 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2296]) ).
thf(2476,plain,
! [SV649: $i,SV369: $i,SV137: $i,SV746: $i] :
( ( ( ~ ( in @ SV746 @ SV137 )
| ~ ( subset @ SV369 @ SV649 )
| ~ ~ ( in @ SV746 @ SV649 )
| ~ ( in @ SV746 @ SV369 ) )
= $true )
| ( ( in @ SV649 @ ( powerset @ SV137 ) )
= $false )
| ( ( in @ SV369 @ ( powerset @ SV137 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2477,plain,
! [SV538: $i,SV374: $i,SV143: $i,SV695: $i] :
( ( ( in @ SV695 @ SV143 )
= $false )
| ( ( in @ ( kpair @ SV695 @ ( ap @ SV143 @ SV374 @ SV538 @ SV695 ) ) @ SV538 )
= $true )
| ( ( in @ SV538 @ ( funcSet @ SV143 @ SV374 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2478,plain,
! [SV650: $i,SV377: $i,SV146: $i] :
( ( ( ~ ! [SY3106: $i] :
( ~ ( in @ SY3106 @ SV146 )
| ~ ( in @ SY3106 @ SV377 )
| ( in @ SY3106 @ SV650 ) ) )
= $true )
| ( ( subset @ SV377 @ SV650 )
= $true )
| ( ( in @ SV650 @ ( powerset @ SV146 ) )
= $false )
| ( ( in @ SV377 @ ( powerset @ SV146 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2299]) ).
thf(2479,plain,
! [SV147: $i] :
( ( ~ ~ ( ~ ! [SY2953: $i] :
( ~ ( in @ SY2953 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY2188: $i] :
( ~ ( in @ SY2188 @ SY2953 )
| ( in @ SY2188 @ SV147 ) ) )
| ~ ! [SY2955: $i,SY2956: $i] :
( ~ ~ ( ~ ( in @ SY2955 @ SV147 )
| ~ ( in @ SY2956 @ SV147 ) )
| ~ ! [SY2957: $i] :
( ~ ( in @ SY2957 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SY2955 @ SY2957 )
| ( in @ SY2956 @ SY2957 ) )
| ~ ( ~ ( in @ SY2956 @ SY2957 )
| ( in @ SY2955 @ SY2957 ) ) ) )
| ( SY2955 = SY2956 ) ) )
| ~ ! [SY2958: $i,SY2959: $i] :
( ~ ~ ( ~ ( in @ SY2958 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY2959 @ ( sK3_SY2186 @ SV147 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2958 )
| ( in @ SX4 @ SY2959 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2959 )
| ( in @ SX4 @ SY2958 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2300]) ).
thf(2480,plain,
! [SV147: $i,SV747: $i] :
( ( ~ ~ ( ~ ! [SY3176: $i] :
( ~ ( in @ SY3176 @ SV747 )
| ( in @ SY3176 @ SV147 ) )
| ~ ~ ! [SY3177: $i] :
~ ( in @ SY3177 @ SV747 ) )
| ~ ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2481,plain,
! [SV651: $i,SV381: $i,SV151: $i,SV748: $i] :
( ( ( ~ ( in @ SV748 @ ( powerset @ SV151 ) )
| ! [SY3183: $i] :
( ~ ( in @ SY3183 @ SV151 )
| ~ ( in @ SY3183 @ ( binintersect @ SV381 @ SV651 ) )
| ( in @ SY3183 @ ( binunion @ SV651 @ SV748 ) ) ) )
= $true )
| ( ( in @ SV651 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV381 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2482,plain,
! [SV652: $i,SV386: $i,SV156: $i,SV749: $i] :
( ( ( ~ ( in @ SV749 @ SV156 )
| ~ ( subset @ SV386 @ ( setminus @ SV156 @ SV652 ) )
| ~ ( in @ SV749 @ SV652 )
| ~ ( in @ SV749 @ SV386 ) )
= $true )
| ( ( in @ SV652 @ ( powerset @ SV156 ) )
= $false )
| ( ( in @ SV386 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(2483,plain,
! [SV388: $i,SV158: $i,SV545: $i] :
( ( ( in @ SV545 @ SV158 )
= $false )
| ( ( in @ SV545 @ SV388 )
= $true )
| ( ( in @ SV545 @ ( setminus @ SV158 @ SV388 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2306]) ).
thf(2484,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ! [SY2231: $i,SY2232: $i] :
( ~ ( SV160 @ SY2231 )
| ~ ( SV160 @ SY2232 )
| ( SY2231 = SY2232 ) ) )
= $false )
| ( ( ~ ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2307]) ).
thf(2485,plain,
! [SV164: $i,SV392: $i,SV546: $i] :
( ( ( in @ SV546 @ SV392 )
= $true )
| ( ( in @ SV546 @ ( symdiff @ SV164 @ SV392 ) )
= $true )
| ( ( in @ SV546 @ SV164 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2310]) ).
thf(2486,plain,
! [SV393: $i,SV165: $i,SV696: $i,SV656: $i] :
( ( ( SV656 = SV696 )
= $false )
| ( ( ~ ( in @ SV656 @ SV165 )
| ( in @ SV696 @ SV393 ) )
= $true )
| ( ( SV165 = SV393 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2311]) ).
thf(2487,plain,
! [SV166: $i,SV394: $i,SV547: $i] :
( ( ( in @ SV547 @ SV394 )
= $true )
| ( ( SV166 != SV394 )
= $true )
| ( ( in @ SV547 @ SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2312]) ).
thf(2488,plain,
! [SV657: $i,SV395: $i,SV167: $i,SV750: $i] :
( ( ( ~ ( in @ SV750 @ SV167 )
| ~ ( in @ SV750 @ ( setminus @ SV167 @ ( binunion @ SV395 @ SV657 ) ) )
| ( in @ SV750 @ ( setminus @ SV167 @ SV395 ) ) )
= $true )
| ( ( in @ SV657 @ ( powerset @ SV167 ) )
= $false )
| ( ( in @ SV395 @ ( powerset @ SV167 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2489,plain,
! [SV548: $i,SV697: $i,SV396: $i,SV168: $i] :
( ( ( func @ SV168 @ SV396 @ SV697 )
= $false )
| ( ( ~ ! [SY3146: $i] :
( ~ ( in @ SY3146 @ SV168 )
| ( ( ap @ SV168 @ SV396 @ SV548 @ SY3146 )
= ( ap @ SV168 @ SV396 @ SV697 @ SY3146 ) ) )
| ( SV548 = SV697 ) )
= $true )
| ( ( func @ SV168 @ SV396 @ SV548 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2314]) ).
thf(2490,plain,
! [SV549: $i,SV397: $o,SV169: $i,SV698: $i] :
( ( ( in @ SV698 @ SV169 )
= $false )
| ( ( in @ ( if @ SV169 @ SV397 @ SV549 @ SV698 ) @ ( setadjoin @ SV549 @ ( setadjoin @ SV698 @ emptyset ) ) )
= $true )
| ( ( in @ SV549 @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2315]) ).
thf(2491,plain,
! [SV550: $i,SV169: $i,SV699: $i] :
( ( ( in @ SV699 @ SV169 )
= $false )
| ( ( in @ ( if @ SV169 @ $true @ SV550 @ SV699 ) @ ( setadjoin @ SV550 @ ( setadjoin @ SV699 @ emptyset ) ) )
= $true )
| ( ( in @ SV550 @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2492,plain,
! [SV551: $i,SV169: $i,SV700: $i] :
( ( ( in @ SV700 @ SV169 )
= $false )
| ( ( in @ ( if @ SV169 @ $false @ SV551 @ SV700 ) @ ( setadjoin @ SV551 @ ( setadjoin @ SV700 @ emptyset ) ) )
= $true )
| ( ( in @ SV551 @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2317]) ).
thf(2493,plain,
! [SV170: $i,SV552: $i > $i,SV398: $i] :
( ( ( in @ ( sK21_SY2977 @ SV398 @ SV552 @ SV170 ) @ SV170 )
= $true )
| ( ( ( lam @ SV170 @ SV398
@ ^ [SY2978: $i] : ( SV552 @ SY2978 ) )
= ( lam @ SV170 @ SV398
@ ^ [SY2979: $i] : ( SV552 @ SY2979 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2318]) ).
thf(2494,plain,
! [SV553: $i,SV399: $o,SV171: $i,SV701: $i] :
( ( ( in @ SV701 @ SV171 )
= $false )
| ( ( ~ ~ SV399
| ( ( dsetconstr @ SV171
@ ^ [SY3147: $i] :
( ~ ( ~ SV399
| ( SY3147 != SV553 ) )
| ~ ( ~ ~ SV399
| ( SY3147 != SV701 ) ) ) )
= ( setadjoin @ SV701 @ emptyset ) ) )
= $true )
| ( ( in @ SV553 @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2320]) ).
thf(2495,plain,
! [SV554: $i,SV171: $i,SV702: $i] :
( ( ( in @ SV702 @ SV171 )
= $false )
| ( ( ~ ~ $true
| ( ( dsetconstr @ SV171
@ ^ [SY3148: $i] :
( ~ ( ~ $true
| ( SY3148 != SV554 ) )
| ~ ( ~ ~ $true
| ( SY3148 != SV702 ) ) ) )
= ( setadjoin @ SV702 @ emptyset ) ) )
= $true )
| ( ( in @ SV554 @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2496,plain,
! [SV555: $i,SV171: $i,SV703: $i] :
( ( ( in @ SV703 @ SV171 )
= $false )
| ( ( ~ ~ $false
| ( ( dsetconstr @ SV171
@ ^ [SY3149: $i] :
( ~ ( ~ $false
| ( SY3149 != SV555 ) )
| ~ ( ~ ~ $false
| ( SY3149 != SV703 ) ) ) )
= ( setadjoin @ SV703 @ emptyset ) ) )
= $true )
| ( ( in @ SV555 @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2497,plain,
! [SV172: $i,SV400: $i,SV751: $i] :
( ( ( ~ ( in @ SV751 @ SV400 )
| ( in @ SV751 @ SV172 ) )
= $true )
| ( ( in @ SV400 @ ( powerset @ SV172 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2323]) ).
thf(2498,plain,
! [SV400: $i,SV172: $i] :
( ( ( ~ ( in @ ( sK43_SY2728 @ SV172 @ SV400 ) @ SV400 )
| ( in @ ( sK43_SY2728 @ SV172 @ SV400 ) @ SV172 ) )
= $false )
| ( ( in @ SV400 @ ( powerset @ SV172 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2324]) ).
thf(2499,plain,
! [SV174: $i,SV557: $i,SV402: $i,SV704: $i] :
( ( ( in @ SV704 @ SV402 )
= $false )
| ( ( ( kfst @ ( kpair @ SV557 @ SV704 ) )
= SV557 )
= $true )
| ( ( in @ SV557 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2500,plain,
! [SV558: $i,SV403: $i,SV175: $i,SV705: $i] :
( ( ( in @ SV705 @ SV175 )
= $false )
| ( ( in @ ( ap @ SV175 @ SV403 @ SV558 @ SV705 ) @ SV403 )
= $true )
| ( ( in @ SV558 @ ( funcSet @ SV175 @ SV403 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2326]) ).
thf(2501,plain,
! [SV176: $i,SV658: $i,SV404: $i] :
( ( ( ~ ( subset @ SV404 @ SV658 ) )
= $true )
| ( ( subset @ ( setminus @ SV176 @ SV658 ) @ ( setminus @ SV176 @ SV404 ) )
= $true )
| ( ( in @ SV658 @ ( powerset @ SV176 ) )
= $false )
| ( ( in @ SV404 @ ( powerset @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2327]) ).
thf(2502,plain,
! [SV408: $i > $o,SV180: $i,SV706: $i] :
( ( ( ~ ( in @ SV706 @ SV180 )
| ~ ( SV408 @ SV706 ) )
= $true )
| ( ( ( ( dsetconstr @ SV180
@ ^ [SY2739: $i] : ( SV408 @ SY2739 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2329]) ).
thf(2503,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( in @ ( sK12_SY2740 @ SV409 @ SV181 ) @ SV181 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2330]) ).
thf(2504,plain,
! [SV181: $i,SV409: $i > $o] :
( ( ( ~ ( in @ ( sK34_SY3112 @ SV409 @ SV181 ) @ SV181 ) )
= $false )
| ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) )
| ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2331]) ).
thf(2505,plain,
! [SV181: $i,SV409: $i > $o] :
( ( ( ~ ( SV409 @ ( sK12_SY2740 @ SV409 @ SV181 ) )
| ~ ( SV409 @ ( sK34_SY3112 @ SV409 @ SV181 ) )
| ( ( sK12_SY2740 @ SV409 @ SV181 )
= ( sK34_SY3112 @ SV409 @ SV181 ) ) )
= $false )
| ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) )
| ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2331]) ).
thf(2506,plain,
! [SV183: $i > $o,SV411: $i > $o] :
( ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2332]) ).
thf(2507,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ( ~ ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
| ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) ) )
| ~ ( ~ ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
| ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2333]) ).
thf(2508,plain,
! [SV561: $i,SV413: $i,SV185: $i,SV707: $i] :
( ( ( in @ SV707 @ SV185 )
= $false )
| ( ( ! [SY3150: $i] :
( ~ ( in @ SY3150 @ SV413 )
| ~ ( in @ ( kpair @ SV707 @ SY3150 ) @ SV561 )
| ( ( ap @ SV185 @ SV413 @ SV561 @ SV707 )
= SY3150 ) ) )
= $true )
| ( ( in @ SV561 @ ( funcSet @ SV185 @ SV413 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2334]) ).
thf(2509,plain,
! [SV659: $i,SV414: $i,SV186: $i] :
( ( ( ~ ! [SY3114: $i] :
( ~ ( in @ SY3114 @ SV186 )
| ~ ( in @ SY3114 @ SV414 )
| ( in @ SY3114 @ SV659 ) ) )
= $true )
| ( ( ~ ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV186 )
| ~ ( in @ SY3115 @ SV659 )
| ( in @ SY3115 @ SV414 ) )
| ( SV414 = SV659 ) )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2335]) ).
thf(2510,plain,
! [SV562: $i,SV415: $i > $o,SV187: $i] :
( ( ( ( dsetconstr @ SV187
@ ^ [SY2759: $i] : ( SV415 @ SY2759 ) )
= emptyset )
= $false )
| ( ( SV415 @ SV562 )
= $false )
| ( ( in @ SV562 @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2336]) ).
thf(2511,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV660 ) )
= $true )
| ( ( ~ ! [SY3116: $i] :
( ~ ( SV188 @ SY3116 )
| ( SV660 = SY3116 ) ) )
= $true )
| ( ( ~ ! [SY2316: $i] :
~ ~ ( ~ ( SV188 @ SY2316 )
| ~ ! [SY2317: $i] :
( ~ ( SV188 @ SY2317 )
| ( SY2316 = SY2317 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2337]) ).
thf(2512,plain,
! [SV564: $i,SV417: $i,SV190: $i,SV708: $i] :
( ( ( in @ SV708 @ SV190 )
= $false )
| ( ( ( ap @ SV190 @ SV417 @ SV564 @ SV708 )
= ( ap @ SV190 @ SV417 @ SV564 @ SV708 ) )
= $true )
| ( ( in @ SV564 @ ( funcSet @ SV190 @ SV417 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2338]) ).
thf(2513,plain,
! [SV661: $i,SV418: $i,SV191: $i,SV752: $i] :
( ( ( ~ ( in @ SV752 @ ( powerset @ SV191 ) )
| ! [SY3184: $i] :
( ~ ( in @ SY3184 @ SV191 )
| ~ ( in @ SY3184 @ ( binintersect @ SV418 @ SV661 ) )
| ( in @ SY3184 @ ( binintersect @ ( binunion @ SV418 @ SV752 ) @ ( binunion @ SV661 @ SV752 ) ) ) ) )
= $true )
| ( ( in @ SV661 @ ( powerset @ SV191 ) )
= $false )
| ( ( in @ SV418 @ ( powerset @ SV191 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2339]) ).
thf(2514,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2340]) ).
thf(2515,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
| ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) ) )
| ~ ( ~ ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
| ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2341]) ).
thf(2516,plain,
! [SV195: $i,SV423: $i,SV565: $i] :
( ( ( in @ SV565 @ SV423 )
= $true )
| ( ( in @ SV565 @ ( setminus @ SV195 @ SV423 ) )
= $true )
| ( ( in @ SV565 @ SV195 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2342]) ).
thf(2517,plain,
! [SV196: $i,SV424: $i,SV566: $i] :
( ( ( ~ ( ~ ( in @ ( sK35_SY2993 @ SV566 @ SV424 @ SV196 ) @ SV196 )
| ~ ~ ! [SY3169: $i] :
~ ~ ( ~ ( in @ SY3169 @ SV424 )
| ( SV566
!= ( kpair @ ( sK35_SY2993 @ SV566 @ SV424 @ SV196 ) @ SY3169 ) ) ) ) )
= $true )
| ( ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2343]) ).
thf(2518,plain,
! [SV567: $i,SV425: $o,SV197: $i,SV709: $i] :
( ( ( in @ SV709 @ SV197 )
= $false )
| ( ( ~ SV425
| ( ( if @ SV197 @ SV425 @ SV567 @ SV709 )
= SV567 ) )
= $true )
| ( ( in @ SV567 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2344]) ).
thf(2519,plain,
! [SV568: $i,SV197: $i,SV710: $i] :
( ( ( in @ SV710 @ SV197 )
= $false )
| ( ( ~ $true
| ( ( if @ SV197 @ $true @ SV568 @ SV710 )
= SV568 ) )
= $true )
| ( ( in @ SV568 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2345]) ).
thf(2520,plain,
! [SV569: $i,SV197: $i,SV711: $i] :
( ( ( in @ SV711 @ SV197 )
= $false )
| ( ( ~ $false
| ( ( if @ SV197 @ $false @ SV569 @ SV711 )
= SV569 ) )
= $true )
| ( ( in @ SV569 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2346]) ).
thf(2521,plain,
! [SV570: $i,SV426: $i,SV198: $i,SV712: $i] :
( ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( ~ ! [SY3151: $i] :
( ~ ( in @ SY3151 @ SV198 )
| ! [SY3152: $i] :
( ~ ( in @ SY3152 @ SV426 )
| ~ ( in @ ( kpair @ SY3151 @ SY3152 ) @ SV570 )
| ( in @ ( kpair @ SY3151 @ SY3152 ) @ SV712 ) ) )
| ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) )
| ( SV570 = SV712 ) )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2347]) ).
thf(2522,plain,
! [SV713: $i > $o,SV571: $i,SV428: $i,SV200: $i] :
( ( ( ! [SY3155: $i] :
( ~ ( in @ SY3155 @ SV200 )
| ! [SY3156: $i] :
( ~ ( in @ SY3156 @ SV428 )
| ~ ( in @ ( kpair @ SY3155 @ SY3156 ) @ SV571 )
| ( SV713 @ ( kpair @ SY3155 @ SY3156 ) ) ) ) )
= $false )
| ( ( ! [SY3157: $i] :
( ~ ( in @ SY3157 @ SV571 )
| ( SV713 @ SY3157 ) ) )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2348]) ).
thf(2523,plain,
! [SV429: $i > $o,SV201: $i,SV714: $i] :
( ( ( ~ ( in @ SV714 @ SV201 )
| ~ ~ ( SV429 @ SV714 ) )
= $true )
| ( ( ~ ! [SY2794: $i] :
( ~ ( in @ SY2794 @ SV201 )
| ( SV429 @ SY2794 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2349]) ).
thf(2524,plain,
! [SV203: $i,SV572: $i > $i,SV430: $i] :
( ( ( in @ ( sK24_SY3007 @ SV430 @ SV572 @ SV203 ) @ SV203 )
= $true )
| ( ( func @ SV203 @ SV430
@ ( dpsetconstr @ SV203 @ SV430
@ ^ [SY3008: $i,SY3009: $i] :
( ( SV572 @ SY3008 )
= SY3009 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2350]) ).
thf(2525,plain,
! [SV206: $i,SV431: $i,SV573: $i] :
( ( ( in @ SV573 @ SV431 )
= $false )
| ( ( in @ SV573 @ ( symdiff @ SV206 @ SV431 ) )
= $true )
| ( ( in @ SV573 @ SV206 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2526,plain,
! [SV209: $i,SV574: $i > $i,SV433: $i] :
( ( ( in @ ( sK25_SY3010 @ SV433 @ SV574 @ SV209 ) @ SV209 )
= $true )
| ( ( ! [SY3011: $i] :
( ~ ( in @ SY3011 @ SV209 )
| ( ( ap @ SV209 @ SV433
@ ( lam @ SV209 @ SV433
@ ^ [SY3012: $i] : ( SV574 @ SY3012 ) )
@ SY3011 )
= ( SV574 @ SY3011 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2354]) ).
thf(2527,plain,
! [SV574: $i > $i,SV433: $i,SV209: $i,SV753: $i] :
( ( ( ~ ( in @ SV753 @ SV209 )
| ( ( ap @ SV209 @ SV433
@ ( lam @ SV209 @ SV433
@ ^ [SY3012: $i] : ( SV574 @ SY3012 ) )
@ SV753 )
= ( SV574 @ SV753 ) ) )
= $true )
| ( ( in @ ( SV574 @ ( sK25_SY3010 @ SV433 @ SV574 @ SV209 ) ) @ SV433 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(2528,plain,
! [SV435: $i,SV211: $i,SV715: $i,SV663: $i] :
( ( ( SV663 = SV715 )
= $false )
| ( ( ( setadjoin @ SV211 @ SV663 )
= ( setadjoin @ SV435 @ SV715 ) )
= $true )
| ( ( SV211 = SV435 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2356]) ).
thf(2529,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( in @ ( sK15_SY2806 @ SV436 @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2357]) ).
thf(2530,plain,
! [SV212: $i,SV436: $i > $o] :
( ( ( ~ ( in @ ( sK36_SY3121 @ SV436 @ SV212 ) @ SV212 ) )
= $false )
| ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) )
| ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2358]) ).
thf(2531,plain,
! [SV212: $i,SV436: $i > $o] :
( ( ( ~ ( SV436 @ ( sK15_SY2806 @ SV436 @ SV212 ) )
| ~ ( SV436 @ ( sK36_SY3121 @ SV436 @ SV212 ) )
| ( ( sK15_SY2806 @ SV436 @ SV212 )
= ( sK36_SY3121 @ SV436 @ SV212 ) ) )
= $false )
| ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) )
| ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2358]) ).
thf(2532,plain,
! [SV214: $i,SV438: $i,SV615: $i,SV575: $i] :
( ( ( SV575 = SV615 )
= $false )
| ( ( SV438 = SV615 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV214 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV214 @ ( setadjoin @ SV438 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV575 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV575 @ ( setadjoin @ SV615 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2359]) ).
thf(2533,plain,
! [SV215: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK44_SY2395 @ SV215 ) @ omega )
| ~ ( in @ ( sK44_SY2395 @ SV215 ) @ SV215 ) )
| ( in @ ( setadjoin @ ( sK44_SY2395 @ SV215 ) @ ( sK44_SY2395 @ SV215 ) ) @ SV215 ) )
= $false )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( ! [SY2396: $i] :
( ~ ( in @ SY2396 @ omega )
| ( in @ SY2396 @ SV215 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2360]) ).
thf(2534,plain,
! [SV216: $i,SV576: $i,SV439: $i,SV716: $i] :
( ( ( in @ SV716 @ SV439 )
= $false )
| ( ( in @ ( kpair @ SV576 @ SV716 ) @ ( powerset @ ( powerset @ ( binunion @ SV216 @ SV439 ) ) ) )
= $true )
| ( ( in @ SV576 @ SV216 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2361]) ).
thf(2535,plain,
! [SV217: $i,SV616: $i,SV577: $i > $i > $o,SV440: $i,SV735: $i] :
( ( ( ~ ( in @ SV735 @ SV440 ) )
= $true )
| ( ( ~ ( SV577 @ SV616 @ SV735 )
| ( in @ ( kpair @ SV616 @ SV735 )
@ ( dpsetconstr @ SV217 @ SV440
@ ^ [SY3017: $i,SY3018: $i] : ( SV577 @ SY3017 @ SY3018 ) ) ) )
= $true )
| ( ( in @ SV616 @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2362]) ).
thf(2536,plain,
! [SV578: $i,SV441: $o,SV218: $i,SV717: $i] :
( ( ( in @ SV717 @ SV218 )
= $false )
| ( ( in @ ( if @ SV218 @ SV441 @ SV578 @ SV717 ) @ SV218 )
= $true )
| ( ( in @ SV578 @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2363]) ).
thf(2537,plain,
! [SV579: $i,SV218: $i,SV718: $i] :
( ( ( in @ SV718 @ SV218 )
= $false )
| ( ( in @ ( if @ SV218 @ $true @ SV579 @ SV718 ) @ SV218 )
= $true )
| ( ( in @ SV579 @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2364]) ).
thf(2538,plain,
! [SV580: $i,SV218: $i,SV719: $i] :
( ( ( in @ SV719 @ SV218 )
= $false )
| ( ( in @ ( if @ SV218 @ $false @ SV580 @ SV719 ) @ SV218 )
= $true )
| ( ( in @ SV580 @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2365]) ).
thf(2539,plain,
! [SV581: $i,SV442: $i,SV219: $i,SV720: $i] :
( ( ( in @ SV720 @ ( funcSet @ SV219 @ SV442 ) )
= $false )
| ( ( ~ ! [SY3158: $i] :
( ~ ( in @ SY3158 @ SV219 )
| ( ( ap @ SV219 @ SV442 @ SV581 @ SY3158 )
= ( ap @ SV219 @ SV442 @ SV720 @ SY3158 ) ) )
| ( SV581 = SV720 ) )
= $true )
| ( ( in @ SV581 @ ( funcSet @ SV219 @ SV442 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2366]) ).
thf(2540,plain,
! [SV582: $i > $i > $o,SV220: $i,SV617: $i,SV443: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ SV443 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV617 @ SV736 )
@ ( dpsetconstr @ SV220 @ SV443
@ ^ [SY3026: $i,SY3027: $i] : ( SV582 @ SY3026 @ SY3027 ) ) )
| ( SV582 @ SV617 @ SV736 ) )
= $true )
| ( ( in @ SV617 @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2367]) ).
thf(2541,plain,
! [SV583: $i,SV444: $i,SV221: $i,SV721: $i] :
( ( ( in @ SV721 @ SV221 )
= $false )
| ( ( in @ ( ap @ SV221 @ SV444 @ SV583 @ SV721 ) @ SV444 )
= $true )
| ( ( func @ SV221 @ SV444 @ SV583 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2368]) ).
thf(2542,plain,
! [SV223: $i,SV446: $i > $o] :
( ( ( ~ ( in @ ( sK26_SY2833 @ SV446 @ SV223 ) @ SV223 )
| ~ ( SV446 @ ( sK26_SY2833 @ SV446 @ SV223 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY2832: $i] : ( SV446 @ SY2832 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2369]) ).
thf(2543,plain,
! [SV225: $i,SV448: $i] :
( ( ( ~ ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 )
| ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 )
| ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 ) ) )
= $true )
| ( ( SV225 = SV448 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2370]) ).
thf(2544,plain,
! [SV449: $i,SV226: $i,SV585: $i] :
( ( ( in @ SV585 @ ( symdiff @ SV226 @ SV449 ) )
= $false )
| ( ( in @ SV585 @ SV449 )
= $false )
| ( ( in @ SV585 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2371]) ).
thf(2545,plain,
! [SV450: $i,SV227: $i,SV664: $i] :
( ( ( ~ ( in @ SV664 @ ( setminus @ SV227 @ ( setminus @ SV227 @ SV450 ) ) ) )
= $true )
| ( ( in @ SV664 @ SV450 )
= $true )
| ( ( in @ SV664 @ SV227 )
= $false )
| ( ( in @ SV450 @ ( powerset @ SV227 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2372]) ).
thf(2546,plain,
! [SV665: $i,SV452: $i,SV229: $i,SV754: $i] :
( ( ( ~ ( in @ SV754 @ ( powerset @ SV229 ) )
| ( in @ ( binintersect @ SV452 @ SV665 ) @ ( powerset @ ( binintersect @ ( binunion @ SV452 @ SV754 ) @ ( binunion @ SV665 @ SV754 ) ) ) ) )
= $true )
| ( ( in @ SV665 @ ( powerset @ SV229 ) )
= $false )
| ( ( in @ SV452 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2373]) ).
thf(2547,plain,
! [SV230: $i] :
( ( ( ~ ( in @ ( sK27_SY2440 @ SV230 ) @ SV230 )
| ~ $true )
= $false )
| ( ( SV230 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2548,plain,
! [SV587: $i,SV453: $o,SV231: $i,SV722: $i] :
( ( ( in @ SV722 @ SV231 )
= $false )
| ( ( ~ SV453
| ( ( dsetconstr @ SV231
@ ^ [SY3159: $i] :
( ~ ( ~ SV453
| ( SY3159 != SV587 ) )
| ~ ( ~ ~ SV453
| ( SY3159 != SV722 ) ) ) )
= ( setadjoin @ SV587 @ emptyset ) ) )
= $true )
| ( ( in @ SV587 @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2375]) ).
thf(2549,plain,
! [SV588: $i,SV231: $i,SV723: $i] :
( ( ( in @ SV723 @ SV231 )
= $false )
| ( ( ~ $true
| ( ( dsetconstr @ SV231
@ ^ [SY3160: $i] :
( ~ ( ~ $true
| ( SY3160 != SV588 ) )
| ~ ( ~ ~ $true
| ( SY3160 != SV723 ) ) ) )
= ( setadjoin @ SV588 @ emptyset ) ) )
= $true )
| ( ( in @ SV588 @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2376]) ).
thf(2550,plain,
! [SV589: $i,SV231: $i,SV724: $i] :
( ( ( in @ SV724 @ SV231 )
= $false )
| ( ( ~ $false
| ( ( dsetconstr @ SV231
@ ^ [SY3161: $i] :
( ~ ( ~ $false
| ( SY3161 != SV589 ) )
| ~ ( ~ ~ $false
| ( SY3161 != SV724 ) ) ) )
= ( setadjoin @ SV589 @ emptyset ) ) )
= $true )
| ( ( in @ SV589 @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2551,plain,
! [SV233: $i,SV455: $i,SV666: $i] :
( ( ( ~ ( in @ SV666 @ SV455 ) )
= $true )
| ( ( ~ ( in @ SV666 @ ( setminus @ SV233 @ SV455 ) ) )
= $true )
| ( ( in @ SV666 @ SV233 )
= $false )
| ( ( in @ SV455 @ ( powerset @ SV233 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2552,plain,
! [SV234: $i,SV591: $i > $i,SV456: $i] :
( ( ( in @ ( sK28_SY3036 @ SV456 @ SV591 @ SV234 ) @ SV234 )
= $true )
| ( ( ! [SY3037: $i] :
( ~ ( in @ SY3037 @ SV234 )
| ( ( ap @ SV234 @ SV456
@ ( lam @ SV234 @ SV456
@ ^ [SY3038: $i] : ( SV591 @ SY3038 ) )
@ SY3037 )
= ( SV591 @ SY3037 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2380]) ).
thf(2553,plain,
! [SV591: $i > $i,SV456: $i,SV234: $i,SV755: $i] :
( ( ( ~ ( in @ SV755 @ SV234 )
| ( ( ap @ SV234 @ SV456
@ ( lam @ SV234 @ SV456
@ ^ [SY3038: $i] : ( SV591 @ SY3038 ) )
@ SV755 )
= ( SV591 @ SV755 ) ) )
= $true )
| ( ( in @ ( SV591 @ ( sK28_SY3036 @ SV456 @ SV591 @ SV234 ) ) @ SV456 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(2554,plain,
! [SV235: $i,SV457: $i] :
( ( ( ~ ( ~ ( in @ ( sK37_SY2850 @ SV457 @ SV235 ) @ SV235 )
| ~ ( in @ ( sK37_SY2850 @ SV457 @ SV235 ) @ SV457 ) ) )
= $true )
| ( ( ( binintersect @ SV235 @ SV457 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2382]) ).
thf(2555,plain,
! [SV242: $i,SV596: $i > $i,SV464: $i] :
( ( ( in @ ( sK29_SY3041 @ SV464 @ SV596 @ SV242 ) @ SV242 )
= $true )
| ( ( func @ SV242 @ SV464
@ ( lam @ SV242 @ SV464
@ ^ [SY3042: $i] : ( SV596 @ SY3042 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2383]) ).
thf(2556,plain,
! [SV667: $i,SV465: $i,SV243: $i,SV756: $i] :
( ( ( ~ ( in @ SV756 @ SV243 )
| ~ ( in @ SV465 @ ( powerset @ SV667 ) )
| ~ ( in @ SV756 @ SV465 )
| ( in @ SV756 @ SV667 ) )
= $true )
| ( ( in @ SV667 @ ( powerset @ SV243 ) )
= $false )
| ( ( in @ SV465 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(2557,plain,
! [SV597: $i,SV466: $o,SV244: $i,SV725: $i] :
( ( ( in @ SV725 @ SV244 )
= $false )
| ( ( ~ ~ SV466
| ( in @ SV725
@ ( dsetconstr @ SV244
@ ^ [SY3162: $i] :
( ~ ( ~ SV466
| ( SY3162 != SV597 ) )
| ~ ( ~ ~ SV466
| ( SY3162 != SV725 ) ) ) ) ) )
= $true )
| ( ( in @ SV597 @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2386]) ).
thf(2558,plain,
! [SV598: $i,SV244: $i,SV726: $i] :
( ( ( in @ SV726 @ SV244 )
= $false )
| ( ( ~ ~ $true
| ( in @ SV726
@ ( dsetconstr @ SV244
@ ^ [SY3163: $i] :
( ~ ( ~ $true
| ( SY3163 != SV598 ) )
| ~ ( ~ ~ $true
| ( SY3163 != SV726 ) ) ) ) ) )
= $true )
| ( ( in @ SV598 @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2387]) ).
thf(2559,plain,
! [SV599: $i,SV244: $i,SV727: $i] :
( ( ( in @ SV727 @ SV244 )
= $false )
| ( ( ~ ~ $false
| ( in @ SV727
@ ( dsetconstr @ SV244
@ ^ [SY3164: $i] :
( ~ ( ~ $false
| ( SY3164 != SV599 ) )
| ~ ( ~ ~ $false
| ( SY3164 != SV727 ) ) ) ) ) )
= $true )
| ( ( in @ SV599 @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2388]) ).
thf(2560,plain,
! [SV600: $i,SV728: $i,SV469: $i,SV247: $i] :
( ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( ~ ! [SY3165: $i] :
( ~ ( in @ SY3165 @ SV247 )
| ( ( ap @ SV247 @ SV469 @ SV600 @ SY3165 )
= ( ap @ SV247 @ SV469 @ SV728 @ SY3165 ) ) )
| ! [SY3166: $i] :
( ~ ( in @ SY3166 @ SV247 )
| ! [SY3167: $i] :
( ~ ( in @ SY3167 @ SV469 )
| ~ ( in @ ( kpair @ SY3166 @ SY3167 ) @ SV728 )
| ( in @ ( kpair @ SY3166 @ SY3167 ) @ SV600 ) ) ) )
= $true )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2389]) ).
thf(2561,plain,
! [SV249: $i > $i > $o,SV471: $i] :
( ( ( ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $false )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2562,plain,
! [SV757: $i,SV471: $i,SV249: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
| ~ ! [SY3187: $i] :
( ~ ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SY3187 )
| ( SV757 = SY3187 ) ) ) )
= $true )
| ( ( ~ ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(2563,plain,
! [SV601: $i,SV474: $o,SV252: $i,SV729: $i] :
( ( ( in @ SV729 @ SV252 )
= $false )
| ( ( ~ ~ SV474
| ( ( if @ SV252 @ SV474 @ SV601 @ SV729 )
= SV729 ) )
= $true )
| ( ( in @ SV601 @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2393]) ).
thf(2564,plain,
! [SV602: $i,SV252: $i,SV730: $i] :
( ( ( in @ SV730 @ SV252 )
= $false )
| ( ( ~ ~ $true
| ( ( if @ SV252 @ $true @ SV602 @ SV730 )
= SV730 ) )
= $true )
| ( ( in @ SV602 @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2394]) ).
thf(2565,plain,
! [SV603: $i,SV252: $i,SV731: $i] :
( ( ( in @ SV731 @ SV252 )
= $false )
| ( ( ~ ~ $false
| ( ( if @ SV252 @ $false @ SV603 @ SV731 )
= SV731 ) )
= $true )
| ( ( in @ SV603 @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2395]) ).
thf(2566,plain,
! [SV253: $i,SV604: $i,SV475: $i,SV732: $i] :
( ( ( in @ SV732 @ SV475 )
= $false )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV604 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV604 @ ( setadjoin @ SV732 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV253 @ SV475 ) ) ) )
= $true )
| ( ( in @ SV604 @ SV253 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2396]) ).
thf(2567,plain,
! [SV476: $i,SV254: $i,SV733: $i,SV669: $i] :
( ( ( SV669 = SV733 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV669 @ SV254 )
| ( in @ SV733 @ SV476 ) )
| ~ ( ~ ( in @ SV733 @ SV476 )
| ( in @ SV669 @ SV254 ) ) ) )
= $true )
| ( ( SV254 = SV476 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2397]) ).
thf(2568,plain,
! [SV670: $i,SV256: $i > $o] :
( ( ( ~ ( SV256 @ SV670 ) )
= $true )
| ( ( ~ ! [SY3127: $i] :
( ~ ( SV256 @ SY3127 )
| ( SV670 = SY3127 ) ) )
= $true )
| ( ( ~ ! [SY2511: $i] :
~ ! [SY2512: $i] :
~ ( ~ ( ~ ( SV256 @ SY2512 )
| ( SY2512 = SY2511 ) )
| ~ ( ( SY2512 != SY2511 )
| ( SV256 @ SY2512 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2398]) ).
thf(2569,plain,
! [SV258: $i,SV605: $i,SV479: $i,SV734: $i] :
( ( ( in @ SV734 @ SV479 )
= $false )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV605 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV605 @ ( setadjoin @ SV734 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV258 @ SV479 ) ) )
= $true )
| ( ( in @ SV605 @ SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2400]) ).
thf(2570,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( SV35 @ SV621 )
= $false )
| ( ( ~ ! [SY3073: $i] :
( ~ ( SV35 @ SY3073 )
| ( SV621 = SY3073 ) ) )
= $true )
| ( ( ~ ! [SY1902: $i] :
~ ~ ( ~ ( SV35 @ SY1902 )
| ~ ! [SY1903: $i] :
( ~ ( SV35 @ SY1903 )
| ( SY1902 = SY1903 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2401]) ).
thf(2571,plain,
! [SV282: $i,SV622: $i,SV36: $i] :
( ( ( subset @ ( setminus @ SV36 @ SV622 ) @ ( setminus @ SV36 @ SV282 ) )
= $false )
| ( ( subset @ SV282 @ SV622 )
= $true )
| ( ( in @ SV622 @ ( powerset @ SV36 ) )
= $false )
| ( ( in @ SV282 @ ( powerset @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2572,plain,
! [SV38: $i,SV484: $i,SV672: $i,SV284: $i,SV758: $i] :
( ( ( ~ ( in @ SV758 @ SV284 )
| ~ ( in @ ( kpair @ SV672 @ SV758 ) @ SV484 )
| ( ( ap @ SV38 @ SV284 @ SV484 @ SV672 )
= SV758 ) )
= $true )
| ( ( in @ SV672 @ SV38 )
= $false )
| ( ( func @ SV38 @ SV284 @ SV484 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(2573,plain,
! [SV673: $i,SV39: $i,SV485: $i,SV285: $o] :
( ( ( ~ SV285 ) = $true )
| ( ( in @ SV485
@ ( dsetconstr @ SV39
@ ^ [SY3129: $i] :
( ~ ( ~ SV285
| ( SY3129 != SV485 ) )
| ~ ( ~ ~ SV285
| ( SY3129 != SV673 ) ) ) ) )
= $true )
| ( ( in @ SV673 @ SV39 )
= $false )
| ( ( in @ SV485 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2404]) ).
thf(2574,plain,
! [SV674: $i,SV39: $i,SV486: $i] :
( ( ( ~ $true ) = $true )
| ( ( in @ SV486
@ ( dsetconstr @ SV39
@ ^ [SY3130: $i] :
( ~ ( ~ $true
| ( SY3130 != SV486 ) )
| ~ ( ~ ~ $true
| ( SY3130 != SV674 ) ) ) ) )
= $true )
| ( ( in @ SV674 @ SV39 )
= $false )
| ( ( in @ SV486 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2405]) ).
thf(2575,plain,
! [SV675: $i,SV39: $i,SV487: $i] :
( ( ( ~ $false ) = $true )
| ( ( in @ SV487
@ ( dsetconstr @ SV39
@ ^ [SY3131: $i] :
( ~ ( ~ $false
| ( SY3131 != SV487 ) )
| ~ ( ~ ~ $false
| ( SY3131 != SV675 ) ) ) ) )
= $true )
| ( ( in @ SV675 @ SV39 )
= $false )
| ( ( in @ SV487 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2406]) ).
thf(2576,plain,
! [SV40: $i,SV286: $i,SV623: $i > $o,SV676: $i > $o] :
( ( ( ~ ( in @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) @ SV40 )
| ! [SY3188: $i] :
( ~ ( in @ SY3188 @ SV286 )
| ( ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 )
!= SY3188 )
| ~ ( ~ ( ~ ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) )
| ( SV676 @ SY3188 ) )
| ~ ( ~ ( SV676 @ SY3188 )
| ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2407]) ).
thf(2577,plain,
! [SV41: $i,SV287: $i > $o] :
( ( ( ~ ( in @ ( sK30_SY2541 @ SV287 @ SV41 ) @ SV41 )
| ~ ( SV287 @ ( sK30_SY2541 @ SV287 @ SV41 ) ) )
= $false )
| ( ( ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV41 )
| ~ ( SV287 @ SY2542 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2408]) ).
thf(2578,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ( ~ ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
| ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 ) ) )
= $true )
| ( ( ~ ( ( ( sK31_SY3079 @ SV624 @ SV44 )
!= SV624 )
| ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) ) ) )
= $true )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2409]) ).
thf(2579,plain,
! [SV291: $i,SV47: $i,SV491: $i] :
( ( ( SV491 = SV47 )
= $true )
| ( ( in @ SV491 @ SV291 )
= $true )
| ( ( in @ SV491 @ ( setadjoin @ SV47 @ SV291 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2411]) ).
thf(2580,plain,
! [SV291: $i,SV47: $i,SV491: $i] :
( ( ( SV491 = SV47 )
= $false )
| ( ( in @ SV491 @ ( setadjoin @ SV47 @ SV291 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2412]) ).
thf(2581,plain,
! [SV47: $i,SV291: $i,SV491: $i] :
( ( ( in @ SV491 @ SV291 )
= $false )
| ( ( in @ SV491 @ ( setadjoin @ SV47 @ SV291 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2412]) ).
thf(2582,plain,
! [SV625: $i,SV305: $i,SV64: $i,SV737: $i] :
( ( ( ~ ( in @ SV737 @ SV64 ) )
= $true )
| ( ( ~ ( in @ SV737 @ ( setminus @ SV64 @ SV305 ) )
| ~ ( in @ SV737 @ ( binintersect @ SV305 @ SV625 ) ) )
= $true )
| ( ( in @ SV625 @ ( powerset @ SV64 ) )
= $false )
| ( ( in @ SV305 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2420]) ).
thf(2583,plain,
! [SV626: $i,SV307: $i,SV66: $i,SV738: $i] :
( ( ( ~ ( in @ SV738 @ SV66 ) )
= $true )
| ( ( ~ ~ ( in @ SV738 @ ( binunion @ SV307 @ SV626 ) )
| ~ ( in @ SV738 @ SV626 ) )
= $true )
| ( ( in @ SV626 @ ( powerset @ SV66 ) )
= $false )
| ( ( in @ SV307 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2421]) ).
thf(2584,plain,
! [SV69: $i,SV310: $i] :
( ( ( ~ ~ ( ~ ( in @ SV310 @ ( sK46_SY2574 @ SV69 @ SV310 ) )
| ~ ( in @ ( sK46_SY2574 @ SV69 @ SV310 ) @ SV69 ) ) )
= $false )
| ( ( in @ SV310 @ ( setunion @ SV69 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2423]) ).
thf(2585,plain,
! [SV69: $i,SV759: $i,SV310: $i] :
( ( ( ~ ~ ( ~ ( in @ SV310 @ SV759 )
| ~ ( in @ SV759 @ SV69 ) ) )
= $true )
| ( ( in @ SV310 @ ( setunion @ SV69 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2424]) ).
thf(2586,plain,
! [SV627: $i,SV311: $i,SV70: $i,SV739: $i] :
( ( ( ~ ( in @ SV739 @ SV70 ) )
= $true )
| ( ( ~ ( in @ SV739 @ ( setminus @ SV70 @ ( binunion @ SV311 @ SV627 ) ) )
| ~ ( in @ SV739 @ SV311 ) )
= $true )
| ( ( in @ SV627 @ ( powerset @ SV70 ) )
= $false )
| ( ( in @ SV311 @ ( powerset @ SV70 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2425]) ).
thf(2587,plain,
! [SV628: $i,SV314: $i,SV73: $i] :
( ( ( ! [SY3083: $i] :
( ~ ( in @ SY3083 @ SV73 )
| ~ ( in @ SY3083 @ SV314 )
| ( in @ SY3083 @ SV628 ) ) )
= $false )
| ( ( in @ SV314 @ ( powerset @ SV628 ) )
= $true )
| ( ( in @ SV628 @ ( powerset @ SV73 ) )
= $false )
| ( ( in @ SV314 @ ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2426]) ).
thf(2588,plain,
! [SV686: $o,SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV74 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SV686 )
| SV686 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2427]) ).
thf(2589,plain,
! [SV74: $i,SV686: $o,SV315: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV315 )
| SV686 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SV686 )
| SV686 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2427]) ).
thf(2590,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV74 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $true )
| $true )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2428]) ).
thf(2591,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV315 )
| $true )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $true )
| $true )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2428]) ).
thf(2592,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV74 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $false )
| $false )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2429]) ).
thf(2593,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV315 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $false )
| $false )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2429]) ).
thf(2594,plain,
! [SV316: $i,SV76: $i,SV510: $i] :
( ( ( in @ SV510 @ SV76 )
= $false )
| ( ( in @ SV510 @ SV316 )
= $true )
| ( ( subset @ SV76 @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2430]) ).
thf(2595,plain,
! [SV79: $i,SV318: $i > $o] :
( ( ( ~ ( in @ ( sK32_SY2591 @ SV318 @ SV79 ) @ SV79 )
| ~ ( SV318 @ ( sK32_SY2591 @ SV318 @ SV79 ) ) )
= $false )
| ( ( ! [SY2592: $i] :
( ~ ( in @ SY2592 @ SV79 )
| ~ ( SV318 @ SY2592 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2596,plain,
! [SV82: $i,SV630: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_SY2017 @ SV630 @ SV82 ) @ SV82 )
| ~ ~ ~ ! [SY3174: $i] :
~ ~ ( ~ ( in @ SY3174 @ ( sK38_SY2017 @ SV630 @ SV82 ) )
| ~ ( in @ SY3174 @ SV82 ) ) ) )
= $true )
| ( ( in @ SV630 @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2432]) ).
thf(2597,plain,
! [SV607: $o,SV322: $i,SV84: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV84 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| SV607 )
| SV607 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2433]) ).
thf(2598,plain,
! [SV84: $i,SV322: $i,SV513: $i,SV607: $o] :
( ( SV607 = $false )
| ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| SV607 )
| SV607 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2433]) ).
thf(2599,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV84 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| $true )
| $true )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2434]) ).
thf(2600,plain,
! [SV84: $i,SV322: $i,SV513: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| $true )
| $true )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2434]) ).
thf(2601,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV84 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| $false )
| $false )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2435]) ).
thf(2602,plain,
! [SV84: $i,SV322: $i,SV513: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| $false )
| $false )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2435]) ).
thf(2603,plain,
! [SV631: $i,SV323: $i,SV85: $i,SV740: $i] :
( ( ( ~ ( in @ SV740 @ SV85 ) )
= $true )
| ( ( ~ ~ ( in @ SV740 @ ( binunion @ SV323 @ SV631 ) )
| ~ ( in @ SV740 @ SV323 ) )
= $true )
| ( ( in @ SV631 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV323 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2436]) ).
thf(2604,plain,
! [SV687: $i,SV325: $i > $o,SV87: $i] :
( ( ( ! [SY2599: $i] :
~ ~ ( ~ ( in @ SY2599 @ SV87 )
| ~ ~ ( SV325 @ SY2599 ) ) )
= $false )
| ( ( SV325 @ SV687 )
= $true )
| ( ( in @ SV687 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2605,plain,
! [SV88: $i,SV326: $i] :
( ( ( ! [SY2601: $i] :
( ~ ( in @ SY2601 @ SV326 )
| ( in @ SY2601 @ SV88 ) ) )
= $false )
| ( ( SV88 = SV326 )
= $true )
| ( ( in @ ( sK7_SY2600 @ SV326 @ SV88 ) @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2606,plain,
! [SV326: $i,SV88: $i] :
( ( ( ~ ( in @ ( sK47_SY2601 @ SV88 @ SV326 ) @ SV326 )
| ( in @ ( sK47_SY2601 @ SV88 @ SV326 ) @ SV88 ) )
= $false )
| ( ( SV88 = SV326 )
= $true )
| ( ( in @ ( sK7_SY2600 @ SV326 @ SV88 ) @ SV326 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2439]) ).
thf(2607,plain,
! [SV632: $i,SV91: $i > $o] :
( ( ( SV91 @ SV632 )
= $false )
| ( ( ~ ! [SY3087: $i] :
( ~ ( SV91 @ SY3087 )
| ( SV632 = SY3087 ) ) )
= $true )
| ( ( ! [SY2037: $i,SY2038: $i] :
( ~ ( SV91 @ SY2037 )
| ~ ( SV91 @ SY2038 )
| ( SY2037 = SY2038 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2440]) ).
thf(2608,plain,
! [SV515: $i,SV331: $i,SV94: $i] :
( ( ( subset @ SV94 @ SV331 )
= $false )
| ( ( in @ SV515 @ SV331 )
= $true )
| ( ( in @ SV515 @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2442]) ).
thf(2609,plain,
! [SV689: $i,SV516: $i,SV332: $i,SV95: $i] :
( ( ( ~ ! [SY3141: $i] :
( ~ ( in @ SY3141 @ SV95 )
| ! [SY3142: $i] :
( ~ ( in @ SY3142 @ SV332 )
| ~ ( in @ ( kpair @ SY3141 @ SY3142 ) @ SV516 )
| ( in @ ( kpair @ SY3141 @ SY3142 ) @ SV689 ) ) ) )
= $true )
| ( ( subset @ SV516 @ SV689 )
= $true )
| ( ( subset @ SV689 @ ( cartprod @ SV95 @ SV332 ) )
= $false )
| ( ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2443]) ).
thf(2610,plain,
! [SV96: $i,SV333: $i] :
( ( ( ~ ( in @ ( sK19_SY2610 @ SV333 @ SV96 ) @ SV96 ) )
= $false )
| ( ( in @ SV333 @ ( setunion @ SV96 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2444]) ).
thf(2611,plain,
! [SV96: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ ( sK19_SY2610 @ SV333 @ SV96 ) ) )
= $false )
| ( ( in @ SV333 @ ( setunion @ SV96 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2444]) ).
thf(2612,plain,
! [SV334: $i,SV97: $i,SV633: $i] :
( ( ( ~ ( in @ SV633 @ ( setminus @ SV97 @ SV334 ) ) )
= $false )
| ( ( in @ SV633 @ SV334 )
= $true )
| ( ( in @ SV633 @ SV97 )
= $false )
| ( ( in @ SV334 @ ( powerset @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2445]) ).
thf(2613,plain,
! [SV335: $i > $o,SV98: $i,SV517: $i] :
( ( ( ~ ( in @ SV517
@ ( dsetconstr @ SV98
@ ^ [SY2613: $i] : ( SV335 @ SY2613 ) ) ) )
= $true )
| ( ( SV335 @ SV517 )
= $true )
| ( ( in @ SV517 @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2446]) ).
thf(2614,plain,
! [SV98: $i,SV517: $i,SV335: $i > $o] :
( ( ( ~ ( SV335 @ SV517 ) )
= $true )
| ( ( in @ SV517
@ ( dsetconstr @ SV98
@ ^ [SY2614: $i] : ( SV335 @ SY2614 ) ) )
= $true )
| ( ( in @ SV517 @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(2615,plain,
! [SV518: $i,SV337: $i > $o,SV100: $i] :
( ( ( ! [SY2926: $i] :
( ~ ( in @ SY2926 @ SV100 )
| ~ ( SV337 @ SY2926 )
| ( SY2926 = SV518 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV100
@ ^ [SY2618: $i] : ( SV337 @ SY2618 ) ) )
= $true )
| ( ( SV337 @ SV518 )
= $false )
| ( ( in @ SV518 @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2448]) ).
thf(2616,plain,
( ( ~ ( in @ sK39_SY3168 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2449]) ).
thf(2617,plain,
( ( ~ ( in @ sK39_SY3168 @ ( binunion @ sK2_SY2624 @ sK9_SY2932 ) )
| ~ ( ~ ( in @ sK39_SY3168 @ sK2_SY2624 )
| sK33_SY3090 )
| ~ ( ~ ( in @ sK39_SY3168 @ sK9_SY2932 )
| sK33_SY3090 )
| sK33_SY3090 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2449]) ).
thf(2618,plain,
! [SV105: $i,SV342: $i,SV522: $i,SV691: $i > $o] :
( ( ( ~ ( in @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ SV105 )
| ! [SY3189: $i] :
( ~ ( in @ SY3189 @ SV342 )
| ~ ( in @ ( kpair @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ SY3189 ) @ SV522 )
| ( SV691 @ ( kpair @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ SY3189 ) ) ) )
= $false )
| ( ( ! [SY3145: $i] :
( ~ ( in @ SY3145 @ SV522 )
| ( SV691 @ SY3145 ) ) )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2451]) ).
thf(2619,plain,
! [SV635: $i,SV106: $i > $o] :
( ( ( SV106 @ SV635 )
= $false )
| ( ( ~ ! [SY3092: $i] :
( ~ ( SV106 @ SY3092 )
| ( SV635 = SY3092 ) ) )
= $true )
| ( ( ! [SY2086: $i,SY2087: $i] :
( ~ ( SV106 @ SY2086 )
| ~ ( SV106 @ SY2087 )
| ( SY2086 = SY2087 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2452]) ).
thf(2620,plain,
! [SV636: $i,SV108: $i > $o] :
( ( ( SV108 @ SV636 )
= $false )
| ( ( ~ ! [SY3093: $i] :
( ~ ( SV108 @ SY3093 )
| ( SV636 = SY3093 ) ) )
= $true )
| ( ( SV108
@ ( descr
@ ^ [SY2093: $i] : ( SV108 @ SY2093 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2453]) ).
thf(2621,plain,
! [SV113: $i,SV347: $i,SV525: $i] :
( ( ( in @ SV525 @ SV347 )
= $true )
| ( ( ~ ( in @ SV525 @ SV113 ) )
= $true )
| ( ( in @ SV525 @ ( setminus @ SV113 @ SV347 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2454]) ).
thf(2622,plain,
! [SV638: $i,SV114: $i > $o] :
( ( ( SV114 @ SV638 )
= $false )
| ( ( ~ ! [SY3096: $i] :
( ~ ( SV114 @ SY3096 )
| ( SV638 = SY3096 ) ) )
= $true )
| ( ( ~ ! [SY2107: $i] :
~ ( SV114 @ SY2107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2455]) ).
thf(2623,plain,
! [SV639: $i,SV348: $i,SV115: $i,SV741: $i] :
( ( ( ~ ( in @ SV741 @ ( powerset @ SV115 ) ) )
= $true )
| ( ( ! [SY3175: $i] :
( ~ ( in @ SY3175 @ SV115 )
| ~ ( in @ SY3175 @ ( binintersect @ SV348 @ SV639 ) )
| ( in @ SY3175 @ ( binunion @ SV348 @ SV741 ) ) ) )
= $true )
| ( ( in @ SV639 @ ( powerset @ SV115 ) )
= $false )
| ( ( in @ SV348 @ ( powerset @ SV115 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2456]) ).
thf(2624,plain,
! [SV350: $i > $o,SV118: $i] :
( ( ( ! [SY2650: $i] :
~ ~ ( ~ ( in @ SY2650 @ SV118 )
| ~ ( SV350 @ SY2650 ) ) )
= $true )
| ( ( in @ ( sK10_SY2649 @ SV350 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2457]) ).
thf(2625,plain,
! [SV350: $i > $o,SV118: $i] :
( ( ( ! [SY2650: $i] :
~ ~ ( ~ ( in @ SY2650 @ SV118 )
| ~ ( SV350 @ SY2650 ) ) )
= $true )
| ( ( SV350 @ ( sK10_SY2649 @ SV350 @ SV118 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2458]) ).
thf(2626,plain,
! [SV692: $i,SV351: $i > $o,SV119: $i] :
( ( ( ! [SY2652: $i] :
~ ~ ( ~ ( in @ SY2652 @ SV119 )
| ~ ~ ( SV351 @ SY2652 ) ) )
= $false )
| ( ( SV351 @ SV692 )
= $true )
| ( ( in @ SV692 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(2627,plain,
! [SV352: $i,SV641: $i,SV120: $i,SV742: $i] :
( ( ( ~ ( in @ SV742 @ SV120 ) )
= $true )
| ( ( ~ ~ ( in @ SV742 @ SV641 )
| ~ ( in @ SV742 @ ( binintersect @ SV352 @ SV641 ) ) )
= $true )
| ( ( in @ SV641 @ ( powerset @ SV120 ) )
= $false )
| ( ( in @ SV352 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2460]) ).
thf(2628,plain,
! [SV642: $i,SV121: $i,SV353: $i] :
( ( ( subset @ SV353 @ ( setminus @ SV121 @ SV642 ) )
= $false )
| ( ( ! [SY3100: $i] :
( ~ ( in @ SY3100 @ SV121 )
| ~ ( in @ SY3100 @ SV642 )
| ( in @ SY3100 @ ( setminus @ SV121 @ SV353 ) ) ) )
= $true )
| ( ( in @ SV642 @ ( powerset @ SV121 ) )
= $false )
| ( ( in @ SV353 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2461]) ).
thf(2629,plain,
! [SV693: $o,SV358: $i,SV126: $i,SV529: $i] :
( ( ( SV529 != SV126 )
= $false )
| ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| SV693 )
| SV693 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2463]) ).
thf(2630,plain,
! [SV126: $i,SV358: $i,SV529: $i,SV693: $o] :
( ( SV693 = $false )
| ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| SV693 )
| SV693 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2463]) ).
thf(2631,plain,
! [SV358: $i,SV126: $i,SV529: $i] :
( ( ( SV529 != SV126 )
= $false )
| ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| $true )
| $true )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2464]) ).
thf(2632,plain,
! [SV126: $i,SV358: $i,SV529: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| $true )
| $true )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2464]) ).
thf(2633,plain,
! [SV358: $i,SV126: $i,SV529: $i] :
( ( ( SV529 != SV126 )
= $false )
| ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| $false )
| $false )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2465]) ).
thf(2634,plain,
! [SV126: $i,SV358: $i,SV529: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| $false )
| $false )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2465]) ).
thf(2635,plain,
! [SV127: $i,SV359: $i,SV530: $i] :
( ( ( in @ SV530 @ SV359 )
= $true )
| ( ( ~ ( in @ SV530 @ ( symdiff @ SV127 @ SV359 ) ) )
= $true )
| ( ( in @ SV530 @ SV127 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2466]) ).
thf(2636,plain,
! [SV643: $i,SV129: $i,SV361: $i] :
( ( ( subset @ SV361 @ ( setminus @ SV129 @ SV643 ) )
= $false )
| ( ( subset @ SV643 @ ( setminus @ SV129 @ SV361 ) )
= $true )
| ( ( in @ SV643 @ ( powerset @ SV129 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2468]) ).
thf(2637,plain,
! [SV644: $i,SV362: $i,SV130: $i,SV743: $i] :
( ( ( ~ ( in @ SV743 @ SV130 ) )
= $true )
| ( ( ~ ~ ( in @ SV743 @ SV362 )
| ~ ( in @ SV743 @ ( binintersect @ SV362 @ SV644 ) ) )
= $true )
| ( ( in @ SV644 @ ( powerset @ SV130 ) )
= $false )
| ( ( in @ SV362 @ ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2469]) ).
thf(2638,plain,
! [SV645: $i,SV363: $i,SV131: $i,SV744: $i] :
( ( ( ~ ( in @ SV744 @ SV131 ) )
= $true )
| ( ( ~ ( in @ SV744 @ ( setminus @ SV131 @ SV363 ) )
| ( in @ SV744 @ ( setminus @ SV131 @ ( binintersect @ SV363 @ SV645 ) ) ) )
= $true )
| ( ( in @ SV645 @ ( powerset @ SV131 ) )
= $false )
| ( ( in @ SV363 @ ( powerset @ SV131 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2470]) ).
thf(2639,plain,
! [SV133: $i,SV365: $i,SV646: $i] :
( ( ( in @ SV646 @ SV365 )
= $false )
| ( ( in @ SV646 @ ( setminus @ SV133 @ ( setminus @ SV133 @ SV365 ) ) )
= $true )
| ( ( in @ SV646 @ SV133 )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV133 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2471]) ).
thf(2640,plain,
! [SV647: $i,SV367: $i > $o,SV135: $i,SV745: $i] :
( ( ( ~ ( in @ SV745 @ SV135 ) )
= $true )
| ( ( ~ ( SV367 @ SV647 )
| ~ ( SV367 @ SV745 )
| ( SV647 = SV745 ) )
= $true )
| ( ( in @ SV647 @ SV135 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV135
@ ^ [SY2676: $i] : ( SV367 @ SY2676 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2472]) ).
thf(2641,plain,
! [SV136: $i,SV648: $o,SV368: $i] :
( ( ( ~ ( in @ SV368 @ ( sK40_SY3104 @ SV648 @ SV136 @ SV368 ) ) )
= $false )
| ( SV648 = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2473]) ).
thf(2642,plain,
! [SV368: $i,SV136: $i,SV648: $o] :
( ( ( ~ ( in @ ( sK40_SY3104 @ SV648 @ SV136 @ SV368 ) @ SV136 )
| SV648 )
= $false )
| ( SV648 = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2473]) ).
thf(2643,plain,
! [SV136: $i,SV368: $i] :
( ( ( ~ ( in @ SV368 @ ( sK41_SX0 @ SV136 @ SV368 ) ) )
= $false )
| ( $true = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2474]) ).
thf(2644,plain,
! [SV368: $i,SV136: $i] :
( ( ( ~ ( in @ ( sK41_SX0 @ SV136 @ SV368 ) @ SV136 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2474]) ).
thf(2645,plain,
! [SV136: $i,SV368: $i] :
( ( ( ~ ( in @ SV368 @ ( sK42_SX0 @ SV136 @ SV368 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2475]) ).
thf(2646,plain,
! [SV368: $i,SV136: $i] :
( ( ( ~ ( in @ ( sK42_SX0 @ SV136 @ SV368 ) @ SV136 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2475]) ).
thf(2647,plain,
! [SV649: $i,SV369: $i,SV137: $i,SV746: $i] :
( ( ( ~ ( in @ SV746 @ SV137 ) )
= $true )
| ( ( ~ ( subset @ SV369 @ SV649 )
| ~ ~ ( in @ SV746 @ SV649 )
| ~ ( in @ SV746 @ SV369 ) )
= $true )
| ( ( in @ SV649 @ ( powerset @ SV137 ) )
= $false )
| ( ( in @ SV369 @ ( powerset @ SV137 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2476]) ).
thf(2648,plain,
! [SV650: $i,SV377: $i,SV146: $i] :
( ( ( ! [SY3106: $i] :
( ~ ( in @ SY3106 @ SV146 )
| ~ ( in @ SY3106 @ SV377 )
| ( in @ SY3106 @ SV650 ) ) )
= $false )
| ( ( subset @ SV377 @ SV650 )
= $true )
| ( ( in @ SV650 @ ( powerset @ SV146 ) )
= $false )
| ( ( in @ SV377 @ ( powerset @ SV146 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2478]) ).
thf(2649,plain,
! [SV147: $i] :
( ( ~ ~ ( ~ ! [SY2953: $i] :
( ~ ( in @ SY2953 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY2188: $i] :
( ~ ( in @ SY2188 @ SY2953 )
| ( in @ SY2188 @ SV147 ) ) )
| ~ ! [SY2955: $i,SY2956: $i] :
( ~ ~ ( ~ ( in @ SY2955 @ SV147 )
| ~ ( in @ SY2956 @ SV147 ) )
| ~ ! [SY2957: $i] :
( ~ ( in @ SY2957 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SY2955 @ SY2957 )
| ( in @ SY2956 @ SY2957 ) )
| ~ ( ~ ( in @ SY2956 @ SY2957 )
| ( in @ SY2955 @ SY2957 ) ) ) )
| ( SY2955 = SY2956 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2479]) ).
thf(2650,plain,
! [SV147: $i] :
( ( ~ ! [SY2958: $i,SY2959: $i] :
( ~ ~ ( ~ ( in @ SY2958 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY2959 @ ( sK3_SY2186 @ SV147 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2958 )
| ( in @ SX4 @ SY2959 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2959 )
| ( in @ SX4 @ SY2958 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2479]) ).
thf(2651,plain,
! [SV147: $i,SV747: $i] :
( ( ( ~ ~ ( ~ ! [SY3176: $i] :
( ~ ( in @ SY3176 @ SV747 )
| ( in @ SY3176 @ SV147 ) )
| ~ ~ ! [SY3177: $i] :
~ ( in @ SY3177 @ SV747 ) ) )
= $true )
| ( ( ~ ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2480]) ).
thf(2652,plain,
! [SV651: $i,SV381: $i,SV151: $i,SV748: $i] :
( ( ( ~ ( in @ SV748 @ ( powerset @ SV151 ) ) )
= $true )
| ( ( ! [SY3183: $i] :
( ~ ( in @ SY3183 @ SV151 )
| ~ ( in @ SY3183 @ ( binintersect @ SV381 @ SV651 ) )
| ( in @ SY3183 @ ( binunion @ SV651 @ SV748 ) ) ) )
= $true )
| ( ( in @ SV651 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV381 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2481]) ).
thf(2653,plain,
! [SV652: $i,SV386: $i,SV156: $i,SV749: $i] :
( ( ( ~ ( in @ SV749 @ SV156 ) )
= $true )
| ( ( ~ ( subset @ SV386 @ ( setminus @ SV156 @ SV652 ) )
| ~ ( in @ SV749 @ SV652 )
| ~ ( in @ SV749 @ SV386 ) )
= $true )
| ( ( in @ SV652 @ ( powerset @ SV156 ) )
= $false )
| ( ( in @ SV386 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2482]) ).
thf(2654,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ! [SY3190: $i] :
( ~ ( SV160 @ ( sK49_SY2231 @ SV653 @ SV160 ) )
| ~ ( SV160 @ SY3190 )
| ( ( sK49_SY2231 @ SV653 @ SV160 )
= SY3190 ) ) )
= $false )
| ( ( ~ ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2484]) ).
thf(2655,plain,
! [SV393: $i,SV696: $i,SV165: $i,SV656: $i] :
( ( ( ~ ( in @ SV656 @ SV165 ) )
= $true )
| ( ( in @ SV696 @ SV393 )
= $true )
| ( ( SV656 = SV696 )
= $false )
| ( ( SV165 = SV393 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2486]) ).
thf(2656,plain,
! [SV547: $i,SV394: $i,SV166: $i] :
( ( ( SV166 = SV394 )
= $false )
| ( ( in @ SV547 @ SV394 )
= $true )
| ( ( in @ SV547 @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2487]) ).
thf(2657,plain,
! [SV657: $i,SV395: $i,SV167: $i,SV750: $i] :
( ( ( ~ ( in @ SV750 @ SV167 ) )
= $true )
| ( ( ~ ( in @ SV750 @ ( setminus @ SV167 @ ( binunion @ SV395 @ SV657 ) ) )
| ( in @ SV750 @ ( setminus @ SV167 @ SV395 ) ) )
= $true )
| ( ( in @ SV657 @ ( powerset @ SV167 ) )
= $false )
| ( ( in @ SV395 @ ( powerset @ SV167 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2488]) ).
thf(2658,plain,
! [SV697: $i,SV548: $i,SV396: $i,SV168: $i] :
( ( ( ~ ! [SY3146: $i] :
( ~ ( in @ SY3146 @ SV168 )
| ( ( ap @ SV168 @ SV396 @ SV548 @ SY3146 )
= ( ap @ SV168 @ SV396 @ SV697 @ SY3146 ) ) ) )
= $true )
| ( ( SV548 = SV697 )
= $true )
| ( ( func @ SV168 @ SV396 @ SV697 )
= $false )
| ( ( func @ SV168 @ SV396 @ SV548 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2489]) ).
thf(2659,plain,
! [SV701: $i,SV553: $i,SV171: $i,SV399: $o] :
( ( ( ~ ~ SV399 )
= $true )
| ( ( ( dsetconstr @ SV171
@ ^ [SY3147: $i] :
( ~ ( ~ SV399
| ( SY3147 != SV553 ) )
| ~ ( ~ ~ SV399
| ( SY3147 != SV701 ) ) ) )
= ( setadjoin @ SV701 @ emptyset ) )
= $true )
| ( ( in @ SV701 @ SV171 )
= $false )
| ( ( in @ SV553 @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2494]) ).
thf(2660,plain,
! [SV702: $i,SV554: $i,SV171: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( ( dsetconstr @ SV171
@ ^ [SY3148: $i] :
( ~ ( ~ $true
| ( SY3148 != SV554 ) )
| ~ ( ~ ~ $true
| ( SY3148 != SV702 ) ) ) )
= ( setadjoin @ SV702 @ emptyset ) )
= $true )
| ( ( in @ SV702 @ SV171 )
= $false )
| ( ( in @ SV554 @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2495]) ).
thf(2661,plain,
! [SV703: $i,SV555: $i,SV171: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( ( dsetconstr @ SV171
@ ^ [SY3149: $i] :
( ~ ( ~ $false
| ( SY3149 != SV555 ) )
| ~ ( ~ ~ $false
| ( SY3149 != SV703 ) ) ) )
= ( setadjoin @ SV703 @ emptyset ) )
= $true )
| ( ( in @ SV703 @ SV171 )
= $false )
| ( ( in @ SV555 @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2496]) ).
thf(2662,plain,
! [SV172: $i,SV400: $i,SV751: $i] :
( ( ( ~ ( in @ SV751 @ SV400 ) )
= $true )
| ( ( in @ SV751 @ SV172 )
= $true )
| ( ( in @ SV400 @ ( powerset @ SV172 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2497]) ).
thf(2663,plain,
! [SV400: $i,SV172: $i] :
( ( ( ~ ( in @ ( sK43_SY2728 @ SV172 @ SV400 ) @ SV400 ) )
= $false )
| ( ( in @ SV400 @ ( powerset @ SV172 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2498]) ).
thf(2664,plain,
! [SV400: $i,SV172: $i] :
( ( ( in @ ( sK43_SY2728 @ SV172 @ SV400 ) @ SV172 )
= $false )
| ( ( in @ SV400 @ ( powerset @ SV172 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2498]) ).
thf(2665,plain,
! [SV176: $i,SV658: $i,SV404: $i] :
( ( ( subset @ SV404 @ SV658 )
= $false )
| ( ( subset @ ( setminus @ SV176 @ SV658 ) @ ( setminus @ SV176 @ SV404 ) )
= $true )
| ( ( in @ SV658 @ ( powerset @ SV176 ) )
= $false )
| ( ( in @ SV404 @ ( powerset @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2666,plain,
! [SV408: $i > $o,SV180: $i,SV706: $i] :
( ( ( ~ ( in @ SV706 @ SV180 ) )
= $true )
| ( ( ~ ( SV408 @ SV706 ) )
= $true )
| ( ( ( ( dsetconstr @ SV180
@ ^ [SY2739: $i] : ( SV408 @ SY2739 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2502]) ).
thf(2667,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ( ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( in @ ( sK12_SY2740 @ SV409 @ SV181 ) @ SV181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2503]) ).
thf(2668,plain,
! [SV181: $i,SV409: $i > $o] :
( ( ( in @ ( sK34_SY3112 @ SV409 @ SV181 ) @ SV181 )
= $true )
| ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) )
| ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2504]) ).
thf(2669,plain,
! [SV181: $i,SV409: $i > $o] :
( ( ( ~ ( SV409 @ ( sK12_SY2740 @ SV409 @ SV181 ) ) )
= $false )
| ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) )
| ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2505]) ).
thf(2670,plain,
! [SV181: $i,SV409: $i > $o] :
( ( ( ~ ( SV409 @ ( sK34_SY3112 @ SV409 @ SV181 ) )
| ( ( sK12_SY2740 @ SV409 @ SV181 )
= ( sK34_SY3112 @ SV409 @ SV181 ) ) )
= $false )
| ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) )
| ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2505]) ).
thf(2671,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2506]) ).
thf(2672,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ( ~ ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
| ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
| ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2507]) ).
thf(2673,plain,
! [SV185: $i,SV561: $i,SV707: $i,SV413: $i,SV760: $i] :
( ( ( ~ ( in @ SV760 @ SV413 )
| ~ ( in @ ( kpair @ SV707 @ SV760 ) @ SV561 )
| ( ( ap @ SV185 @ SV413 @ SV561 @ SV707 )
= SV760 ) )
= $true )
| ( ( in @ SV707 @ SV185 )
= $false )
| ( ( in @ SV561 @ ( funcSet @ SV185 @ SV413 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2508]) ).
thf(2674,plain,
! [SV659: $i,SV414: $i,SV186: $i] :
( ( ( ! [SY3114: $i] :
( ~ ( in @ SY3114 @ SV186 )
| ~ ( in @ SY3114 @ SV414 )
| ( in @ SY3114 @ SV659 ) ) )
= $false )
| ( ( ~ ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV186 )
| ~ ( in @ SY3115 @ SV659 )
| ( in @ SY3115 @ SV414 ) )
| ( SV414 = SV659 ) )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2509]) ).
thf(2675,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( SV188 @ SV660 )
= $false )
| ( ( ~ ! [SY3116: $i] :
( ~ ( SV188 @ SY3116 )
| ( SV660 = SY3116 ) ) )
= $true )
| ( ( ~ ! [SY2316: $i] :
~ ~ ( ~ ( SV188 @ SY2316 )
| ~ ! [SY2317: $i] :
( ~ ( SV188 @ SY2317 )
| ( SY2316 = SY2317 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2511]) ).
thf(2676,plain,
! [SV661: $i,SV418: $i,SV191: $i,SV752: $i] :
( ( ( ~ ( in @ SV752 @ ( powerset @ SV191 ) ) )
= $true )
| ( ( ! [SY3184: $i] :
( ~ ( in @ SY3184 @ SV191 )
| ~ ( in @ SY3184 @ ( binintersect @ SV418 @ SV661 ) )
| ( in @ SY3184 @ ( binintersect @ ( binunion @ SV418 @ SV752 ) @ ( binunion @ SV661 @ SV752 ) ) ) ) )
= $true )
| ( ( in @ SV661 @ ( powerset @ SV191 ) )
= $false )
| ( ( in @ SV418 @ ( powerset @ SV191 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2513]) ).
thf(2677,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(2678,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
| ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
| ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2515]) ).
thf(2679,plain,
! [SV196: $i,SV424: $i,SV566: $i] :
( ( ( ~ ( in @ ( sK35_SY2993 @ SV566 @ SV424 @ SV196 ) @ SV196 )
| ~ ~ ! [SY3169: $i] :
~ ~ ( ~ ( in @ SY3169 @ SV424 )
| ( SV566
!= ( kpair @ ( sK35_SY2993 @ SV566 @ SV424 @ SV196 ) @ SY3169 ) ) ) )
= $false )
| ( ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2517]) ).
thf(2680,plain,
! [SV709: $i,SV567: $i,SV197: $i,SV425: $o] :
( ( ( ~ SV425 ) = $true )
| ( ( ( if @ SV197 @ SV425 @ SV567 @ SV709 )
= SV567 )
= $true )
| ( ( in @ SV709 @ SV197 )
= $false )
| ( ( in @ SV567 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2518]) ).
thf(2681,plain,
! [SV710: $i,SV568: $i,SV197: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( if @ SV197 @ $true @ SV568 @ SV710 )
= SV568 )
= $true )
| ( ( in @ SV710 @ SV197 )
= $false )
| ( ( in @ SV568 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2519]) ).
thf(2682,plain,
! [SV711: $i,SV569: $i,SV197: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( if @ SV197 @ $false @ SV569 @ SV711 )
= SV569 )
= $true )
| ( ( in @ SV711 @ SV197 )
= $false )
| ( ( in @ SV569 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2520]) ).
thf(2683,plain,
! [SV712: $i,SV570: $i,SV426: $i,SV198: $i] :
( ( ( ~ ! [SY3151: $i] :
( ~ ( in @ SY3151 @ SV198 )
| ! [SY3152: $i] :
( ~ ( in @ SY3152 @ SV426 )
| ~ ( in @ ( kpair @ SY3151 @ SY3152 ) @ SV570 )
| ( in @ ( kpair @ SY3151 @ SY3152 ) @ SV712 ) ) ) )
= $true )
| ( ( ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) )
| ( SV570 = SV712 ) )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2521]) ).
thf(2684,plain,
! [SV200: $i,SV428: $i,SV571: $i,SV713: $i > $o] :
( ( ( ~ ( in @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ SV200 )
| ! [SY3191: $i] :
( ~ ( in @ SY3191 @ SV428 )
| ~ ( in @ ( kpair @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ SY3191 ) @ SV571 )
| ( SV713 @ ( kpair @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ SY3191 ) ) ) )
= $false )
| ( ( ! [SY3157: $i] :
( ~ ( in @ SY3157 @ SV571 )
| ( SV713 @ SY3157 ) ) )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2522]) ).
thf(2685,plain,
! [SV429: $i > $o,SV201: $i,SV714: $i] :
( ( ( ~ ( in @ SV714 @ SV201 ) )
= $true )
| ( ( ~ ~ ( SV429 @ SV714 ) )
= $true )
| ( ( ~ ! [SY2794: $i] :
( ~ ( in @ SY2794 @ SV201 )
| ( SV429 @ SY2794 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2523]) ).
thf(2686,plain,
! [SV574: $i > $i,SV433: $i,SV209: $i,SV761: $i] :
( ( ( ~ ( in @ SV761 @ SV209 )
| ( ( ap @ SV209 @ SV433
@ ( lam @ SV209 @ SV433
@ ^ [SY3012: $i] : ( SV574 @ SY3012 ) )
@ SV761 )
= ( SV574 @ SV761 ) ) )
= $true )
| ( ( in @ ( sK25_SY3010 @ SV433 @ SV574 @ SV209 ) @ SV209 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2526]) ).
thf(2687,plain,
! [SV574: $i > $i,SV433: $i,SV209: $i,SV753: $i] :
( ( ( ~ ( in @ SV753 @ SV209 ) )
= $true )
| ( ( ( ap @ SV209 @ SV433
@ ( lam @ SV209 @ SV433
@ ^ [SY3012: $i] : ( SV574 @ SY3012 ) )
@ SV753 )
= ( SV574 @ SV753 ) )
= $true )
| ( ( in @ ( SV574 @ ( sK25_SY3010 @ SV433 @ SV574 @ SV209 ) ) @ SV433 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2527]) ).
thf(2688,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ( ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( in @ ( sK15_SY2806 @ SV436 @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2529]) ).
thf(2689,plain,
! [SV212: $i,SV436: $i > $o] :
( ( ( in @ ( sK36_SY3121 @ SV436 @ SV212 ) @ SV212 )
= $true )
| ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) )
| ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2530]) ).
thf(2690,plain,
! [SV212: $i,SV436: $i > $o] :
( ( ( ~ ( SV436 @ ( sK15_SY2806 @ SV436 @ SV212 ) ) )
= $false )
| ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) )
| ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2531]) ).
thf(2691,plain,
! [SV212: $i,SV436: $i > $o] :
( ( ( ~ ( SV436 @ ( sK36_SY3121 @ SV436 @ SV212 ) )
| ( ( sK15_SY2806 @ SV436 @ SV212 )
= ( sK36_SY3121 @ SV436 @ SV212 ) ) )
= $false )
| ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) )
| ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2531]) ).
thf(2692,plain,
! [SV215: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK44_SY2395 @ SV215 ) @ omega )
| ~ ( in @ ( sK44_SY2395 @ SV215 ) @ SV215 ) ) )
= $false )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( ! [SY2396: $i] :
( ~ ( in @ SY2396 @ omega )
| ( in @ SY2396 @ SV215 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2533]) ).
thf(2693,plain,
! [SV215: $i] :
( ( ( in @ ( setadjoin @ ( sK44_SY2395 @ SV215 ) @ ( sK44_SY2395 @ SV215 ) ) @ SV215 )
= $false )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( ! [SY2396: $i] :
( ~ ( in @ SY2396 @ omega )
| ( in @ SY2396 @ SV215 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2533]) ).
thf(2694,plain,
! [SV217: $i,SV616: $i,SV577: $i > $i > $o,SV440: $i,SV735: $i] :
( ( ( in @ SV735 @ SV440 )
= $false )
| ( ( ~ ( SV577 @ SV616 @ SV735 )
| ( in @ ( kpair @ SV616 @ SV735 )
@ ( dpsetconstr @ SV217 @ SV440
@ ^ [SY3017: $i,SY3018: $i] : ( SV577 @ SY3017 @ SY3018 ) ) ) )
= $true )
| ( ( in @ SV616 @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2535]) ).
thf(2695,plain,
! [SV720: $i,SV581: $i,SV442: $i,SV219: $i] :
( ( ( ~ ! [SY3158: $i] :
( ~ ( in @ SY3158 @ SV219 )
| ( ( ap @ SV219 @ SV442 @ SV581 @ SY3158 )
= ( ap @ SV219 @ SV442 @ SV720 @ SY3158 ) ) ) )
= $true )
| ( ( SV581 = SV720 )
= $true )
| ( ( in @ SV720 @ ( funcSet @ SV219 @ SV442 ) )
= $false )
| ( ( in @ SV581 @ ( funcSet @ SV219 @ SV442 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2539]) ).
thf(2696,plain,
! [SV582: $i > $i > $o,SV220: $i,SV617: $i,SV443: $i,SV736: $i] :
( ( ( in @ SV736 @ SV443 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV617 @ SV736 )
@ ( dpsetconstr @ SV220 @ SV443
@ ^ [SY3026: $i,SY3027: $i] : ( SV582 @ SY3026 @ SY3027 ) ) )
| ( SV582 @ SV617 @ SV736 ) )
= $true )
| ( ( in @ SV617 @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2540]) ).
thf(2697,plain,
! [SV223: $i,SV446: $i > $o] :
( ( ( ~ ( in @ ( sK26_SY2833 @ SV446 @ SV223 ) @ SV223 ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY2832: $i] : ( SV446 @ SY2832 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2542]) ).
thf(2698,plain,
! [SV223: $i,SV446: $i > $o] :
( ( ( ~ ( SV446 @ ( sK26_SY2833 @ SV446 @ SV223 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY2832: $i] : ( SV446 @ SY2832 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2542]) ).
thf(2699,plain,
! [SV225: $i,SV448: $i] :
( ( ( ~ ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 )
| ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 ) ) )
= $true )
| ( ( SV225 = SV448 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2543]) ).
thf(2700,plain,
! [SV225: $i,SV448: $i] :
( ( ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 )
| ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 ) ) )
= $true )
| ( ( SV225 = SV448 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2543]) ).
thf(2701,plain,
! [SV450: $i,SV227: $i,SV664: $i] :
( ( ( in @ SV664 @ ( setminus @ SV227 @ ( setminus @ SV227 @ SV450 ) ) )
= $false )
| ( ( in @ SV664 @ SV450 )
= $true )
| ( ( in @ SV664 @ SV227 )
= $false )
| ( ( in @ SV450 @ ( powerset @ SV227 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2545]) ).
thf(2702,plain,
! [SV665: $i,SV452: $i,SV229: $i,SV754: $i] :
( ( ( ~ ( in @ SV754 @ ( powerset @ SV229 ) ) )
= $true )
| ( ( in @ ( binintersect @ SV452 @ SV665 ) @ ( powerset @ ( binintersect @ ( binunion @ SV452 @ SV754 ) @ ( binunion @ SV665 @ SV754 ) ) ) )
= $true )
| ( ( in @ SV665 @ ( powerset @ SV229 ) )
= $false )
| ( ( in @ SV452 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2546]) ).
thf(2703,plain,
! [SV230: $i] :
( ( ( ~ ( in @ ( sK27_SY2440 @ SV230 ) @ SV230 ) )
= $false )
| ( ( SV230 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2547]) ).
thf(2704,plain,
! [SV230: $i] :
( ( ( ~ $true ) = $false )
| ( ( SV230 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2547]) ).
thf(2705,plain,
! [SV722: $i,SV587: $i,SV231: $i,SV453: $o] :
( ( ( ~ SV453 ) = $true )
| ( ( ( dsetconstr @ SV231
@ ^ [SY3159: $i] :
( ~ ( ~ SV453
| ( SY3159 != SV587 ) )
| ~ ( ~ ~ SV453
| ( SY3159 != SV722 ) ) ) )
= ( setadjoin @ SV587 @ emptyset ) )
= $true )
| ( ( in @ SV722 @ SV231 )
= $false )
| ( ( in @ SV587 @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2548]) ).
thf(2706,plain,
! [SV723: $i,SV588: $i,SV231: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( dsetconstr @ SV231
@ ^ [SY3160: $i] :
( ~ ( ~ $true
| ( SY3160 != SV588 ) )
| ~ ( ~ ~ $true
| ( SY3160 != SV723 ) ) ) )
= ( setadjoin @ SV588 @ emptyset ) )
= $true )
| ( ( in @ SV723 @ SV231 )
= $false )
| ( ( in @ SV588 @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2549]) ).
thf(2707,plain,
! [SV724: $i,SV589: $i,SV231: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( dsetconstr @ SV231
@ ^ [SY3161: $i] :
( ~ ( ~ $false
| ( SY3161 != SV589 ) )
| ~ ( ~ ~ $false
| ( SY3161 != SV724 ) ) ) )
= ( setadjoin @ SV589 @ emptyset ) )
= $true )
| ( ( in @ SV724 @ SV231 )
= $false )
| ( ( in @ SV589 @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(2708,plain,
! [SV233: $i,SV455: $i,SV666: $i] :
( ( ( in @ SV666 @ SV455 )
= $false )
| ( ( ~ ( in @ SV666 @ ( setminus @ SV233 @ SV455 ) ) )
= $true )
| ( ( in @ SV666 @ SV233 )
= $false )
| ( ( in @ SV455 @ ( powerset @ SV233 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2551]) ).
thf(2709,plain,
! [SV591: $i > $i,SV456: $i,SV234: $i,SV762: $i] :
( ( ( ~ ( in @ SV762 @ SV234 )
| ( ( ap @ SV234 @ SV456
@ ( lam @ SV234 @ SV456
@ ^ [SY3038: $i] : ( SV591 @ SY3038 ) )
@ SV762 )
= ( SV591 @ SV762 ) ) )
= $true )
| ( ( in @ ( sK28_SY3036 @ SV456 @ SV591 @ SV234 ) @ SV234 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2552]) ).
thf(2710,plain,
! [SV591: $i > $i,SV456: $i,SV234: $i,SV755: $i] :
( ( ( ~ ( in @ SV755 @ SV234 ) )
= $true )
| ( ( ( ap @ SV234 @ SV456
@ ( lam @ SV234 @ SV456
@ ^ [SY3038: $i] : ( SV591 @ SY3038 ) )
@ SV755 )
= ( SV591 @ SV755 ) )
= $true )
| ( ( in @ ( SV591 @ ( sK28_SY3036 @ SV456 @ SV591 @ SV234 ) ) @ SV456 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2553]) ).
thf(2711,plain,
! [SV235: $i,SV457: $i] :
( ( ( ~ ( in @ ( sK37_SY2850 @ SV457 @ SV235 ) @ SV235 )
| ~ ( in @ ( sK37_SY2850 @ SV457 @ SV235 ) @ SV457 ) )
= $false )
| ( ( ( binintersect @ SV235 @ SV457 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2554]) ).
thf(2712,plain,
! [SV667: $i,SV465: $i,SV243: $i,SV756: $i] :
( ( ( ~ ( in @ SV756 @ SV243 ) )
= $true )
| ( ( ~ ( in @ SV465 @ ( powerset @ SV667 ) )
| ~ ( in @ SV756 @ SV465 )
| ( in @ SV756 @ SV667 ) )
= $true )
| ( ( in @ SV667 @ ( powerset @ SV243 ) )
= $false )
| ( ( in @ SV465 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2556]) ).
thf(2713,plain,
! [SV597: $i,SV244: $i,SV725: $i,SV466: $o] :
( ( ( ~ ~ SV466 )
= $true )
| ( ( in @ SV725
@ ( dsetconstr @ SV244
@ ^ [SY3162: $i] :
( ~ ( ~ SV466
| ( SY3162 != SV597 ) )
| ~ ( ~ ~ SV466
| ( SY3162 != SV725 ) ) ) ) )
= $true )
| ( ( in @ SV725 @ SV244 )
= $false )
| ( ( in @ SV597 @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2557]) ).
thf(2714,plain,
! [SV598: $i,SV244: $i,SV726: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( in @ SV726
@ ( dsetconstr @ SV244
@ ^ [SY3163: $i] :
( ~ ( ~ $true
| ( SY3163 != SV598 ) )
| ~ ( ~ ~ $true
| ( SY3163 != SV726 ) ) ) ) )
= $true )
| ( ( in @ SV726 @ SV244 )
= $false )
| ( ( in @ SV598 @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2558]) ).
thf(2715,plain,
! [SV599: $i,SV244: $i,SV727: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( in @ SV727
@ ( dsetconstr @ SV244
@ ^ [SY3164: $i] :
( ~ ( ~ $false
| ( SY3164 != SV599 ) )
| ~ ( ~ ~ $false
| ( SY3164 != SV727 ) ) ) ) )
= $true )
| ( ( in @ SV727 @ SV244 )
= $false )
| ( ( in @ SV599 @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2559]) ).
thf(2716,plain,
! [SV728: $i,SV600: $i,SV469: $i,SV247: $i] :
( ( ( ~ ! [SY3165: $i] :
( ~ ( in @ SY3165 @ SV247 )
| ( ( ap @ SV247 @ SV469 @ SV600 @ SY3165 )
= ( ap @ SV247 @ SV469 @ SV728 @ SY3165 ) ) ) )
= $true )
| ( ( ! [SY3166: $i] :
( ~ ( in @ SY3166 @ SV247 )
| ! [SY3167: $i] :
( ~ ( in @ SY3167 @ SV469 )
| ~ ( in @ ( kpair @ SY3166 @ SY3167 ) @ SV728 )
| ( in @ ( kpair @ SY3166 @ SY3167 ) @ SV600 ) ) ) )
= $true )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2560]) ).
thf(2717,plain,
! [SV471: $i,SV249: $i > $i > $o] :
( ( ( ~ ! [SY3194: $i] :
~ ( ~ ( ~ ( in @ SY3194 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY3194 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY3194 ) )
| ( in @ SY3194 @ ( sK51_SY2874 @ SV249 @ SV471 ) ) ) ) )
= $false )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2561]) ).
thf(2718,plain,
! [SV757: $i,SV471: $i,SV249: $i > $i > $o] :
( ( ( ~ ( ~ ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
| ~ ! [SY3187: $i] :
( ~ ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SY3187 )
| ( SV757 = SY3187 ) ) ) )
= $false )
| ( ( ~ ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2562]) ).
thf(2719,plain,
! [SV729: $i,SV601: $i,SV252: $i,SV474: $o] :
( ( ( ~ ~ SV474 )
= $true )
| ( ( ( if @ SV252 @ SV474 @ SV601 @ SV729 )
= SV729 )
= $true )
| ( ( in @ SV729 @ SV252 )
= $false )
| ( ( in @ SV601 @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2563]) ).
thf(2720,plain,
! [SV730: $i,SV602: $i,SV252: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( ( if @ SV252 @ $true @ SV602 @ SV730 )
= SV730 )
= $true )
| ( ( in @ SV730 @ SV252 )
= $false )
| ( ( in @ SV602 @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2564]) ).
thf(2721,plain,
! [SV731: $i,SV603: $i,SV252: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( ( if @ SV252 @ $false @ SV603 @ SV731 )
= SV731 )
= $true )
| ( ( in @ SV731 @ SV252 )
= $false )
| ( ( in @ SV603 @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2565]) ).
thf(2722,plain,
! [SV476: $i,SV733: $i,SV254: $i,SV669: $i] :
( ( ( ~ ( ~ ( in @ SV669 @ SV254 )
| ( in @ SV733 @ SV476 ) )
| ~ ( ~ ( in @ SV733 @ SV476 )
| ( in @ SV669 @ SV254 ) ) )
= $false )
| ( ( SV669 = SV733 )
= $false )
| ( ( SV254 = SV476 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2567]) ).
thf(2723,plain,
! [SV670: $i,SV256: $i > $o] :
( ( ( SV256 @ SV670 )
= $false )
| ( ( ~ ! [SY3127: $i] :
( ~ ( SV256 @ SY3127 )
| ( SV670 = SY3127 ) ) )
= $true )
| ( ( ~ ! [SY2511: $i] :
~ ! [SY2512: $i] :
~ ( ~ ( ~ ( SV256 @ SY2512 )
| ( SY2512 = SY2511 ) )
| ~ ( ( SY2512 != SY2511 )
| ( SV256 @ SY2512 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2568]) ).
thf(2724,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ! [SY3073: $i] :
( ~ ( SV35 @ SY3073 )
| ( SV621 = SY3073 ) ) )
= $false )
| ( ( SV35 @ SV621 )
= $false )
| ( ( ~ ! [SY1902: $i] :
~ ~ ( ~ ( SV35 @ SY1902 )
| ~ ! [SY1903: $i] :
( ~ ( SV35 @ SY1903 )
| ( SY1902 = SY1903 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2570]) ).
thf(2725,plain,
! [SV38: $i,SV484: $i,SV672: $i,SV284: $i,SV758: $i] :
( ( ( ~ ( in @ SV758 @ SV284 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV672 @ SV758 ) @ SV484 )
| ( ( ap @ SV38 @ SV284 @ SV484 @ SV672 )
= SV758 ) )
= $true )
| ( ( in @ SV672 @ SV38 )
= $false )
| ( ( func @ SV38 @ SV284 @ SV484 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2572]) ).
thf(2726,plain,
! [SV673: $i,SV39: $i,SV485: $i,SV285: $o] :
( ( SV285 = $false )
| ( ( in @ SV485
@ ( dsetconstr @ SV39
@ ^ [SY3129: $i] :
( ~ ( ~ SV285
| ( SY3129 != SV485 ) )
| ~ ( ~ ~ SV285
| ( SY3129 != SV673 ) ) ) ) )
= $true )
| ( ( in @ SV673 @ SV39 )
= $false )
| ( ( in @ SV485 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2573]) ).
thf(2727,plain,
! [SV674: $i,SV39: $i,SV486: $i] :
( ( $true = $false )
| ( ( in @ SV486
@ ( dsetconstr @ SV39
@ ^ [SY3130: $i] :
( ~ ( ~ $true
| ( SY3130 != SV486 ) )
| ~ ( ~ ~ $true
| ( SY3130 != SV674 ) ) ) ) )
= $true )
| ( ( in @ SV674 @ SV39 )
= $false )
| ( ( in @ SV486 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2728,plain,
! [SV675: $i,SV39: $i,SV487: $i] :
( ( $false = $false )
| ( ( in @ SV487
@ ( dsetconstr @ SV39
@ ^ [SY3131: $i] :
( ~ ( ~ $false
| ( SY3131 != SV487 ) )
| ~ ( ~ ~ $false
| ( SY3131 != SV675 ) ) ) ) )
= $true )
| ( ( in @ SV675 @ SV39 )
= $false )
| ( ( in @ SV487 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2729,plain,
! [SV40: $i,SV286: $i,SV623: $i > $o,SV676: $i > $o] :
( ( ( ~ ( in @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) @ SV40 ) )
= $false )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2576]) ).
thf(2730,plain,
! [SV40: $i,SV623: $i > $o,SV676: $i > $o,SV286: $i] :
( ( ( ! [SY3188: $i] :
( ~ ( in @ SY3188 @ SV286 )
| ( ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 )
!= SY3188 )
| ~ ( ~ ( ~ ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) )
| ( SV676 @ SY3188 ) )
| ~ ( ~ ( SV676 @ SY3188 )
| ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2576]) ).
thf(2731,plain,
! [SV41: $i,SV287: $i > $o] :
( ( ( ~ ( in @ ( sK30_SY2541 @ SV287 @ SV41 ) @ SV41 ) )
= $false )
| ( ( ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV41 )
| ~ ( SV287 @ SY2542 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2577]) ).
thf(2732,plain,
! [SV41: $i,SV287: $i > $o] :
( ( ( ~ ( SV287 @ ( sK30_SY2541 @ SV287 @ SV41 ) ) )
= $false )
| ( ( ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV41 )
| ~ ( SV287 @ SY2542 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2577]) ).
thf(2733,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
| ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 ) )
= $false )
| ( ( ~ ( ( ( sK31_SY3079 @ SV624 @ SV44 )
!= SV624 )
| ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) ) ) )
= $true )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2578]) ).
thf(2734,plain,
! [SV625: $i,SV305: $i,SV64: $i,SV737: $i] :
( ( ( in @ SV737 @ SV64 )
= $false )
| ( ( ~ ( in @ SV737 @ ( setminus @ SV64 @ SV305 ) )
| ~ ( in @ SV737 @ ( binintersect @ SV305 @ SV625 ) ) )
= $true )
| ( ( in @ SV625 @ ( powerset @ SV64 ) )
= $false )
| ( ( in @ SV305 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2582]) ).
thf(2735,plain,
! [SV626: $i,SV307: $i,SV66: $i,SV738: $i] :
( ( ( in @ SV738 @ SV66 )
= $false )
| ( ( ~ ~ ( in @ SV738 @ ( binunion @ SV307 @ SV626 ) )
| ~ ( in @ SV738 @ SV626 ) )
= $true )
| ( ( in @ SV626 @ ( powerset @ SV66 ) )
= $false )
| ( ( in @ SV307 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2583]) ).
thf(2736,plain,
! [SV69: $i,SV310: $i] :
( ( ( ~ ( ~ ( in @ SV310 @ ( sK46_SY2574 @ SV69 @ SV310 ) )
| ~ ( in @ ( sK46_SY2574 @ SV69 @ SV310 ) @ SV69 ) ) )
= $true )
| ( ( in @ SV310 @ ( setunion @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2584]) ).
thf(2737,plain,
! [SV69: $i,SV759: $i,SV310: $i] :
( ( ( ~ ( ~ ( in @ SV310 @ SV759 )
| ~ ( in @ SV759 @ SV69 ) ) )
= $false )
| ( ( in @ SV310 @ ( setunion @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2738,plain,
! [SV627: $i,SV311: $i,SV70: $i,SV739: $i] :
( ( ( in @ SV739 @ SV70 )
= $false )
| ( ( ~ ( in @ SV739 @ ( setminus @ SV70 @ ( binunion @ SV311 @ SV627 ) ) )
| ~ ( in @ SV739 @ SV311 ) )
= $true )
| ( ( in @ SV627 @ ( powerset @ SV70 ) )
= $false )
| ( ( in @ SV311 @ ( powerset @ SV70 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2586]) ).
thf(2739,plain,
! [SV73: $i,SV314: $i,SV628: $i] :
( ( ( ~ ( in @ ( sK52_SY3083 @ SV628 @ SV314 @ SV73 ) @ SV73 )
| ~ ( in @ ( sK52_SY3083 @ SV628 @ SV314 @ SV73 ) @ SV314 )
| ( in @ ( sK52_SY3083 @ SV628 @ SV314 @ SV73 ) @ SV628 ) )
= $false )
| ( ( in @ SV314 @ ( powerset @ SV628 ) )
= $true )
| ( ( in @ SV628 @ ( powerset @ SV73 ) )
= $false )
| ( ( in @ SV314 @ ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2587]) ).
thf(2740,plain,
! [SV686: $o,SV315: $i,SV74: $i,SV509: $i] :
( ( ( in @ SV509 @ SV74 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SV686 )
| SV686 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2588]) ).
thf(2741,plain,
! [SV686: $o,SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV315 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SV686 )
| SV686 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2589]) ).
thf(2742,plain,
! [SV315: $i,SV74: $i,SV509: $i,SV686: $o] :
( ( SV686 = $false )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SV686 )
| SV686 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2589]) ).
thf(2743,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( in @ SV509 @ SV74 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $true )
| $true )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2590]) ).
thf(2744,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV315 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $true )
| $true )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2591]) ).
thf(2745,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $true )
| $true )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2591]) ).
thf(2746,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( in @ SV509 @ SV74 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $false )
| $false )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2592]) ).
thf(2747,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV315 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $false )
| $false )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2593]) ).
thf(2748,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $false )
| $false )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2593]) ).
thf(2749,plain,
! [SV79: $i,SV318: $i > $o] :
( ( ( ~ ( in @ ( sK32_SY2591 @ SV318 @ SV79 ) @ SV79 ) )
= $false )
| ( ( ! [SY2592: $i] :
( ~ ( in @ SY2592 @ SV79 )
| ~ ( SV318 @ SY2592 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2595]) ).
thf(2750,plain,
! [SV79: $i,SV318: $i > $o] :
( ( ( ~ ( SV318 @ ( sK32_SY2591 @ SV318 @ SV79 ) ) )
= $false )
| ( ( ! [SY2592: $i] :
( ~ ( in @ SY2592 @ SV79 )
| ~ ( SV318 @ SY2592 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2595]) ).
thf(2751,plain,
! [SV82: $i,SV630: $i] :
( ( ( ~ ( in @ ( sK38_SY2017 @ SV630 @ SV82 ) @ SV82 )
| ~ ~ ~ ! [SY3174: $i] :
~ ~ ( ~ ( in @ SY3174 @ ( sK38_SY2017 @ SV630 @ SV82 ) )
| ~ ( in @ SY3174 @ SV82 ) ) )
= $false )
| ( ( in @ SV630 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2596]) ).
thf(2752,plain,
! [SV607: $o,SV322: $i,SV84: $i,SV513: $i] :
( ( ( in @ SV513 @ SV84 )
= $true )
| ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| SV607 )
| SV607 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2597]) ).
thf(2753,plain,
! [SV84: $i,SV607: $o,SV322: $i,SV513: $i] :
( ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| SV607 ) )
= $true )
| ( SV607 = $true )
| ( SV607 = $false )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2598]) ).
thf(2754,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( ( in @ SV513 @ SV84 )
= $true )
| ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| $true )
| $true )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2599]) ).
thf(2755,plain,
! [SV84: $i,SV322: $i,SV513: $i] :
( ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2600]) ).
thf(2756,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( ( in @ SV513 @ SV84 )
= $true )
| ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| $false )
| $false )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2601]) ).
thf(2757,plain,
! [SV84: $i,SV322: $i,SV513: $i] :
( ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2602]) ).
thf(2758,plain,
! [SV631: $i,SV323: $i,SV85: $i,SV740: $i] :
( ( ( in @ SV740 @ SV85 )
= $false )
| ( ( ~ ~ ( in @ SV740 @ ( binunion @ SV323 @ SV631 ) )
| ~ ( in @ SV740 @ SV323 ) )
= $true )
| ( ( in @ SV631 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV323 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2603]) ).
thf(2759,plain,
! [SV87: $i,SV325: $i > $o,SV687: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK53_SY2599 @ SV687 @ SV325 @ SV87 ) @ SV87 )
| ~ ~ ( SV325 @ ( sK53_SY2599 @ SV687 @ SV325 @ SV87 ) ) ) )
= $false )
| ( ( SV325 @ SV687 )
= $true )
| ( ( in @ SV687 @ SV87 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2604]) ).
thf(2760,plain,
! [SV326: $i,SV88: $i] :
( ( ( ~ ( in @ ( sK54_SY2601 @ SV88 @ SV326 ) @ SV326 )
| ( in @ ( sK54_SY2601 @ SV88 @ SV326 ) @ SV88 ) )
= $false )
| ( ( SV88 = SV326 )
= $true )
| ( ( in @ ( sK7_SY2600 @ SV326 @ SV88 ) @ SV88 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2605]) ).
thf(2761,plain,
! [SV326: $i,SV88: $i] :
( ( ( ~ ( in @ ( sK47_SY2601 @ SV88 @ SV326 ) @ SV326 ) )
= $false )
| ( ( SV88 = SV326 )
= $true )
| ( ( in @ ( sK7_SY2600 @ SV326 @ SV88 ) @ SV326 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2606]) ).
thf(2762,plain,
! [SV326: $i,SV88: $i] :
( ( ( in @ ( sK47_SY2601 @ SV88 @ SV326 ) @ SV88 )
= $false )
| ( ( SV88 = SV326 )
= $true )
| ( ( in @ ( sK7_SY2600 @ SV326 @ SV88 ) @ SV326 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2606]) ).
thf(2763,plain,
! [SV632: $i,SV91: $i > $o] :
( ( ( ! [SY3087: $i] :
( ~ ( SV91 @ SY3087 )
| ( SV632 = SY3087 ) ) )
= $false )
| ( ( SV91 @ SV632 )
= $false )
| ( ( ! [SY2037: $i,SY2038: $i] :
( ~ ( SV91 @ SY2037 )
| ~ ( SV91 @ SY2038 )
| ( SY2037 = SY2038 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2607]) ).
thf(2764,plain,
! [SV689: $i,SV516: $i,SV332: $i,SV95: $i] :
( ( ( ! [SY3141: $i] :
( ~ ( in @ SY3141 @ SV95 )
| ! [SY3142: $i] :
( ~ ( in @ SY3142 @ SV332 )
| ~ ( in @ ( kpair @ SY3141 @ SY3142 ) @ SV516 )
| ( in @ ( kpair @ SY3141 @ SY3142 ) @ SV689 ) ) ) )
= $false )
| ( ( subset @ SV516 @ SV689 )
= $true )
| ( ( subset @ SV689 @ ( cartprod @ SV95 @ SV332 ) )
= $false )
| ( ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2609]) ).
thf(2765,plain,
! [SV96: $i,SV333: $i] :
( ( ( in @ ( sK19_SY2610 @ SV333 @ SV96 ) @ SV96 )
= $true )
| ( ( in @ SV333 @ ( setunion @ SV96 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2610]) ).
thf(2766,plain,
! [SV96: $i,SV333: $i] :
( ( ( in @ SV333 @ ( sK19_SY2610 @ SV333 @ SV96 ) )
= $true )
| ( ( in @ SV333 @ ( setunion @ SV96 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2611]) ).
thf(2767,plain,
! [SV334: $i,SV97: $i,SV633: $i] :
( ( ( in @ SV633 @ ( setminus @ SV97 @ SV334 ) )
= $true )
| ( ( in @ SV633 @ SV334 )
= $true )
| ( ( in @ SV633 @ SV97 )
= $false )
| ( ( in @ SV334 @ ( powerset @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2612]) ).
thf(2768,plain,
! [SV335: $i > $o,SV98: $i,SV517: $i] :
( ( ( in @ SV517
@ ( dsetconstr @ SV98
@ ^ [SY2613: $i] : ( SV335 @ SY2613 ) ) )
= $false )
| ( ( SV335 @ SV517 )
= $true )
| ( ( in @ SV517 @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2613]) ).
thf(2769,plain,
! [SV98: $i,SV517: $i,SV335: $i > $o] :
( ( ( SV335 @ SV517 )
= $false )
| ( ( in @ SV517
@ ( dsetconstr @ SV98
@ ^ [SY2614: $i] : ( SV335 @ SY2614 ) ) )
= $true )
| ( ( in @ SV517 @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2614]) ).
thf(2770,plain,
! [SV100: $i,SV337: $i > $o,SV518: $i] :
( ( ( ~ ( in @ ( sK55_SY2926 @ SV518 @ SV337 @ SV100 ) @ SV100 )
| ~ ( SV337 @ ( sK55_SY2926 @ SV518 @ SV337 @ SV100 ) )
| ( ( sK55_SY2926 @ SV518 @ SV337 @ SV100 )
= SV518 ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV100
@ ^ [SY2618: $i] : ( SV337 @ SY2618 ) ) )
= $true )
| ( ( SV337 @ SV518 )
= $false )
| ( ( in @ SV518 @ SV100 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2615]) ).
thf(2771,plain,
( ( in @ sK39_SY3168 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2616]) ).
thf(2772,plain,
( ( ~ ( in @ sK39_SY3168 @ ( binunion @ sK2_SY2624 @ sK9_SY2932 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2617]) ).
thf(2773,plain,
( ( ~ ( ~ ( in @ sK39_SY3168 @ sK2_SY2624 )
| sK33_SY3090 )
| ~ ( ~ ( in @ sK39_SY3168 @ sK9_SY2932 )
| sK33_SY3090 )
| sK33_SY3090 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2617]) ).
thf(2774,plain,
! [SV105: $i,SV342: $i,SV522: $i,SV691: $i > $o] :
( ( ( ~ ( in @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ SV105 ) )
= $false )
| ( ( ! [SY3145: $i] :
( ~ ( in @ SY3145 @ SV522 )
| ( SV691 @ SY3145 ) ) )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2618]) ).
thf(2775,plain,
! [SV105: $i,SV522: $i,SV691: $i > $o,SV342: $i] :
( ( ( ! [SY3189: $i] :
( ~ ( in @ SY3189 @ SV342 )
| ~ ( in @ ( kpair @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ SY3189 ) @ SV522 )
| ( SV691 @ ( kpair @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ SY3189 ) ) ) )
= $false )
| ( ( ! [SY3145: $i] :
( ~ ( in @ SY3145 @ SV522 )
| ( SV691 @ SY3145 ) ) )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2618]) ).
thf(2776,plain,
! [SV635: $i,SV106: $i > $o] :
( ( ( ! [SY3092: $i] :
( ~ ( SV106 @ SY3092 )
| ( SV635 = SY3092 ) ) )
= $false )
| ( ( SV106 @ SV635 )
= $false )
| ( ( ! [SY2086: $i,SY2087: $i] :
( ~ ( SV106 @ SY2086 )
| ~ ( SV106 @ SY2087 )
| ( SY2086 = SY2087 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2619]) ).
thf(2777,plain,
! [SV636: $i,SV108: $i > $o] :
( ( ( ! [SY3093: $i] :
( ~ ( SV108 @ SY3093 )
| ( SV636 = SY3093 ) ) )
= $false )
| ( ( SV108 @ SV636 )
= $false )
| ( ( SV108
@ ( descr
@ ^ [SY2093: $i] : ( SV108 @ SY2093 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2620]) ).
thf(2778,plain,
! [SV347: $i,SV113: $i,SV525: $i] :
( ( ( in @ SV525 @ SV113 )
= $false )
| ( ( in @ SV525 @ SV347 )
= $true )
| ( ( in @ SV525 @ ( setminus @ SV113 @ SV347 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2621]) ).
thf(2779,plain,
! [SV638: $i,SV114: $i > $o] :
( ( ( ! [SY3096: $i] :
( ~ ( SV114 @ SY3096 )
| ( SV638 = SY3096 ) ) )
= $false )
| ( ( SV114 @ SV638 )
= $false )
| ( ( ~ ! [SY2107: $i] :
~ ( SV114 @ SY2107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2622]) ).
thf(2780,plain,
! [SV639: $i,SV348: $i,SV115: $i,SV741: $i] :
( ( ( in @ SV741 @ ( powerset @ SV115 ) )
= $false )
| ( ( ! [SY3175: $i] :
( ~ ( in @ SY3175 @ SV115 )
| ~ ( in @ SY3175 @ ( binintersect @ SV348 @ SV639 ) )
| ( in @ SY3175 @ ( binunion @ SV348 @ SV741 ) ) ) )
= $true )
| ( ( in @ SV639 @ ( powerset @ SV115 ) )
= $false )
| ( ( in @ SV348 @ ( powerset @ SV115 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2623]) ).
thf(2781,plain,
! [SV350: $i > $o,SV118: $i,SV763: $i] :
( ( ( ~ ~ ( ~ ( in @ SV763 @ SV118 )
| ~ ( SV350 @ SV763 ) ) )
= $true )
| ( ( in @ ( sK10_SY2649 @ SV350 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2624]) ).
thf(2782,plain,
! [SV350: $i > $o,SV118: $i,SV764: $i] :
( ( ( ~ ~ ( ~ ( in @ SV764 @ SV118 )
| ~ ( SV350 @ SV764 ) ) )
= $true )
| ( ( SV350 @ ( sK10_SY2649 @ SV350 @ SV118 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2625]) ).
thf(2783,plain,
! [SV119: $i,SV351: $i > $o,SV692: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK56_SY2652 @ SV692 @ SV351 @ SV119 ) @ SV119 )
| ~ ~ ( SV351 @ ( sK56_SY2652 @ SV692 @ SV351 @ SV119 ) ) ) )
= $false )
| ( ( SV351 @ SV692 )
= $true )
| ( ( in @ SV692 @ SV119 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2626]) ).
thf(2784,plain,
! [SV352: $i,SV641: $i,SV120: $i,SV742: $i] :
( ( ( in @ SV742 @ SV120 )
= $false )
| ( ( ~ ~ ( in @ SV742 @ SV641 )
| ~ ( in @ SV742 @ ( binintersect @ SV352 @ SV641 ) ) )
= $true )
| ( ( in @ SV641 @ ( powerset @ SV120 ) )
= $false )
| ( ( in @ SV352 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2627]) ).
thf(2785,plain,
! [SV353: $i,SV642: $i,SV121: $i,SV765: $i] :
( ( ( ~ ( in @ SV765 @ SV121 )
| ~ ( in @ SV765 @ SV642 )
| ( in @ SV765 @ ( setminus @ SV121 @ SV353 ) ) )
= $true )
| ( ( subset @ SV353 @ ( setminus @ SV121 @ SV642 ) )
= $false )
| ( ( in @ SV642 @ ( powerset @ SV121 ) )
= $false )
| ( ( in @ SV353 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2628]) ).
thf(2786,plain,
! [SV693: $o,SV358: $i,SV126: $i,SV529: $i] :
( ( ( SV529 = SV126 )
= $true )
| ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| SV693 )
| SV693 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2629]) ).
thf(2787,plain,
! [SV126: $i,SV693: $o,SV358: $i,SV529: $i] :
( ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| SV693 ) )
= $true )
| ( SV693 = $true )
| ( SV693 = $false )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2630]) ).
thf(2788,plain,
! [SV358: $i,SV126: $i,SV529: $i] :
( ( ( SV529 = SV126 )
= $true )
| ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| $true )
| $true )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2631]) ).
thf(2789,plain,
! [SV126: $i,SV358: $i,SV529: $i] :
( ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2632]) ).
thf(2790,plain,
! [SV358: $i,SV126: $i,SV529: $i] :
( ( ( SV529 = SV126 )
= $true )
| ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| $false )
| $false )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2633]) ).
thf(2791,plain,
! [SV126: $i,SV358: $i,SV529: $i] :
( ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2634]) ).
thf(2792,plain,
! [SV359: $i,SV127: $i,SV530: $i] :
( ( ( in @ SV530 @ ( symdiff @ SV127 @ SV359 ) )
= $false )
| ( ( in @ SV530 @ SV359 )
= $true )
| ( ( in @ SV530 @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2635]) ).
thf(2793,plain,
! [SV644: $i,SV362: $i,SV130: $i,SV743: $i] :
( ( ( in @ SV743 @ SV130 )
= $false )
| ( ( ~ ~ ( in @ SV743 @ SV362 )
| ~ ( in @ SV743 @ ( binintersect @ SV362 @ SV644 ) ) )
= $true )
| ( ( in @ SV644 @ ( powerset @ SV130 ) )
= $false )
| ( ( in @ SV362 @ ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2637]) ).
thf(2794,plain,
! [SV645: $i,SV363: $i,SV131: $i,SV744: $i] :
( ( ( in @ SV744 @ SV131 )
= $false )
| ( ( ~ ( in @ SV744 @ ( setminus @ SV131 @ SV363 ) )
| ( in @ SV744 @ ( setminus @ SV131 @ ( binintersect @ SV363 @ SV645 ) ) ) )
= $true )
| ( ( in @ SV645 @ ( powerset @ SV131 ) )
= $false )
| ( ( in @ SV363 @ ( powerset @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2638]) ).
thf(2795,plain,
! [SV647: $i,SV367: $i > $o,SV135: $i,SV745: $i] :
( ( ( in @ SV745 @ SV135 )
= $false )
| ( ( ~ ( SV367 @ SV647 )
| ~ ( SV367 @ SV745 )
| ( SV647 = SV745 ) )
= $true )
| ( ( in @ SV647 @ SV135 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV135
@ ^ [SY2676: $i] : ( SV367 @ SY2676 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2640]) ).
thf(2796,plain,
! [SV136: $i,SV648: $o,SV368: $i] :
( ( ( in @ SV368 @ ( sK40_SY3104 @ SV648 @ SV136 @ SV368 ) )
= $true )
| ( SV648 = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2641]) ).
thf(2797,plain,
! [SV368: $i,SV136: $i,SV648: $o] :
( ( ( ~ ( in @ ( sK40_SY3104 @ SV648 @ SV136 @ SV368 ) @ SV136 ) )
= $false )
| ( SV648 = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2642]) ).
thf(2798,plain,
! [SV136: $i,SV368: $i,SV648: $o] :
( ( SV648 = $false )
| ( SV648 = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2642]) ).
thf(2799,plain,
! [SV136: $i,SV368: $i] :
( ( ( in @ SV368 @ ( sK41_SX0 @ SV136 @ SV368 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2643]) ).
thf(2800,plain,
! [SV368: $i,SV136: $i] :
( ( ( ~ ( in @ ( sK41_SX0 @ SV136 @ SV368 ) @ SV136 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2644]) ).
thf(2801,plain,
! [SV136: $i,SV368: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2644]) ).
thf(2802,plain,
! [SV136: $i,SV368: $i] :
( ( ( in @ SV368 @ ( sK42_SX0 @ SV136 @ SV368 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2645]) ).
thf(2803,plain,
! [SV368: $i,SV136: $i] :
( ( ( ~ ( in @ ( sK42_SX0 @ SV136 @ SV368 ) @ SV136 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2646]) ).
thf(2804,plain,
! [SV136: $i,SV368: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2646]) ).
thf(2805,plain,
! [SV649: $i,SV369: $i,SV137: $i,SV746: $i] :
( ( ( in @ SV746 @ SV137 )
= $false )
| ( ( ~ ( subset @ SV369 @ SV649 )
| ~ ~ ( in @ SV746 @ SV649 )
| ~ ( in @ SV746 @ SV369 ) )
= $true )
| ( ( in @ SV649 @ ( powerset @ SV137 ) )
= $false )
| ( ( in @ SV369 @ ( powerset @ SV137 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2647]) ).
thf(2806,plain,
! [SV146: $i,SV377: $i,SV650: $i] :
( ( ( ~ ( in @ ( sK57_SY3106 @ SV650 @ SV377 @ SV146 ) @ SV146 )
| ~ ( in @ ( sK57_SY3106 @ SV650 @ SV377 @ SV146 ) @ SV377 )
| ( in @ ( sK57_SY3106 @ SV650 @ SV377 @ SV146 ) @ SV650 ) )
= $false )
| ( ( subset @ SV377 @ SV650 )
= $true )
| ( ( in @ SV650 @ ( powerset @ SV146 ) )
= $false )
| ( ( in @ SV377 @ ( powerset @ SV146 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2648]) ).
thf(2807,plain,
! [SV147: $i] :
( ( ~ ( ~ ! [SY2953: $i] :
( ~ ( in @ SY2953 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY2188: $i] :
( ~ ( in @ SY2188 @ SY2953 )
| ( in @ SY2188 @ SV147 ) ) )
| ~ ! [SY2955: $i,SY2956: $i] :
( ~ ~ ( ~ ( in @ SY2955 @ SV147 )
| ~ ( in @ SY2956 @ SV147 ) )
| ~ ! [SY2957: $i] :
( ~ ( in @ SY2957 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SY2955 @ SY2957 )
| ( in @ SY2956 @ SY2957 ) )
| ~ ( ~ ( in @ SY2956 @ SY2957 )
| ( in @ SY2955 @ SY2957 ) ) ) )
| ( SY2955 = SY2956 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2649]) ).
thf(2808,plain,
! [SV147: $i] :
( ( ! [SY2958: $i,SY2959: $i] :
( ~ ~ ( ~ ( in @ SY2958 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY2959 @ ( sK3_SY2186 @ SV147 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2958 )
| ( in @ SX4 @ SY2959 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2959 )
| ( in @ SX4 @ SY2958 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2650]) ).
thf(2809,plain,
! [SV147: $i,SV747: $i] :
( ( ( ~ ( ~ ! [SY3176: $i] :
( ~ ( in @ SY3176 @ SV747 )
| ( in @ SY3176 @ SV147 ) )
| ~ ~ ! [SY3177: $i] :
~ ( in @ SY3177 @ SV747 ) ) )
= $false )
| ( ( ~ ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2651]) ).
thf(2810,plain,
! [SV651: $i,SV381: $i,SV151: $i,SV748: $i] :
( ( ( in @ SV748 @ ( powerset @ SV151 ) )
= $false )
| ( ( ! [SY3183: $i] :
( ~ ( in @ SY3183 @ SV151 )
| ~ ( in @ SY3183 @ ( binintersect @ SV381 @ SV651 ) )
| ( in @ SY3183 @ ( binunion @ SV651 @ SV748 ) ) ) )
= $true )
| ( ( in @ SV651 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV381 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(2811,plain,
! [SV652: $i,SV386: $i,SV156: $i,SV749: $i] :
( ( ( in @ SV749 @ SV156 )
= $false )
| ( ( ~ ( subset @ SV386 @ ( setminus @ SV156 @ SV652 ) )
| ~ ( in @ SV749 @ SV652 )
| ~ ( in @ SV749 @ SV386 ) )
= $true )
| ( ( in @ SV652 @ ( powerset @ SV156 ) )
= $false )
| ( ( in @ SV386 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2653]) ).
thf(2812,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ( SV160 @ ( sK49_SY2231 @ SV653 @ SV160 ) )
| ~ ( SV160 @ ( sK58_SY3190 @ SV653 @ SV160 ) )
| ( ( sK49_SY2231 @ SV653 @ SV160 )
= ( sK58_SY3190 @ SV653 @ SV160 ) ) )
= $false )
| ( ( ~ ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2654]) ).
thf(2813,plain,
! [SV393: $i,SV696: $i,SV165: $i,SV656: $i] :
( ( ( in @ SV656 @ SV165 )
= $false )
| ( ( in @ SV696 @ SV393 )
= $true )
| ( ( SV656 = SV696 )
= $false )
| ( ( SV165 = SV393 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2655]) ).
thf(2814,plain,
! [SV657: $i,SV395: $i,SV167: $i,SV750: $i] :
( ( ( in @ SV750 @ SV167 )
= $false )
| ( ( ~ ( in @ SV750 @ ( setminus @ SV167 @ ( binunion @ SV395 @ SV657 ) ) )
| ( in @ SV750 @ ( setminus @ SV167 @ SV395 ) ) )
= $true )
| ( ( in @ SV657 @ ( powerset @ SV167 ) )
= $false )
| ( ( in @ SV395 @ ( powerset @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2657]) ).
thf(2815,plain,
! [SV697: $i,SV548: $i,SV396: $i,SV168: $i] :
( ( ( ! [SY3146: $i] :
( ~ ( in @ SY3146 @ SV168 )
| ( ( ap @ SV168 @ SV396 @ SV548 @ SY3146 )
= ( ap @ SV168 @ SV396 @ SV697 @ SY3146 ) ) ) )
= $false )
| ( ( SV548 = SV697 )
= $true )
| ( ( func @ SV168 @ SV396 @ SV697 )
= $false )
| ( ( func @ SV168 @ SV396 @ SV548 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2658]) ).
thf(2816,plain,
! [SV701: $i,SV553: $i,SV171: $i,SV399: $o] :
( ( ( ~ SV399 ) = $false )
| ( ( ( dsetconstr @ SV171
@ ^ [SY3147: $i] :
( ~ ( ~ SV399
| ( SY3147 != SV553 ) )
| ~ ( ~ ~ SV399
| ( SY3147 != SV701 ) ) ) )
= ( setadjoin @ SV701 @ emptyset ) )
= $true )
| ( ( in @ SV701 @ SV171 )
= $false )
| ( ( in @ SV553 @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2659]) ).
thf(2817,plain,
! [SV702: $i,SV554: $i,SV171: $i] :
( ( ( ~ $true ) = $false )
| ( ( ( dsetconstr @ SV171
@ ^ [SY3148: $i] :
( ~ ( ~ $true
| ( SY3148 != SV554 ) )
| ~ ( ~ ~ $true
| ( SY3148 != SV702 ) ) ) )
= ( setadjoin @ SV702 @ emptyset ) )
= $true )
| ( ( in @ SV702 @ SV171 )
= $false )
| ( ( in @ SV554 @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2660]) ).
thf(2818,plain,
! [SV703: $i,SV555: $i,SV171: $i] :
( ( ( ~ $false ) = $false )
| ( ( ( dsetconstr @ SV171
@ ^ [SY3149: $i] :
( ~ ( ~ $false
| ( SY3149 != SV555 ) )
| ~ ( ~ ~ $false
| ( SY3149 != SV703 ) ) ) )
= ( setadjoin @ SV703 @ emptyset ) )
= $true )
| ( ( in @ SV703 @ SV171 )
= $false )
| ( ( in @ SV555 @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2661]) ).
thf(2819,plain,
! [SV172: $i,SV400: $i,SV751: $i] :
( ( ( in @ SV751 @ SV400 )
= $false )
| ( ( in @ SV751 @ SV172 )
= $true )
| ( ( in @ SV400 @ ( powerset @ SV172 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2662]) ).
thf(2820,plain,
! [SV400: $i,SV172: $i] :
( ( ( in @ ( sK43_SY2728 @ SV172 @ SV400 ) @ SV400 )
= $true )
| ( ( in @ SV400 @ ( powerset @ SV172 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2663]) ).
thf(2821,plain,
! [SV408: $i > $o,SV180: $i,SV706: $i] :
( ( ( in @ SV706 @ SV180 )
= $false )
| ( ( ~ ( SV408 @ SV706 ) )
= $true )
| ( ( ( ( dsetconstr @ SV180
@ ^ [SY2739: $i] : ( SV408 @ SY2739 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2666]) ).
thf(2822,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ( ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( in @ ( sK12_SY2740 @ SV409 @ SV181 ) @ SV181 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2667]) ).
thf(2823,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( in @ ( sK34_SY3112 @ SV409 @ SV181 ) @ SV181 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2668]) ).
thf(2824,plain,
! [SV181: $i,SV409: $i > $o] :
( ( ( SV409 @ ( sK12_SY2740 @ SV409 @ SV181 ) )
= $true )
| ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) )
| ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2669]) ).
thf(2825,plain,
! [SV181: $i,SV409: $i > $o] :
( ( ( ~ ( SV409 @ ( sK34_SY3112 @ SV409 @ SV181 ) ) )
= $false )
| ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) )
| ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2670]) ).
thf(2826,plain,
! [SV181: $i,SV409: $i > $o] :
( ( ( ( sK12_SY2740 @ SV409 @ SV181 )
= ( sK34_SY3112 @ SV409 @ SV181 ) )
= $false )
| ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) )
| ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2670]) ).
thf(2827,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2671]) ).
thf(2828,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
| ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) ) )
= $false )
| ( ( ~ ( ~ ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
| ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2672]) ).
thf(2829,plain,
! [SV185: $i,SV561: $i,SV707: $i,SV413: $i,SV760: $i] :
( ( ( ~ ( in @ SV760 @ SV413 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV707 @ SV760 ) @ SV561 )
| ( ( ap @ SV185 @ SV413 @ SV561 @ SV707 )
= SV760 ) )
= $true )
| ( ( in @ SV707 @ SV185 )
= $false )
| ( ( in @ SV561 @ ( funcSet @ SV185 @ SV413 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2673]) ).
thf(2830,plain,
! [SV186: $i,SV414: $i,SV659: $i] :
( ( ( ~ ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV186 )
| ~ ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV414 )
| ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV659 ) )
= $false )
| ( ( ~ ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV186 )
| ~ ( in @ SY3115 @ SV659 )
| ( in @ SY3115 @ SV414 ) )
| ( SV414 = SV659 ) )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2674]) ).
thf(2831,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ! [SY3116: $i] :
( ~ ( SV188 @ SY3116 )
| ( SV660 = SY3116 ) ) )
= $false )
| ( ( SV188 @ SV660 )
= $false )
| ( ( ~ ! [SY2316: $i] :
~ ~ ( ~ ( SV188 @ SY2316 )
| ~ ! [SY2317: $i] :
( ~ ( SV188 @ SY2317 )
| ( SY2316 = SY2317 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2675]) ).
thf(2832,plain,
! [SV661: $i,SV418: $i,SV191: $i,SV752: $i] :
( ( ( in @ SV752 @ ( powerset @ SV191 ) )
= $false )
| ( ( ! [SY3184: $i] :
( ~ ( in @ SY3184 @ SV191 )
| ~ ( in @ SY3184 @ ( binintersect @ SV418 @ SV661 ) )
| ( in @ SY3184 @ ( binintersect @ ( binunion @ SV418 @ SV752 ) @ ( binunion @ SV661 @ SV752 ) ) ) ) )
= $true )
| ( ( in @ SV661 @ ( powerset @ SV191 ) )
= $false )
| ( ( in @ SV418 @ ( powerset @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2676]) ).
thf(2833,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2677]) ).
thf(2834,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2677]) ).
thf(2835,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
| ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) ) )
= $false )
| ( ( ~ ( ~ ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
| ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2678]) ).
thf(2836,plain,
! [SV196: $i,SV424: $i,SV566: $i] :
( ( ( ~ ( in @ ( sK35_SY2993 @ SV566 @ SV424 @ SV196 ) @ SV196 ) )
= $false )
| ( ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2679]) ).
thf(2837,plain,
! [SV196: $i,SV566: $i,SV424: $i] :
( ( ( ~ ~ ! [SY3169: $i] :
~ ~ ( ~ ( in @ SY3169 @ SV424 )
| ( SV566
!= ( kpair @ ( sK35_SY2993 @ SV566 @ SV424 @ SV196 ) @ SY3169 ) ) ) )
= $false )
| ( ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2679]) ).
thf(2838,plain,
! [SV709: $i,SV567: $i,SV197: $i,SV425: $o] :
( ( SV425 = $false )
| ( ( ( if @ SV197 @ SV425 @ SV567 @ SV709 )
= SV567 )
= $true )
| ( ( in @ SV709 @ SV197 )
= $false )
| ( ( in @ SV567 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2680]) ).
thf(2839,plain,
! [SV710: $i,SV568: $i,SV197: $i] :
( ( $true = $false )
| ( ( ( if @ SV197 @ $true @ SV568 @ SV710 )
= SV568 )
= $true )
| ( ( in @ SV710 @ SV197 )
= $false )
| ( ( in @ SV568 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2681]) ).
thf(2840,plain,
! [SV711: $i,SV569: $i,SV197: $i] :
( ( $false = $false )
| ( ( ( if @ SV197 @ $false @ SV569 @ SV711 )
= SV569 )
= $true )
| ( ( in @ SV711 @ SV197 )
= $false )
| ( ( in @ SV569 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2682]) ).
thf(2841,plain,
! [SV712: $i,SV570: $i,SV426: $i,SV198: $i] :
( ( ( ! [SY3151: $i] :
( ~ ( in @ SY3151 @ SV198 )
| ! [SY3152: $i] :
( ~ ( in @ SY3152 @ SV426 )
| ~ ( in @ ( kpair @ SY3151 @ SY3152 ) @ SV570 )
| ( in @ ( kpair @ SY3151 @ SY3152 ) @ SV712 ) ) ) )
= $false )
| ( ( ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) )
| ( SV570 = SV712 ) )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(2842,plain,
! [SV200: $i,SV428: $i,SV571: $i,SV713: $i > $o] :
( ( ( ~ ( in @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ SV200 ) )
= $false )
| ( ( ! [SY3157: $i] :
( ~ ( in @ SY3157 @ SV571 )
| ( SV713 @ SY3157 ) ) )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2684]) ).
thf(2843,plain,
! [SV200: $i,SV571: $i,SV713: $i > $o,SV428: $i] :
( ( ( ! [SY3191: $i] :
( ~ ( in @ SY3191 @ SV428 )
| ~ ( in @ ( kpair @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ SY3191 ) @ SV571 )
| ( SV713 @ ( kpair @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ SY3191 ) ) ) )
= $false )
| ( ( ! [SY3157: $i] :
( ~ ( in @ SY3157 @ SV571 )
| ( SV713 @ SY3157 ) ) )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2684]) ).
thf(2844,plain,
! [SV429: $i > $o,SV201: $i,SV714: $i] :
( ( ( in @ SV714 @ SV201 )
= $false )
| ( ( ~ ~ ( SV429 @ SV714 ) )
= $true )
| ( ( ~ ! [SY2794: $i] :
( ~ ( in @ SY2794 @ SV201 )
| ( SV429 @ SY2794 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2685]) ).
thf(2845,plain,
! [SV574: $i > $i,SV433: $i,SV209: $i,SV761: $i] :
( ( ( ~ ( in @ SV761 @ SV209 ) )
= $true )
| ( ( ( ap @ SV209 @ SV433
@ ( lam @ SV209 @ SV433
@ ^ [SY3012: $i] : ( SV574 @ SY3012 ) )
@ SV761 )
= ( SV574 @ SV761 ) )
= $true )
| ( ( in @ ( sK25_SY3010 @ SV433 @ SV574 @ SV209 ) @ SV209 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2686]) ).
thf(2846,plain,
! [SV574: $i > $i,SV433: $i,SV209: $i,SV753: $i] :
( ( ( in @ SV753 @ SV209 )
= $false )
| ( ( ( ap @ SV209 @ SV433
@ ( lam @ SV209 @ SV433
@ ^ [SY3012: $i] : ( SV574 @ SY3012 ) )
@ SV753 )
= ( SV574 @ SV753 ) )
= $true )
| ( ( in @ ( SV574 @ ( sK25_SY3010 @ SV433 @ SV574 @ SV209 ) ) @ SV433 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2687]) ).
thf(2847,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ( ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( in @ ( sK15_SY2806 @ SV436 @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2688]) ).
thf(2848,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( in @ ( sK36_SY3121 @ SV436 @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2689]) ).
thf(2849,plain,
! [SV212: $i,SV436: $i > $o] :
( ( ( SV436 @ ( sK15_SY2806 @ SV436 @ SV212 ) )
= $true )
| ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) )
| ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2690]) ).
thf(2850,plain,
! [SV212: $i,SV436: $i > $o] :
( ( ( ~ ( SV436 @ ( sK36_SY3121 @ SV436 @ SV212 ) ) )
= $false )
| ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) )
| ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2691]) ).
thf(2851,plain,
! [SV212: $i,SV436: $i > $o] :
( ( ( ( sK15_SY2806 @ SV436 @ SV212 )
= ( sK36_SY3121 @ SV436 @ SV212 ) )
= $false )
| ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) )
| ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2691]) ).
thf(2852,plain,
! [SV215: $i] :
( ( ( ~ ( ~ ( in @ ( sK44_SY2395 @ SV215 ) @ omega )
| ~ ( in @ ( sK44_SY2395 @ SV215 ) @ SV215 ) ) )
= $true )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( ! [SY2396: $i] :
( ~ ( in @ SY2396 @ omega )
| ( in @ SY2396 @ SV215 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2692]) ).
thf(2853,plain,
! [SV215: $i,SV766: $i] :
( ( ( ~ ( in @ SV766 @ omega )
| ( in @ SV766 @ SV215 ) )
= $true )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( in @ ( setadjoin @ ( sK44_SY2395 @ SV215 ) @ ( sK44_SY2395 @ SV215 ) ) @ SV215 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2693]) ).
thf(2854,plain,
! [SV440: $i,SV217: $i,SV735: $i,SV616: $i,SV577: $i > $i > $o] :
( ( ( ~ ( SV577 @ SV616 @ SV735 ) )
= $true )
| ( ( in @ ( kpair @ SV616 @ SV735 )
@ ( dpsetconstr @ SV217 @ SV440
@ ^ [SY3017: $i,SY3018: $i] : ( SV577 @ SY3017 @ SY3018 ) ) )
= $true )
| ( ( in @ SV735 @ SV440 )
= $false )
| ( ( in @ SV616 @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2694]) ).
thf(2855,plain,
! [SV720: $i,SV581: $i,SV442: $i,SV219: $i] :
( ( ( ! [SY3158: $i] :
( ~ ( in @ SY3158 @ SV219 )
| ( ( ap @ SV219 @ SV442 @ SV581 @ SY3158 )
= ( ap @ SV219 @ SV442 @ SV720 @ SY3158 ) ) ) )
= $false )
| ( ( SV581 = SV720 )
= $true )
| ( ( in @ SV720 @ ( funcSet @ SV219 @ SV442 ) )
= $false )
| ( ( in @ SV581 @ ( funcSet @ SV219 @ SV442 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2695]) ).
thf(2856,plain,
! [SV582: $i > $i > $o,SV443: $i,SV220: $i,SV736: $i,SV617: $i] :
( ( ( ~ ( in @ ( kpair @ SV617 @ SV736 )
@ ( dpsetconstr @ SV220 @ SV443
@ ^ [SY3026: $i,SY3027: $i] : ( SV582 @ SY3026 @ SY3027 ) ) ) )
= $true )
| ( ( SV582 @ SV617 @ SV736 )
= $true )
| ( ( in @ SV736 @ SV443 )
= $false )
| ( ( in @ SV617 @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2696]) ).
thf(2857,plain,
! [SV223: $i,SV446: $i > $o] :
( ( ( in @ ( sK26_SY2833 @ SV446 @ SV223 ) @ SV223 )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY2832: $i] : ( SV446 @ SY2832 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2697]) ).
thf(2858,plain,
! [SV223: $i,SV446: $i > $o] :
( ( ( SV446 @ ( sK26_SY2833 @ SV446 @ SV223 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY2832: $i] : ( SV446 @ SY2832 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2698]) ).
thf(2859,plain,
! [SV225: $i,SV448: $i] :
( ( ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 )
| ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 ) ) )
= $true )
| ( ( SV225 = SV448 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2699]) ).
thf(2860,plain,
! [SV225: $i,SV448: $i] :
( ( ( ~ ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 )
| ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 ) )
= $false )
| ( ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 )
= $false )
| ( ( SV225 = SV448 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2700]) ).
thf(2861,plain,
! [SV665: $i,SV452: $i,SV229: $i,SV754: $i] :
( ( ( in @ SV754 @ ( powerset @ SV229 ) )
= $false )
| ( ( in @ ( binintersect @ SV452 @ SV665 ) @ ( powerset @ ( binintersect @ ( binunion @ SV452 @ SV754 ) @ ( binunion @ SV665 @ SV754 ) ) ) )
= $true )
| ( ( in @ SV665 @ ( powerset @ SV229 ) )
= $false )
| ( ( in @ SV452 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2702]) ).
thf(2862,plain,
! [SV230: $i] :
( ( ( in @ ( sK27_SY2440 @ SV230 ) @ SV230 )
= $true )
| ( ( SV230 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2703]) ).
thf(2863,plain,
! [SV230: $i] :
( ( $true = $true )
| ( ( SV230 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2704]) ).
thf(2864,plain,
! [SV722: $i,SV587: $i,SV231: $i,SV453: $o] :
( ( SV453 = $false )
| ( ( ( dsetconstr @ SV231
@ ^ [SY3159: $i] :
( ~ ( ~ SV453
| ( SY3159 != SV587 ) )
| ~ ( ~ ~ SV453
| ( SY3159 != SV722 ) ) ) )
= ( setadjoin @ SV587 @ emptyset ) )
= $true )
| ( ( in @ SV722 @ SV231 )
= $false )
| ( ( in @ SV587 @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2705]) ).
thf(2865,plain,
! [SV723: $i,SV588: $i,SV231: $i] :
( ( $true = $false )
| ( ( ( dsetconstr @ SV231
@ ^ [SY3160: $i] :
( ~ ( ~ $true
| ( SY3160 != SV588 ) )
| ~ ( ~ ~ $true
| ( SY3160 != SV723 ) ) ) )
= ( setadjoin @ SV588 @ emptyset ) )
= $true )
| ( ( in @ SV723 @ SV231 )
= $false )
| ( ( in @ SV588 @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2706]) ).
thf(2866,plain,
! [SV724: $i,SV589: $i,SV231: $i] :
( ( $false = $false )
| ( ( ( dsetconstr @ SV231
@ ^ [SY3161: $i] :
( ~ ( ~ $false
| ( SY3161 != SV589 ) )
| ~ ( ~ ~ $false
| ( SY3161 != SV724 ) ) ) )
= ( setadjoin @ SV589 @ emptyset ) )
= $true )
| ( ( in @ SV724 @ SV231 )
= $false )
| ( ( in @ SV589 @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2707]) ).
thf(2867,plain,
! [SV455: $i,SV233: $i,SV666: $i] :
( ( ( in @ SV666 @ ( setminus @ SV233 @ SV455 ) )
= $false )
| ( ( in @ SV666 @ SV455 )
= $false )
| ( ( in @ SV666 @ SV233 )
= $false )
| ( ( in @ SV455 @ ( powerset @ SV233 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2708]) ).
thf(2868,plain,
! [SV591: $i > $i,SV456: $i,SV234: $i,SV762: $i] :
( ( ( ~ ( in @ SV762 @ SV234 ) )
= $true )
| ( ( ( ap @ SV234 @ SV456
@ ( lam @ SV234 @ SV456
@ ^ [SY3038: $i] : ( SV591 @ SY3038 ) )
@ SV762 )
= ( SV591 @ SV762 ) )
= $true )
| ( ( in @ ( sK28_SY3036 @ SV456 @ SV591 @ SV234 ) @ SV234 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2709]) ).
thf(2869,plain,
! [SV591: $i > $i,SV456: $i,SV234: $i,SV755: $i] :
( ( ( in @ SV755 @ SV234 )
= $false )
| ( ( ( ap @ SV234 @ SV456
@ ( lam @ SV234 @ SV456
@ ^ [SY3038: $i] : ( SV591 @ SY3038 ) )
@ SV755 )
= ( SV591 @ SV755 ) )
= $true )
| ( ( in @ ( SV591 @ ( sK28_SY3036 @ SV456 @ SV591 @ SV234 ) ) @ SV456 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(2870,plain,
! [SV235: $i,SV457: $i] :
( ( ( ~ ( in @ ( sK37_SY2850 @ SV457 @ SV235 ) @ SV235 ) )
= $false )
| ( ( ( binintersect @ SV235 @ SV457 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2711]) ).
thf(2871,plain,
! [SV235: $i,SV457: $i] :
( ( ( ~ ( in @ ( sK37_SY2850 @ SV457 @ SV235 ) @ SV457 ) )
= $false )
| ( ( ( binintersect @ SV235 @ SV457 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2711]) ).
thf(2872,plain,
! [SV667: $i,SV465: $i,SV243: $i,SV756: $i] :
( ( ( in @ SV756 @ SV243 )
= $false )
| ( ( ~ ( in @ SV465 @ ( powerset @ SV667 ) )
| ~ ( in @ SV756 @ SV465 )
| ( in @ SV756 @ SV667 ) )
= $true )
| ( ( in @ SV667 @ ( powerset @ SV243 ) )
= $false )
| ( ( in @ SV465 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2712]) ).
thf(2873,plain,
! [SV597: $i,SV244: $i,SV725: $i,SV466: $o] :
( ( ( ~ SV466 ) = $false )
| ( ( in @ SV725
@ ( dsetconstr @ SV244
@ ^ [SY3162: $i] :
( ~ ( ~ SV466
| ( SY3162 != SV597 ) )
| ~ ( ~ ~ SV466
| ( SY3162 != SV725 ) ) ) ) )
= $true )
| ( ( in @ SV725 @ SV244 )
= $false )
| ( ( in @ SV597 @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2713]) ).
thf(2874,plain,
! [SV598: $i,SV244: $i,SV726: $i] :
( ( ( ~ $true ) = $false )
| ( ( in @ SV726
@ ( dsetconstr @ SV244
@ ^ [SY3163: $i] :
( ~ ( ~ $true
| ( SY3163 != SV598 ) )
| ~ ( ~ ~ $true
| ( SY3163 != SV726 ) ) ) ) )
= $true )
| ( ( in @ SV726 @ SV244 )
= $false )
| ( ( in @ SV598 @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2714]) ).
thf(2875,plain,
! [SV599: $i,SV244: $i,SV727: $i] :
( ( ( ~ $false ) = $false )
| ( ( in @ SV727
@ ( dsetconstr @ SV244
@ ^ [SY3164: $i] :
( ~ ( ~ $false
| ( SY3164 != SV599 ) )
| ~ ( ~ ~ $false
| ( SY3164 != SV727 ) ) ) ) )
= $true )
| ( ( in @ SV727 @ SV244 )
= $false )
| ( ( in @ SV599 @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2715]) ).
thf(2876,plain,
! [SV728: $i,SV600: $i,SV469: $i,SV247: $i] :
( ( ( ! [SY3165: $i] :
( ~ ( in @ SY3165 @ SV247 )
| ( ( ap @ SV247 @ SV469 @ SV600 @ SY3165 )
= ( ap @ SV247 @ SV469 @ SV728 @ SY3165 ) ) ) )
= $false )
| ( ( ! [SY3166: $i] :
( ~ ( in @ SY3166 @ SV247 )
| ! [SY3167: $i] :
( ~ ( in @ SY3167 @ SV469 )
| ~ ( in @ ( kpair @ SY3166 @ SY3167 ) @ SV728 )
| ( in @ ( kpair @ SY3166 @ SY3167 ) @ SV600 ) ) ) )
= $true )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2716]) ).
thf(2877,plain,
! [SV471: $i,SV249: $i > $i > $o] :
( ( ( ! [SY3194: $i] :
~ ( ~ ( ~ ( in @ SY3194 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY3194 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY3194 ) )
| ( in @ SY3194 @ ( sK51_SY2874 @ SV249 @ SV471 ) ) ) ) )
= $true )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2717]) ).
thf(2878,plain,
! [SV757: $i,SV471: $i,SV249: $i > $i > $o] :
( ( ( ~ ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
| ~ ! [SY3187: $i] :
( ~ ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SY3187 )
| ( SV757 = SY3187 ) ) )
= $true )
| ( ( ~ ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2718]) ).
thf(2879,plain,
! [SV729: $i,SV601: $i,SV252: $i,SV474: $o] :
( ( ( ~ SV474 ) = $false )
| ( ( ( if @ SV252 @ SV474 @ SV601 @ SV729 )
= SV729 )
= $true )
| ( ( in @ SV729 @ SV252 )
= $false )
| ( ( in @ SV601 @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2719]) ).
thf(2880,plain,
! [SV730: $i,SV602: $i,SV252: $i] :
( ( ( ~ $true ) = $false )
| ( ( ( if @ SV252 @ $true @ SV602 @ SV730 )
= SV730 )
= $true )
| ( ( in @ SV730 @ SV252 )
= $false )
| ( ( in @ SV602 @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2720]) ).
thf(2881,plain,
! [SV731: $i,SV603: $i,SV252: $i] :
( ( ( ~ $false ) = $false )
| ( ( ( if @ SV252 @ $false @ SV603 @ SV731 )
= SV731 )
= $true )
| ( ( in @ SV731 @ SV252 )
= $false )
| ( ( in @ SV603 @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2721]) ).
thf(2882,plain,
! [SV476: $i,SV733: $i,SV254: $i,SV669: $i] :
( ( ( ~ ( ~ ( in @ SV669 @ SV254 )
| ( in @ SV733 @ SV476 ) ) )
= $false )
| ( ( SV669 = SV733 )
= $false )
| ( ( SV254 = SV476 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2722]) ).
thf(2883,plain,
! [SV254: $i,SV669: $i,SV476: $i,SV733: $i] :
( ( ( ~ ( ~ ( in @ SV733 @ SV476 )
| ( in @ SV669 @ SV254 ) ) )
= $false )
| ( ( SV669 = SV733 )
= $false )
| ( ( SV254 = SV476 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2722]) ).
thf(2884,plain,
! [SV670: $i,SV256: $i > $o] :
( ( ( ! [SY3127: $i] :
( ~ ( SV256 @ SY3127 )
| ( SV670 = SY3127 ) ) )
= $false )
| ( ( SV256 @ SV670 )
= $false )
| ( ( ~ ! [SY2511: $i] :
~ ! [SY2512: $i] :
~ ( ~ ( ~ ( SV256 @ SY2512 )
| ( SY2512 = SY2511 ) )
| ~ ( ( SY2512 != SY2511 )
| ( SV256 @ SY2512 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2723]) ).
thf(2885,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ~ ( SV35 @ ( sK60_SY3073 @ SV621 @ SV35 ) )
| ( SV621
= ( sK60_SY3073 @ SV621 @ SV35 ) ) )
= $false )
| ( ( SV35 @ SV621 )
= $false )
| ( ( ~ ! [SY1902: $i] :
~ ~ ( ~ ( SV35 @ SY1902 )
| ~ ! [SY1903: $i] :
( ~ ( SV35 @ SY1903 )
| ( SY1902 = SY1903 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2724]) ).
thf(2886,plain,
! [SV38: $i,SV484: $i,SV672: $i,SV284: $i,SV758: $i] :
( ( ( in @ SV758 @ SV284 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV672 @ SV758 ) @ SV484 )
| ( ( ap @ SV38 @ SV284 @ SV484 @ SV672 )
= SV758 ) )
= $true )
| ( ( in @ SV672 @ SV38 )
= $false )
| ( ( func @ SV38 @ SV284 @ SV484 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2725]) ).
thf(2887,plain,
! [SV40: $i,SV286: $i,SV623: $i > $o,SV676: $i > $o] :
( ( ( in @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) @ SV40 )
= $true )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2729]) ).
thf(2888,plain,
! [SV286: $i,SV676: $i > $o,SV623: $i > $o,SV40: $i] :
( ( ( ~ ( in @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) @ SV286 )
| ( ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 )
!= ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
| ~ ( ~ ( ~ ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) )
| ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) ) )
| ~ ( ~ ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
| ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2730]) ).
thf(2889,plain,
! [SV41: $i,SV287: $i > $o] :
( ( ( in @ ( sK30_SY2541 @ SV287 @ SV41 ) @ SV41 )
= $true )
| ( ( ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV41 )
| ~ ( SV287 @ SY2542 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2731]) ).
thf(2890,plain,
! [SV41: $i,SV287: $i > $o] :
( ( ( SV287 @ ( sK30_SY2541 @ SV287 @ SV41 ) )
= $true )
| ( ( ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV41 )
| ~ ( SV287 @ SY2542 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2732]) ).
thf(2891,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) ) )
= $false )
| ( ( ~ ( ( ( sK31_SY3079 @ SV624 @ SV44 )
!= SV624 )
| ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) ) ) )
= $true )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2733]) ).
thf(2892,plain,
! [SV44: $i > $o,SV624: $i] :
( ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( ~ ( ( ( sK31_SY3079 @ SV624 @ SV44 )
!= SV624 )
| ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) ) ) )
= $true )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2733]) ).
thf(2893,plain,
! [SV625: $i,SV305: $i,SV64: $i,SV737: $i] :
( ( ( ~ ( in @ SV737 @ ( setminus @ SV64 @ SV305 ) ) )
= $true )
| ( ( ~ ( in @ SV737 @ ( binintersect @ SV305 @ SV625 ) ) )
= $true )
| ( ( in @ SV737 @ SV64 )
= $false )
| ( ( in @ SV625 @ ( powerset @ SV64 ) )
= $false )
| ( ( in @ SV305 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2734]) ).
thf(2894,plain,
! [SV66: $i,SV626: $i,SV307: $i,SV738: $i] :
( ( ( ~ ~ ( in @ SV738 @ ( binunion @ SV307 @ SV626 ) ) )
= $true )
| ( ( ~ ( in @ SV738 @ SV626 ) )
= $true )
| ( ( in @ SV738 @ SV66 )
= $false )
| ( ( in @ SV626 @ ( powerset @ SV66 ) )
= $false )
| ( ( in @ SV307 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2735]) ).
thf(2895,plain,
! [SV69: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ ( sK46_SY2574 @ SV69 @ SV310 ) )
| ~ ( in @ ( sK46_SY2574 @ SV69 @ SV310 ) @ SV69 ) )
= $false )
| ( ( in @ SV310 @ ( setunion @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2736]) ).
thf(2896,plain,
! [SV69: $i,SV759: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ SV759 )
| ~ ( in @ SV759 @ SV69 ) )
= $true )
| ( ( in @ SV310 @ ( setunion @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2737]) ).
thf(2897,plain,
! [SV627: $i,SV311: $i,SV70: $i,SV739: $i] :
( ( ( ~ ( in @ SV739 @ ( setminus @ SV70 @ ( binunion @ SV311 @ SV627 ) ) ) )
= $true )
| ( ( ~ ( in @ SV739 @ SV311 ) )
= $true )
| ( ( in @ SV739 @ SV70 )
= $false )
| ( ( in @ SV627 @ ( powerset @ SV70 ) )
= $false )
| ( ( in @ SV311 @ ( powerset @ SV70 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2738]) ).
thf(2898,plain,
! [SV73: $i,SV314: $i,SV628: $i] :
( ( ( ~ ( in @ ( sK52_SY3083 @ SV628 @ SV314 @ SV73 ) @ SV73 ) )
= $false )
| ( ( in @ SV314 @ ( powerset @ SV628 ) )
= $true )
| ( ( in @ SV628 @ ( powerset @ SV73 ) )
= $false )
| ( ( in @ SV314 @ ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2739]) ).
thf(2899,plain,
! [SV73: $i,SV314: $i,SV628: $i] :
( ( ( ~ ( in @ ( sK52_SY3083 @ SV628 @ SV314 @ SV73 ) @ SV314 )
| ( in @ ( sK52_SY3083 @ SV628 @ SV314 @ SV73 ) @ SV628 ) )
= $false )
| ( ( in @ SV314 @ ( powerset @ SV628 ) )
= $true )
| ( ( in @ SV628 @ ( powerset @ SV73 ) )
= $false )
| ( ( in @ SV314 @ ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2739]) ).
thf(2900,plain,
! [SV686: $o,SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SV686 ) )
= $true )
| ( SV686 = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2740]) ).
thf(2901,plain,
! [SV686: $o,SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SV686 )
| SV686 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2741]) ).
thf(2902,plain,
! [SV686: $o,SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SV686 ) )
= $true )
| ( SV686 = $true )
| ( SV686 = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2742]) ).
thf(2903,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2743]) ).
thf(2904,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $true )
| $true )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2744]) ).
thf(2905,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2745]) ).
thf(2906,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2746]) ).
thf(2907,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $false )
| $false )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2747]) ).
thf(2908,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2748]) ).
thf(2909,plain,
! [SV79: $i,SV318: $i > $o] :
( ( ( in @ ( sK32_SY2591 @ SV318 @ SV79 ) @ SV79 )
= $true )
| ( ( ! [SY2592: $i] :
( ~ ( in @ SY2592 @ SV79 )
| ~ ( SV318 @ SY2592 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2749]) ).
thf(2910,plain,
! [SV79: $i,SV318: $i > $o] :
( ( ( SV318 @ ( sK32_SY2591 @ SV318 @ SV79 ) )
= $true )
| ( ( ! [SY2592: $i] :
( ~ ( in @ SY2592 @ SV79 )
| ~ ( SV318 @ SY2592 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2750]) ).
thf(2911,plain,
! [SV82: $i,SV630: $i] :
( ( ( ~ ( in @ ( sK38_SY2017 @ SV630 @ SV82 ) @ SV82 ) )
= $false )
| ( ( in @ SV630 @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2751]) ).
thf(2912,plain,
! [SV82: $i,SV630: $i] :
( ( ( ~ ~ ~ ! [SY3174: $i] :
~ ~ ( ~ ( in @ SY3174 @ ( sK38_SY2017 @ SV630 @ SV82 ) )
| ~ ( in @ SY3174 @ SV82 ) ) )
= $false )
| ( ( in @ SV630 @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2751]) ).
thf(2913,plain,
! [SV84: $i,SV607: $o,SV322: $i,SV513: $i] :
( ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| SV607 ) )
= $true )
| ( SV607 = $true )
| ( ( in @ SV513 @ SV84 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2752]) ).
thf(2914,plain,
! [SV84: $i,SV607: $o,SV322: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV322 )
| SV607 )
= $false )
| ( SV607 = $true )
| ( SV607 = $false )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(2915,plain,
! [SV84: $i,SV322: $i,SV513: $i] :
( ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV513 @ SV84 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2754]) ).
thf(2916,plain,
! [SV84: $i,SV322: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV322 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2755]) ).
thf(2917,plain,
! [SV84: $i,SV322: $i,SV513: $i] :
( ( ( ~ ( ~ ( in @ SV513 @ SV322 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV513 @ SV84 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2756]) ).
thf(2918,plain,
! [SV84: $i,SV322: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV322 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2757]) ).
thf(2919,plain,
! [SV85: $i,SV631: $i,SV323: $i,SV740: $i] :
( ( ( ~ ~ ( in @ SV740 @ ( binunion @ SV323 @ SV631 ) ) )
= $true )
| ( ( ~ ( in @ SV740 @ SV323 ) )
= $true )
| ( ( in @ SV740 @ SV85 )
= $false )
| ( ( in @ SV631 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV323 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2758]) ).
thf(2920,plain,
! [SV87: $i,SV325: $i > $o,SV687: $i] :
( ( ( ~ ( ~ ( in @ ( sK53_SY2599 @ SV687 @ SV325 @ SV87 ) @ SV87 )
| ~ ~ ( SV325 @ ( sK53_SY2599 @ SV687 @ SV325 @ SV87 ) ) ) )
= $true )
| ( ( SV325 @ SV687 )
= $true )
| ( ( in @ SV687 @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2759]) ).
thf(2921,plain,
! [SV326: $i,SV88: $i] :
( ( ( ~ ( in @ ( sK54_SY2601 @ SV88 @ SV326 ) @ SV326 ) )
= $false )
| ( ( SV88 = SV326 )
= $true )
| ( ( in @ ( sK7_SY2600 @ SV326 @ SV88 ) @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2760]) ).
thf(2922,plain,
! [SV326: $i,SV88: $i] :
( ( ( in @ ( sK54_SY2601 @ SV88 @ SV326 ) @ SV88 )
= $false )
| ( ( SV88 = SV326 )
= $true )
| ( ( in @ ( sK7_SY2600 @ SV326 @ SV88 ) @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2760]) ).
thf(2923,plain,
! [SV326: $i,SV88: $i] :
( ( ( in @ ( sK47_SY2601 @ SV88 @ SV326 ) @ SV326 )
= $true )
| ( ( SV88 = SV326 )
= $true )
| ( ( in @ ( sK7_SY2600 @ SV326 @ SV88 ) @ SV326 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2761]) ).
thf(2924,plain,
! [SV632: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ ( sK62_SY3087 @ SV632 @ SV91 ) )
| ( SV632
= ( sK62_SY3087 @ SV632 @ SV91 ) ) )
= $false )
| ( ( SV91 @ SV632 )
= $false )
| ( ( ! [SY2037: $i,SY2038: $i] :
( ~ ( SV91 @ SY2037 )
| ~ ( SV91 @ SY2038 )
| ( SY2037 = SY2038 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2763]) ).
thf(2925,plain,
! [SV95: $i,SV332: $i,SV516: $i,SV689: $i] :
( ( ( ~ ( in @ ( sK63_SY3141 @ SV689 @ SV516 @ SV332 @ SV95 ) @ SV95 )
| ! [SY3197: $i] :
( ~ ( in @ SY3197 @ SV332 )
| ~ ( in @ ( kpair @ ( sK63_SY3141 @ SV689 @ SV516 @ SV332 @ SV95 ) @ SY3197 ) @ SV516 )
| ( in @ ( kpair @ ( sK63_SY3141 @ SV689 @ SV516 @ SV332 @ SV95 ) @ SY3197 ) @ SV689 ) ) )
= $false )
| ( ( subset @ SV516 @ SV689 )
= $true )
| ( ( subset @ SV689 @ ( cartprod @ SV95 @ SV332 ) )
= $false )
| ( ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2764]) ).
thf(2926,plain,
! [SV100: $i,SV337: $i > $o,SV518: $i] :
( ( ( ~ ( in @ ( sK55_SY2926 @ SV518 @ SV337 @ SV100 ) @ SV100 ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV100
@ ^ [SY2618: $i] : ( SV337 @ SY2618 ) ) )
= $true )
| ( ( SV337 @ SV518 )
= $false )
| ( ( in @ SV518 @ SV100 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2770]) ).
thf(2927,plain,
! [SV100: $i,SV518: $i,SV337: $i > $o] :
( ( ( ~ ( SV337 @ ( sK55_SY2926 @ SV518 @ SV337 @ SV100 ) )
| ( ( sK55_SY2926 @ SV518 @ SV337 @ SV100 )
= SV518 ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV100
@ ^ [SY2618: $i] : ( SV337 @ SY2618 ) ) )
= $true )
| ( ( SV337 @ SV518 )
= $false )
| ( ( in @ SV518 @ SV100 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2770]) ).
thf(2928,plain,
( ( in @ sK39_SY3168 @ ( binunion @ sK2_SY2624 @ sK9_SY2932 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2772]) ).
thf(2929,plain,
( ( ~ ( ~ ( in @ sK39_SY3168 @ sK2_SY2624 )
| sK33_SY3090 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2773]) ).
thf(2930,plain,
( ( ~ ( ~ ( in @ sK39_SY3168 @ sK9_SY2932 )
| sK33_SY3090 )
| sK33_SY3090 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2773]) ).
thf(2931,plain,
! [SV105: $i,SV342: $i,SV522: $i,SV691: $i > $o] :
( ( ( in @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ SV105 )
= $true )
| ( ( ! [SY3145: $i] :
( ~ ( in @ SY3145 @ SV522 )
| ( SV691 @ SY3145 ) ) )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2774]) ).
thf(2932,plain,
! [SV342: $i,SV691: $i > $o,SV522: $i,SV105: $i] :
( ( ( ~ ( in @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) @ SV342 )
| ~ ( in @ ( kpair @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) ) @ SV522 )
| ( SV691 @ ( kpair @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) ) ) )
= $false )
| ( ( ! [SY3145: $i] :
( ~ ( in @ SY3145 @ SV522 )
| ( SV691 @ SY3145 ) ) )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2775]) ).
thf(2933,plain,
! [SV635: $i,SV106: $i > $o] :
( ( ( ~ ( SV106 @ ( sK65_SY3092 @ SV635 @ SV106 ) )
| ( SV635
= ( sK65_SY3092 @ SV635 @ SV106 ) ) )
= $false )
| ( ( SV106 @ SV635 )
= $false )
| ( ( ! [SY2086: $i,SY2087: $i] :
( ~ ( SV106 @ SY2086 )
| ~ ( SV106 @ SY2087 )
| ( SY2086 = SY2087 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2776]) ).
thf(2934,plain,
! [SV636: $i,SV108: $i > $o] :
( ( ( ~ ( SV108 @ ( sK66_SY3093 @ SV636 @ SV108 ) )
| ( SV636
= ( sK66_SY3093 @ SV636 @ SV108 ) ) )
= $false )
| ( ( SV108 @ SV636 )
= $false )
| ( ( SV108
@ ( descr
@ ^ [SY2093: $i] : ( SV108 @ SY2093 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2777]) ).
thf(2935,plain,
! [SV638: $i,SV114: $i > $o] :
( ( ( ~ ( SV114 @ ( sK67_SY3096 @ SV638 @ SV114 ) )
| ( SV638
= ( sK67_SY3096 @ SV638 @ SV114 ) ) )
= $false )
| ( ( SV114 @ SV638 )
= $false )
| ( ( ~ ! [SY2107: $i] :
~ ( SV114 @ SY2107 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2779]) ).
thf(2936,plain,
! [SV741: $i,SV639: $i,SV348: $i,SV115: $i,SV767: $i] :
( ( ( ~ ( in @ SV767 @ SV115 )
| ~ ( in @ SV767 @ ( binintersect @ SV348 @ SV639 ) )
| ( in @ SV767 @ ( binunion @ SV348 @ SV741 ) ) )
= $true )
| ( ( in @ SV741 @ ( powerset @ SV115 ) )
= $false )
| ( ( in @ SV639 @ ( powerset @ SV115 ) )
= $false )
| ( ( in @ SV348 @ ( powerset @ SV115 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2780]) ).
thf(2937,plain,
! [SV350: $i > $o,SV118: $i,SV763: $i] :
( ( ( ~ ( ~ ( in @ SV763 @ SV118 )
| ~ ( SV350 @ SV763 ) ) )
= $false )
| ( ( in @ ( sK10_SY2649 @ SV350 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2781]) ).
thf(2938,plain,
! [SV350: $i > $o,SV118: $i,SV764: $i] :
( ( ( ~ ( ~ ( in @ SV764 @ SV118 )
| ~ ( SV350 @ SV764 ) ) )
= $false )
| ( ( SV350 @ ( sK10_SY2649 @ SV350 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2782]) ).
thf(2939,plain,
! [SV119: $i,SV351: $i > $o,SV692: $i] :
( ( ( ~ ( ~ ( in @ ( sK56_SY2652 @ SV692 @ SV351 @ SV119 ) @ SV119 )
| ~ ~ ( SV351 @ ( sK56_SY2652 @ SV692 @ SV351 @ SV119 ) ) ) )
= $true )
| ( ( SV351 @ SV692 )
= $true )
| ( ( in @ SV692 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2783]) ).
thf(2940,plain,
! [SV120: $i,SV352: $i,SV641: $i,SV742: $i] :
( ( ( ~ ~ ( in @ SV742 @ SV641 ) )
= $true )
| ( ( ~ ( in @ SV742 @ ( binintersect @ SV352 @ SV641 ) ) )
= $true )
| ( ( in @ SV742 @ SV120 )
= $false )
| ( ( in @ SV641 @ ( powerset @ SV120 ) )
= $false )
| ( ( in @ SV352 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2784]) ).
thf(2941,plain,
! [SV353: $i,SV642: $i,SV121: $i,SV765: $i] :
( ( ( ~ ( in @ SV765 @ SV121 ) )
= $true )
| ( ( ~ ( in @ SV765 @ SV642 )
| ( in @ SV765 @ ( setminus @ SV121 @ SV353 ) ) )
= $true )
| ( ( subset @ SV353 @ ( setminus @ SV121 @ SV642 ) )
= $false )
| ( ( in @ SV642 @ ( powerset @ SV121 ) )
= $false )
| ( ( in @ SV353 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2785]) ).
thf(2942,plain,
! [SV126: $i,SV693: $o,SV358: $i,SV529: $i] :
( ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| SV693 ) )
= $true )
| ( SV693 = $true )
| ( ( SV529 = SV126 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2786]) ).
thf(2943,plain,
! [SV126: $i,SV693: $o,SV358: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ SV358 )
| SV693 )
= $false )
| ( SV693 = $true )
| ( SV693 = $false )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2787]) ).
thf(2944,plain,
! [SV126: $i,SV358: $i,SV529: $i] :
( ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( SV529 = SV126 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2788]) ).
thf(2945,plain,
! [SV126: $i,SV358: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ SV358 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(2946,plain,
! [SV126: $i,SV358: $i,SV529: $i] :
( ( ( ~ ( ~ ( in @ SV529 @ SV358 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( SV529 = SV126 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2790]) ).
thf(2947,plain,
! [SV126: $i,SV358: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ SV358 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(2948,plain,
! [SV130: $i,SV644: $i,SV362: $i,SV743: $i] :
( ( ( ~ ~ ( in @ SV743 @ SV362 ) )
= $true )
| ( ( ~ ( in @ SV743 @ ( binintersect @ SV362 @ SV644 ) ) )
= $true )
| ( ( in @ SV743 @ SV130 )
= $false )
| ( ( in @ SV644 @ ( powerset @ SV130 ) )
= $false )
| ( ( in @ SV362 @ ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2793]) ).
thf(2949,plain,
! [SV645: $i,SV363: $i,SV131: $i,SV744: $i] :
( ( ( ~ ( in @ SV744 @ ( setminus @ SV131 @ SV363 ) ) )
= $true )
| ( ( in @ SV744 @ ( setminus @ SV131 @ ( binintersect @ SV363 @ SV645 ) ) )
= $true )
| ( ( in @ SV744 @ SV131 )
= $false )
| ( ( in @ SV645 @ ( powerset @ SV131 ) )
= $false )
| ( ( in @ SV363 @ ( powerset @ SV131 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2794]) ).
thf(2950,plain,
! [SV135: $i,SV745: $i,SV647: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ SV647 ) )
= $true )
| ( ( ~ ( SV367 @ SV745 )
| ( SV647 = SV745 ) )
= $true )
| ( ( in @ SV745 @ SV135 )
= $false )
| ( ( in @ SV647 @ SV135 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV135
@ ^ [SY2676: $i] : ( SV367 @ SY2676 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2795]) ).
thf(2951,plain,
! [SV368: $i,SV136: $i,SV648: $o] :
( ( ( in @ ( sK40_SY3104 @ SV648 @ SV136 @ SV368 ) @ SV136 )
= $true )
| ( SV648 = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2797]) ).
thf(2952,plain,
! [SV368: $i,SV136: $i] :
( ( ( in @ ( sK41_SX0 @ SV136 @ SV368 ) @ SV136 )
= $true )
| ( $true = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2800]) ).
thf(2953,plain,
! [SV368: $i,SV136: $i] :
( ( ( in @ ( sK42_SX0 @ SV136 @ SV368 ) @ SV136 )
= $true )
| ( $false = $true )
| ( ( in @ SV368 @ ( setunion @ SV136 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2803]) ).
thf(2954,plain,
! [SV137: $i,SV746: $i,SV649: $i,SV369: $i] :
( ( ( ~ ( subset @ SV369 @ SV649 ) )
= $true )
| ( ( ~ ~ ( in @ SV746 @ SV649 )
| ~ ( in @ SV746 @ SV369 ) )
= $true )
| ( ( in @ SV746 @ SV137 )
= $false )
| ( ( in @ SV649 @ ( powerset @ SV137 ) )
= $false )
| ( ( in @ SV369 @ ( powerset @ SV137 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2805]) ).
thf(2955,plain,
! [SV146: $i,SV377: $i,SV650: $i] :
( ( ( ~ ( in @ ( sK57_SY3106 @ SV650 @ SV377 @ SV146 ) @ SV146 ) )
= $false )
| ( ( subset @ SV377 @ SV650 )
= $true )
| ( ( in @ SV650 @ ( powerset @ SV146 ) )
= $false )
| ( ( in @ SV377 @ ( powerset @ SV146 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2806]) ).
thf(2956,plain,
! [SV146: $i,SV377: $i,SV650: $i] :
( ( ( ~ ( in @ ( sK57_SY3106 @ SV650 @ SV377 @ SV146 ) @ SV377 )
| ( in @ ( sK57_SY3106 @ SV650 @ SV377 @ SV146 ) @ SV650 ) )
= $false )
| ( ( subset @ SV377 @ SV650 )
= $true )
| ( ( in @ SV650 @ ( powerset @ SV146 ) )
= $false )
| ( ( in @ SV377 @ ( powerset @ SV146 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2806]) ).
thf(2957,plain,
! [SV147: $i] :
( ( ~ ! [SY2953: $i] :
( ~ ( in @ SY2953 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY2188: $i] :
( ~ ( in @ SY2188 @ SY2953 )
| ( in @ SY2188 @ SV147 ) ) )
| ~ ! [SY2955: $i,SY2956: $i] :
( ~ ~ ( ~ ( in @ SY2955 @ SV147 )
| ~ ( in @ SY2956 @ SV147 ) )
| ~ ! [SY2957: $i] :
( ~ ( in @ SY2957 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SY2955 @ SY2957 )
| ( in @ SY2956 @ SY2957 ) )
| ~ ( ~ ( in @ SY2956 @ SY2957 )
| ( in @ SY2955 @ SY2957 ) ) ) )
| ( SY2955 = SY2956 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2807]) ).
thf(2958,plain,
! [SV147: $i,SV768: $i] :
( ( ! [SY3198: $i] :
( ~ ~ ( ~ ( in @ SV768 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3198 @ ( sK3_SY2186 @ SV147 ) ) )
| ! [SY3199: $i] :
( ~ ( in @ SY3199 @ SV768 )
| ( in @ SY3199 @ SY3198 ) )
| ! [SY3200: $i] :
( ~ ( in @ SY3200 @ SY3198 )
| ( in @ SY3200 @ SV768 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2808]) ).
thf(2959,plain,
! [SV147: $i,SV747: $i] :
( ( ( ~ ! [SY3176: $i] :
( ~ ( in @ SY3176 @ SV747 )
| ( in @ SY3176 @ SV147 ) )
| ~ ~ ! [SY3177: $i] :
~ ( in @ SY3177 @ SV747 ) )
= $true )
| ( ( ~ ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2809]) ).
thf(2960,plain,
! [SV748: $i,SV651: $i,SV381: $i,SV151: $i,SV769: $i] :
( ( ( ~ ( in @ SV769 @ SV151 )
| ~ ( in @ SV769 @ ( binintersect @ SV381 @ SV651 ) )
| ( in @ SV769 @ ( binunion @ SV651 @ SV748 ) ) )
= $true )
| ( ( in @ SV748 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV651 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV381 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2810]) ).
thf(2961,plain,
! [SV749: $i,SV652: $i,SV156: $i,SV386: $i] :
( ( ( ~ ( subset @ SV386 @ ( setminus @ SV156 @ SV652 ) ) )
= $true )
| ( ( ~ ( in @ SV749 @ SV652 )
| ~ ( in @ SV749 @ SV386 ) )
= $true )
| ( ( in @ SV749 @ SV156 )
= $false )
| ( ( in @ SV652 @ ( powerset @ SV156 ) )
= $false )
| ( ( in @ SV386 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2811]) ).
thf(2962,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ( SV160 @ ( sK49_SY2231 @ SV653 @ SV160 ) ) )
= $false )
| ( ( ~ ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2812]) ).
thf(2963,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ( SV160 @ ( sK58_SY3190 @ SV653 @ SV160 ) )
| ( ( sK49_SY2231 @ SV653 @ SV160 )
= ( sK58_SY3190 @ SV653 @ SV160 ) ) )
= $false )
| ( ( ~ ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2812]) ).
thf(2964,plain,
! [SV657: $i,SV395: $i,SV167: $i,SV750: $i] :
( ( ( ~ ( in @ SV750 @ ( setminus @ SV167 @ ( binunion @ SV395 @ SV657 ) ) ) )
= $true )
| ( ( in @ SV750 @ ( setminus @ SV167 @ SV395 ) )
= $true )
| ( ( in @ SV750 @ SV167 )
= $false )
| ( ( in @ SV657 @ ( powerset @ SV167 ) )
= $false )
| ( ( in @ SV395 @ ( powerset @ SV167 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2814]) ).
thf(2965,plain,
! [SV168: $i,SV396: $i,SV548: $i,SV697: $i] :
( ( ( ~ ( in @ ( sK68_SY3146 @ SV697 @ SV548 @ SV396 @ SV168 ) @ SV168 )
| ( ( ap @ SV168 @ SV396 @ SV548 @ ( sK68_SY3146 @ SV697 @ SV548 @ SV396 @ SV168 ) )
= ( ap @ SV168 @ SV396 @ SV697 @ ( sK68_SY3146 @ SV697 @ SV548 @ SV396 @ SV168 ) ) ) )
= $false )
| ( ( SV548 = SV697 )
= $true )
| ( ( func @ SV168 @ SV396 @ SV697 )
= $false )
| ( ( func @ SV168 @ SV396 @ SV548 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2815]) ).
thf(2966,plain,
! [SV701: $i,SV553: $i,SV171: $i,SV399: $o] :
( ( SV399 = $true )
| ( ( ( dsetconstr @ SV171
@ ^ [SY3147: $i] :
( ~ ( ~ SV399
| ( SY3147 != SV553 ) )
| ~ ( ~ ~ SV399
| ( SY3147 != SV701 ) ) ) )
= ( setadjoin @ SV701 @ emptyset ) )
= $true )
| ( ( in @ SV701 @ SV171 )
= $false )
| ( ( in @ SV553 @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2816]) ).
thf(2967,plain,
! [SV702: $i,SV554: $i,SV171: $i] :
( ( $true = $true )
| ( ( ( dsetconstr @ SV171
@ ^ [SY3148: $i] :
( ~ ( ~ $true
| ( SY3148 != SV554 ) )
| ~ ( ~ ~ $true
| ( SY3148 != SV702 ) ) ) )
= ( setadjoin @ SV702 @ emptyset ) )
= $true )
| ( ( in @ SV702 @ SV171 )
= $false )
| ( ( in @ SV554 @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2817]) ).
thf(2968,plain,
! [SV703: $i,SV555: $i,SV171: $i] :
( ( $false = $true )
| ( ( ( dsetconstr @ SV171
@ ^ [SY3149: $i] :
( ~ ( ~ $false
| ( SY3149 != SV555 ) )
| ~ ( ~ ~ $false
| ( SY3149 != SV703 ) ) ) )
= ( setadjoin @ SV703 @ emptyset ) )
= $true )
| ( ( in @ SV703 @ SV171 )
= $false )
| ( ( in @ SV555 @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2818]) ).
thf(2969,plain,
! [SV180: $i,SV706: $i,SV408: $i > $o] :
( ( ( SV408 @ SV706 )
= $false )
| ( ( in @ SV706 @ SV180 )
= $false )
| ( ( ( ( dsetconstr @ SV180
@ ^ [SY2739: $i] : ( SV408 @ SY2739 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2821]) ).
thf(2970,plain,
! [SV409: $i > $o,SV181: $i,SV770: $i] :
( ( ( ~ ~ ( ~ ( in @ SV770 @ SV181 )
| ~ ( SV409 @ SV770 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( in @ ( sK12_SY2740 @ SV409 @ SV181 ) @ SV181 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2822]) ).
thf(2971,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ( ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( in @ ( sK34_SY3112 @ SV409 @ SV181 ) @ SV181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2823]) ).
thf(2972,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( SV409 @ ( sK12_SY2740 @ SV409 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2824]) ).
thf(2973,plain,
! [SV181: $i,SV409: $i > $o] :
( ( ( SV409 @ ( sK34_SY3112 @ SV409 @ SV181 ) )
= $true )
| ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) )
| ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2825]) ).
thf(2974,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( ( sK12_SY2740 @ SV409 @ SV181 )
= ( sK34_SY3112 @ SV409 @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2826]) ).
thf(2975,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2827]) ).
thf(2976,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) ) )
= $false )
| ( ( ~ ( ~ ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
| ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2828]) ).
thf(2977,plain,
! [SV183: $i > $o,SV411: $i > $o] :
( ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( ~ ( ~ ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
| ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2828]) ).
thf(2978,plain,
! [SV185: $i,SV561: $i,SV707: $i,SV413: $i,SV760: $i] :
( ( ( in @ SV760 @ SV413 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV707 @ SV760 ) @ SV561 )
| ( ( ap @ SV185 @ SV413 @ SV561 @ SV707 )
= SV760 ) )
= $true )
| ( ( in @ SV707 @ SV185 )
= $false )
| ( ( in @ SV561 @ ( funcSet @ SV185 @ SV413 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2829]) ).
thf(2979,plain,
! [SV186: $i,SV414: $i,SV659: $i] :
( ( ( ~ ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV186 ) )
= $false )
| ( ( ~ ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV186 )
| ~ ( in @ SY3115 @ SV659 )
| ( in @ SY3115 @ SV414 ) )
| ( SV414 = SV659 ) )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2830]) ).
thf(2980,plain,
! [SV186: $i,SV414: $i,SV659: $i] :
( ( ( ~ ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV414 )
| ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV659 ) )
= $false )
| ( ( ~ ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV186 )
| ~ ( in @ SY3115 @ SV659 )
| ( in @ SY3115 @ SV414 ) )
| ( SV414 = SV659 ) )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2830]) ).
thf(2981,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK69_SY3116 @ SV660 @ SV188 ) )
| ( SV660
= ( sK69_SY3116 @ SV660 @ SV188 ) ) )
= $false )
| ( ( SV188 @ SV660 )
= $false )
| ( ( ~ ! [SY2316: $i] :
~ ~ ( ~ ( SV188 @ SY2316 )
| ~ ! [SY2317: $i] :
( ~ ( SV188 @ SY2317 )
| ( SY2316 = SY2317 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2831]) ).
thf(2982,plain,
! [SV752: $i,SV661: $i,SV418: $i,SV191: $i,SV771: $i] :
( ( ( ~ ( in @ SV771 @ SV191 )
| ~ ( in @ SV771 @ ( binintersect @ SV418 @ SV661 ) )
| ( in @ SV771 @ ( binintersect @ ( binunion @ SV418 @ SV752 ) @ ( binunion @ SV661 @ SV752 ) ) ) )
= $true )
| ( ( in @ SV752 @ ( powerset @ SV191 ) )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV191 ) )
= $false )
| ( ( in @ SV418 @ ( powerset @ SV191 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(2983,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2833]) ).
thf(2984,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2834]) ).
thf(2985,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) ) )
= $false )
| ( ( ~ ( ~ ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
| ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2835]) ).
thf(2986,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( ~ ( ~ ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
| ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2835]) ).
thf(2987,plain,
! [SV196: $i,SV424: $i,SV566: $i] :
( ( ( in @ ( sK35_SY2993 @ SV566 @ SV424 @ SV196 ) @ SV196 )
= $true )
| ( ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2836]) ).
thf(2988,plain,
! [SV196: $i,SV566: $i,SV424: $i] :
( ( ( ~ ! [SY3169: $i] :
~ ~ ( ~ ( in @ SY3169 @ SV424 )
| ( SV566
!= ( kpair @ ( sK35_SY2993 @ SV566 @ SV424 @ SV196 ) @ SY3169 ) ) ) )
= $true )
| ( ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2837]) ).
thf(2989,plain,
! [SV198: $i,SV426: $i,SV570: $i,SV712: $i] :
( ( ( ~ ( in @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SV198 )
| ! [SY3201: $i] :
( ~ ( in @ SY3201 @ SV426 )
| ~ ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SY3201 ) @ SV570 )
| ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SY3201 ) @ SV712 ) ) )
= $false )
| ( ( ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) )
| ( SV570 = SV712 ) )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2841]) ).
thf(2990,plain,
! [SV200: $i,SV428: $i,SV571: $i,SV713: $i > $o] :
( ( ( in @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ SV200 )
= $true )
| ( ( ! [SY3157: $i] :
( ~ ( in @ SY3157 @ SV571 )
| ( SV713 @ SY3157 ) ) )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2842]) ).
thf(2991,plain,
! [SV428: $i,SV713: $i > $o,SV571: $i,SV200: $i] :
( ( ( ~ ( in @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) @ SV428 )
| ~ ( in @ ( kpair @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) ) @ SV571 )
| ( SV713 @ ( kpair @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) ) ) )
= $false )
| ( ( ! [SY3157: $i] :
( ~ ( in @ SY3157 @ SV571 )
| ( SV713 @ SY3157 ) ) )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2843]) ).
thf(2992,plain,
! [SV201: $i,SV714: $i,SV429: $i > $o] :
( ( ( ~ ( SV429 @ SV714 ) )
= $false )
| ( ( in @ SV714 @ SV201 )
= $false )
| ( ( ~ ! [SY2794: $i] :
( ~ ( in @ SY2794 @ SV201 )
| ( SV429 @ SY2794 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2844]) ).
thf(2993,plain,
! [SV574: $i > $i,SV433: $i,SV209: $i,SV761: $i] :
( ( ( in @ SV761 @ SV209 )
= $false )
| ( ( ( ap @ SV209 @ SV433
@ ( lam @ SV209 @ SV433
@ ^ [SY3012: $i] : ( SV574 @ SY3012 ) )
@ SV761 )
= ( SV574 @ SV761 ) )
= $true )
| ( ( in @ ( sK25_SY3010 @ SV433 @ SV574 @ SV209 ) @ SV209 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2845]) ).
thf(2994,plain,
! [SV436: $i > $o,SV212: $i,SV772: $i] :
( ( ( ~ ~ ( ~ ( in @ SV772 @ SV212 )
| ~ ( SV436 @ SV772 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( in @ ( sK15_SY2806 @ SV436 @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(2995,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ( ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( in @ ( sK36_SY3121 @ SV436 @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2848]) ).
thf(2996,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( SV436 @ ( sK15_SY2806 @ SV436 @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2849]) ).
thf(2997,plain,
! [SV212: $i,SV436: $i > $o] :
( ( ( SV436 @ ( sK36_SY3121 @ SV436 @ SV212 ) )
= $true )
| ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) )
| ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2850]) ).
thf(2998,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( ( sK15_SY2806 @ SV436 @ SV212 )
= ( sK36_SY3121 @ SV436 @ SV212 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2851]) ).
thf(2999,plain,
! [SV215: $i] :
( ( ( ~ ( in @ ( sK44_SY2395 @ SV215 ) @ omega )
| ~ ( in @ ( sK44_SY2395 @ SV215 ) @ SV215 ) )
= $false )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( ! [SY2396: $i] :
( ~ ( in @ SY2396 @ omega )
| ( in @ SY2396 @ SV215 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2852]) ).
thf(3000,plain,
! [SV215: $i,SV766: $i] :
( ( ( ~ ( in @ SV766 @ omega ) )
= $true )
| ( ( in @ SV766 @ SV215 )
= $true )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( in @ ( setadjoin @ ( sK44_SY2395 @ SV215 ) @ ( sK44_SY2395 @ SV215 ) ) @ SV215 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2853]) ).
thf(3001,plain,
! [SV440: $i,SV217: $i,SV735: $i,SV616: $i,SV577: $i > $i > $o] :
( ( ( SV577 @ SV616 @ SV735 )
= $false )
| ( ( in @ ( kpair @ SV616 @ SV735 )
@ ( dpsetconstr @ SV217 @ SV440
@ ^ [SY3017: $i,SY3018: $i] : ( SV577 @ SY3017 @ SY3018 ) ) )
= $true )
| ( ( in @ SV735 @ SV440 )
= $false )
| ( ( in @ SV616 @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2854]) ).
thf(3002,plain,
! [SV219: $i,SV442: $i,SV581: $i,SV720: $i] :
( ( ( ~ ( in @ ( sK72_SY3158 @ SV720 @ SV581 @ SV442 @ SV219 ) @ SV219 )
| ( ( ap @ SV219 @ SV442 @ SV581 @ ( sK72_SY3158 @ SV720 @ SV581 @ SV442 @ SV219 ) )
= ( ap @ SV219 @ SV442 @ SV720 @ ( sK72_SY3158 @ SV720 @ SV581 @ SV442 @ SV219 ) ) ) )
= $false )
| ( ( SV581 = SV720 )
= $true )
| ( ( in @ SV720 @ ( funcSet @ SV219 @ SV442 ) )
= $false )
| ( ( in @ SV581 @ ( funcSet @ SV219 @ SV442 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2855]) ).
thf(3003,plain,
! [SV582: $i > $i > $o,SV443: $i,SV220: $i,SV736: $i,SV617: $i] :
( ( ( in @ ( kpair @ SV617 @ SV736 )
@ ( dpsetconstr @ SV220 @ SV443
@ ^ [SY3026: $i,SY3027: $i] : ( SV582 @ SY3026 @ SY3027 ) ) )
= $false )
| ( ( SV582 @ SV617 @ SV736 )
= $true )
| ( ( in @ SV736 @ SV443 )
= $false )
| ( ( in @ SV617 @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2856]) ).
thf(3004,plain,
! [SV225: $i,SV448: $i] :
( ( ( ~ ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 )
| ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 ) )
= $false )
| ( ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 )
= $true )
| ( ( SV225 = SV448 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2859]) ).
thf(3005,plain,
! [SV225: $i,SV448: $i] :
( ( ( ~ ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 ) )
= $false )
| ( ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 )
= $false )
| ( ( SV225 = SV448 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2860]) ).
thf(3006,plain,
! [SV225: $i,SV448: $i] :
( ( ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 )
= $false )
| ( ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 )
= $false )
| ( ( SV225 = SV448 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2860]) ).
thf(3007,plain,
! [SV591: $i > $i,SV456: $i,SV234: $i,SV762: $i] :
( ( ( in @ SV762 @ SV234 )
= $false )
| ( ( ( ap @ SV234 @ SV456
@ ( lam @ SV234 @ SV456
@ ^ [SY3038: $i] : ( SV591 @ SY3038 ) )
@ SV762 )
= ( SV591 @ SV762 ) )
= $true )
| ( ( in @ ( sK28_SY3036 @ SV456 @ SV591 @ SV234 ) @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2868]) ).
thf(3008,plain,
! [SV235: $i,SV457: $i] :
( ( ( in @ ( sK37_SY2850 @ SV457 @ SV235 ) @ SV235 )
= $true )
| ( ( ( binintersect @ SV235 @ SV457 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2870]) ).
thf(3009,plain,
! [SV235: $i,SV457: $i] :
( ( ( in @ ( sK37_SY2850 @ SV457 @ SV235 ) @ SV457 )
= $true )
| ( ( ( binintersect @ SV235 @ SV457 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2871]) ).
thf(3010,plain,
! [SV243: $i,SV756: $i,SV667: $i,SV465: $i] :
( ( ( ~ ( in @ SV465 @ ( powerset @ SV667 ) ) )
= $true )
| ( ( ~ ( in @ SV756 @ SV465 )
| ( in @ SV756 @ SV667 ) )
= $true )
| ( ( in @ SV756 @ SV243 )
= $false )
| ( ( in @ SV667 @ ( powerset @ SV243 ) )
= $false )
| ( ( in @ SV465 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2872]) ).
thf(3011,plain,
! [SV597: $i,SV244: $i,SV725: $i,SV466: $o] :
( ( SV466 = $true )
| ( ( in @ SV725
@ ( dsetconstr @ SV244
@ ^ [SY3162: $i] :
( ~ ( ~ SV466
| ( SY3162 != SV597 ) )
| ~ ( ~ ~ SV466
| ( SY3162 != SV725 ) ) ) ) )
= $true )
| ( ( in @ SV725 @ SV244 )
= $false )
| ( ( in @ SV597 @ SV244 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2873]) ).
thf(3012,plain,
! [SV598: $i,SV244: $i,SV726: $i] :
( ( $true = $true )
| ( ( in @ SV726
@ ( dsetconstr @ SV244
@ ^ [SY3163: $i] :
( ~ ( ~ $true
| ( SY3163 != SV598 ) )
| ~ ( ~ ~ $true
| ( SY3163 != SV726 ) ) ) ) )
= $true )
| ( ( in @ SV726 @ SV244 )
= $false )
| ( ( in @ SV598 @ SV244 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2874]) ).
thf(3013,plain,
! [SV599: $i,SV244: $i,SV727: $i] :
( ( $false = $true )
| ( ( in @ SV727
@ ( dsetconstr @ SV244
@ ^ [SY3164: $i] :
( ~ ( ~ $false
| ( SY3164 != SV599 ) )
| ~ ( ~ ~ $false
| ( SY3164 != SV727 ) ) ) ) )
= $true )
| ( ( in @ SV727 @ SV244 )
= $false )
| ( ( in @ SV599 @ SV244 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2875]) ).
thf(3014,plain,
! [SV247: $i,SV469: $i,SV600: $i,SV728: $i] :
( ( ( ~ ( in @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) @ SV247 )
| ( ( ap @ SV247 @ SV469 @ SV600 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) )
= ( ap @ SV247 @ SV469 @ SV728 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) ) ) )
= $false )
| ( ( ! [SY3166: $i] :
( ~ ( in @ SY3166 @ SV247 )
| ! [SY3167: $i] :
( ~ ( in @ SY3167 @ SV469 )
| ~ ( in @ ( kpair @ SY3166 @ SY3167 ) @ SV728 )
| ( in @ ( kpair @ SY3166 @ SY3167 ) @ SV600 ) ) ) )
= $true )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2876]) ).
thf(3015,plain,
! [SV471: $i,SV249: $i > $i > $o,SV773: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
| ~ ! [SY3202: $i] :
~ ~ ( ~ ( in @ SY3202 @ SV471 )
| ~ ( SV249 @ SY3202 @ SV773 ) ) )
| ~ ( ~ ~ ! [SY3203: $i] :
~ ~ ( ~ ( in @ SY3203 @ SV471 )
| ~ ( SV249 @ SY3203 @ SV773 ) )
| ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) ) ) ) )
= $true )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(3016,plain,
! [SV757: $i,SV471: $i,SV249: $i > $i > $o] :
( ( ( ~ ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 ) )
= $true )
| ( ( ~ ! [SY3187: $i] :
( ~ ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SY3187 )
| ( SV757 = SY3187 ) ) )
= $true )
| ( ( ~ ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2878]) ).
thf(3017,plain,
! [SV729: $i,SV601: $i,SV252: $i,SV474: $o] :
( ( SV474 = $true )
| ( ( ( if @ SV252 @ SV474 @ SV601 @ SV729 )
= SV729 )
= $true )
| ( ( in @ SV729 @ SV252 )
= $false )
| ( ( in @ SV601 @ SV252 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2879]) ).
thf(3018,plain,
! [SV730: $i,SV602: $i,SV252: $i] :
( ( $true = $true )
| ( ( ( if @ SV252 @ $true @ SV602 @ SV730 )
= SV730 )
= $true )
| ( ( in @ SV730 @ SV252 )
= $false )
| ( ( in @ SV602 @ SV252 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2880]) ).
thf(3019,plain,
! [SV731: $i,SV603: $i,SV252: $i] :
( ( $false = $true )
| ( ( ( if @ SV252 @ $false @ SV603 @ SV731 )
= SV731 )
= $true )
| ( ( in @ SV731 @ SV252 )
= $false )
| ( ( in @ SV603 @ SV252 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2881]) ).
thf(3020,plain,
! [SV476: $i,SV733: $i,SV254: $i,SV669: $i] :
( ( ( ~ ( in @ SV669 @ SV254 )
| ( in @ SV733 @ SV476 ) )
= $true )
| ( ( SV669 = SV733 )
= $false )
| ( ( SV254 = SV476 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2882]) ).
thf(3021,plain,
! [SV254: $i,SV669: $i,SV476: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV476 )
| ( in @ SV669 @ SV254 ) )
= $true )
| ( ( SV669 = SV733 )
= $false )
| ( ( SV254 = SV476 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2883]) ).
thf(3022,plain,
! [SV670: $i,SV256: $i > $o] :
( ( ( ~ ( SV256 @ ( sK74_SY3127 @ SV670 @ SV256 ) )
| ( SV670
= ( sK74_SY3127 @ SV670 @ SV256 ) ) )
= $false )
| ( ( SV256 @ SV670 )
= $false )
| ( ( ~ ! [SY2511: $i] :
~ ! [SY2512: $i] :
~ ( ~ ( ~ ( SV256 @ SY2512 )
| ( SY2512 = SY2511 ) )
| ~ ( ( SY2512 != SY2511 )
| ( SV256 @ SY2512 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2884]) ).
thf(3023,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ~ ( SV35 @ ( sK60_SY3073 @ SV621 @ SV35 ) ) )
= $false )
| ( ( SV35 @ SV621 )
= $false )
| ( ( ~ ! [SY1902: $i] :
~ ~ ( ~ ( SV35 @ SY1902 )
| ~ ! [SY1903: $i] :
( ~ ( SV35 @ SY1903 )
| ( SY1902 = SY1903 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2885]) ).
thf(3024,plain,
! [SV35: $i > $o,SV621: $i] :
( ( ( SV621
= ( sK60_SY3073 @ SV621 @ SV35 ) )
= $false )
| ( ( SV35 @ SV621 )
= $false )
| ( ( ~ ! [SY1902: $i] :
~ ~ ( ~ ( SV35 @ SY1902 )
| ~ ! [SY1903: $i] :
( ~ ( SV35 @ SY1903 )
| ( SY1902 = SY1903 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2885]) ).
thf(3025,plain,
! [SV284: $i,SV38: $i,SV484: $i,SV758: $i,SV672: $i] :
( ( ( ~ ( in @ ( kpair @ SV672 @ SV758 ) @ SV484 ) )
= $true )
| ( ( ( ap @ SV38 @ SV284 @ SV484 @ SV672 )
= SV758 )
= $true )
| ( ( in @ SV758 @ SV284 )
= $false )
| ( ( in @ SV672 @ SV38 )
= $false )
| ( ( func @ SV38 @ SV284 @ SV484 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2886]) ).
thf(3026,plain,
! [SV286: $i,SV676: $i > $o,SV623: $i > $o,SV40: $i] :
( ( ( ~ ( in @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) @ SV286 ) )
= $false )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2888]) ).
thf(3027,plain,
! [SV40: $i,SV286: $i,SV623: $i > $o,SV676: $i > $o] :
( ( ( ( ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 )
!= ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
| ~ ( ~ ( ~ ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) )
| ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) ) )
| ~ ( ~ ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
| ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2888]) ).
thf(3028,plain,
! [SV287: $i > $o,SV41: $i,SV774: $i] :
( ( ( ~ ( in @ SV774 @ SV41 )
| ~ ( SV287 @ SV774 ) )
= $true )
| ( ( in @ ( sK30_SY2541 @ SV287 @ SV41 ) @ SV41 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2889]) ).
thf(3029,plain,
! [SV287: $i > $o,SV41: $i,SV775: $i] :
( ( ( ~ ( in @ SV775 @ SV41 )
| ~ ( SV287 @ SV775 ) )
= $true )
| ( ( SV287 @ ( sK30_SY2541 @ SV287 @ SV41 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2890]) ).
thf(3030,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( ~ ( ( ( sK31_SY3079 @ SV624 @ SV44 )
!= SV624 )
| ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) ) ) )
= $true )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2891]) ).
thf(3031,plain,
! [SV44: $i > $o,SV624: $i] :
( ( ( ( ( sK31_SY3079 @ SV624 @ SV44 )
!= SV624 )
| ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) ) )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2892]) ).
thf(3032,plain,
! [SV625: $i,SV305: $i,SV64: $i,SV737: $i] :
( ( ( in @ SV737 @ ( setminus @ SV64 @ SV305 ) )
= $false )
| ( ( ~ ( in @ SV737 @ ( binintersect @ SV305 @ SV625 ) ) )
= $true )
| ( ( in @ SV737 @ SV64 )
= $false )
| ( ( in @ SV625 @ ( powerset @ SV64 ) )
= $false )
| ( ( in @ SV305 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2893]) ).
thf(3033,plain,
! [SV66: $i,SV626: $i,SV307: $i,SV738: $i] :
( ( ( ~ ( in @ SV738 @ ( binunion @ SV307 @ SV626 ) ) )
= $false )
| ( ( ~ ( in @ SV738 @ SV626 ) )
= $true )
| ( ( in @ SV738 @ SV66 )
= $false )
| ( ( in @ SV626 @ ( powerset @ SV66 ) )
= $false )
| ( ( in @ SV307 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2894]) ).
thf(3034,plain,
! [SV69: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ ( sK46_SY2574 @ SV69 @ SV310 ) ) )
= $false )
| ( ( in @ SV310 @ ( setunion @ SV69 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2895]) ).
thf(3035,plain,
! [SV310: $i,SV69: $i] :
( ( ( ~ ( in @ ( sK46_SY2574 @ SV69 @ SV310 ) @ SV69 ) )
= $false )
| ( ( in @ SV310 @ ( setunion @ SV69 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2895]) ).
thf(3036,plain,
! [SV69: $i,SV759: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ SV759 ) )
= $true )
| ( ( ~ ( in @ SV759 @ SV69 ) )
= $true )
| ( ( in @ SV310 @ ( setunion @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2896]) ).
thf(3037,plain,
! [SV627: $i,SV311: $i,SV70: $i,SV739: $i] :
( ( ( in @ SV739 @ ( setminus @ SV70 @ ( binunion @ SV311 @ SV627 ) ) )
= $false )
| ( ( ~ ( in @ SV739 @ SV311 ) )
= $true )
| ( ( in @ SV739 @ SV70 )
= $false )
| ( ( in @ SV627 @ ( powerset @ SV70 ) )
= $false )
| ( ( in @ SV311 @ ( powerset @ SV70 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2897]) ).
thf(3038,plain,
! [SV73: $i,SV314: $i,SV628: $i] :
( ( ( in @ ( sK52_SY3083 @ SV628 @ SV314 @ SV73 ) @ SV73 )
= $true )
| ( ( in @ SV314 @ ( powerset @ SV628 ) )
= $true )
| ( ( in @ SV628 @ ( powerset @ SV73 ) )
= $false )
| ( ( in @ SV314 @ ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2898]) ).
thf(3039,plain,
! [SV73: $i,SV314: $i,SV628: $i] :
( ( ( ~ ( in @ ( sK52_SY3083 @ SV628 @ SV314 @ SV73 ) @ SV314 ) )
= $false )
| ( ( in @ SV314 @ ( powerset @ SV628 ) )
= $true )
| ( ( in @ SV628 @ ( powerset @ SV73 ) )
= $false )
| ( ( in @ SV314 @ ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2899]) ).
thf(3040,plain,
! [SV73: $i,SV314: $i,SV628: $i] :
( ( ( in @ ( sK52_SY3083 @ SV628 @ SV314 @ SV73 ) @ SV628 )
= $false )
| ( ( in @ SV314 @ ( powerset @ SV628 ) )
= $true )
| ( ( in @ SV628 @ ( powerset @ SV73 ) )
= $false )
| ( ( in @ SV314 @ ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2899]) ).
thf(3041,plain,
! [SV686: $o,SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SV686 )
= $false )
| ( SV686 = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2900]) ).
thf(3042,plain,
! [SV686: $o,SV74: $i,SV315: $i,SV509: $i] :
( ( ( in @ SV509 @ SV315 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SV686 )
| SV686 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2901]) ).
thf(3043,plain,
! [SV686: $o,SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SV686 )
= $false )
| ( SV686 = $true )
| ( SV686 = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2902]) ).
thf(3044,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2903]) ).
thf(3045,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( in @ SV509 @ SV315 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $true )
| $true )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2904]) ).
thf(3046,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2905]) ).
thf(3047,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2906]) ).
thf(3048,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( in @ SV509 @ SV315 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $false )
| $false )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2907]) ).
thf(3049,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2908]) ).
thf(3050,plain,
! [SV318: $i > $o,SV79: $i,SV776: $i] :
( ( ( ~ ( in @ SV776 @ SV79 )
| ~ ( SV318 @ SV776 ) )
= $true )
| ( ( in @ ( sK32_SY2591 @ SV318 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2909]) ).
thf(3051,plain,
! [SV318: $i > $o,SV79: $i,SV777: $i] :
( ( ( ~ ( in @ SV777 @ SV79 )
| ~ ( SV318 @ SV777 ) )
= $true )
| ( ( SV318 @ ( sK32_SY2591 @ SV318 @ SV79 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(3052,plain,
! [SV82: $i,SV630: $i] :
( ( ( in @ ( sK38_SY2017 @ SV630 @ SV82 ) @ SV82 )
= $true )
| ( ( in @ SV630 @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2911]) ).
thf(3053,plain,
! [SV82: $i,SV630: $i] :
( ( ( ~ ~ ! [SY3174: $i] :
~ ~ ( ~ ( in @ SY3174 @ ( sK38_SY2017 @ SV630 @ SV82 ) )
| ~ ( in @ SY3174 @ SV82 ) ) )
= $true )
| ( ( in @ SV630 @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2912]) ).
thf(3054,plain,
! [SV84: $i,SV607: $o,SV322: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV322 )
| SV607 )
= $false )
| ( SV607 = $true )
| ( ( in @ SV513 @ SV84 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2913]) ).
thf(3055,plain,
! [SV84: $i,SV607: $o,SV322: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV322 ) )
= $false )
| ( SV607 = $true )
| ( SV607 = $false )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2914]) ).
thf(3056,plain,
! [SV322: $i,SV84: $i,SV513: $i,SV607: $o] :
( ( SV607 = $false )
| ( SV607 = $true )
| ( SV607 = $false )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2914]) ).
thf(3057,plain,
! [SV84: $i,SV322: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV322 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV513 @ SV84 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2915]) ).
thf(3058,plain,
! [SV84: $i,SV322: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV322 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2916]) ).
thf(3059,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2916]) ).
thf(3060,plain,
! [SV84: $i,SV322: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV322 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV513 @ SV84 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2917]) ).
thf(3061,plain,
! [SV84: $i,SV322: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV322 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2918]) ).
thf(3062,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2918]) ).
thf(3063,plain,
! [SV85: $i,SV631: $i,SV323: $i,SV740: $i] :
( ( ( ~ ( in @ SV740 @ ( binunion @ SV323 @ SV631 ) ) )
= $false )
| ( ( ~ ( in @ SV740 @ SV323 ) )
= $true )
| ( ( in @ SV740 @ SV85 )
= $false )
| ( ( in @ SV631 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV323 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2919]) ).
thf(3064,plain,
! [SV87: $i,SV325: $i > $o,SV687: $i] :
( ( ( ~ ( in @ ( sK53_SY2599 @ SV687 @ SV325 @ SV87 ) @ SV87 )
| ~ ~ ( SV325 @ ( sK53_SY2599 @ SV687 @ SV325 @ SV87 ) ) )
= $false )
| ( ( SV325 @ SV687 )
= $true )
| ( ( in @ SV687 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2920]) ).
thf(3065,plain,
! [SV326: $i,SV88: $i] :
( ( ( in @ ( sK54_SY2601 @ SV88 @ SV326 ) @ SV326 )
= $true )
| ( ( SV88 = SV326 )
= $true )
| ( ( in @ ( sK7_SY2600 @ SV326 @ SV88 ) @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2921]) ).
thf(3066,plain,
! [SV632: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ ( sK62_SY3087 @ SV632 @ SV91 ) ) )
= $false )
| ( ( SV91 @ SV632 )
= $false )
| ( ( ! [SY2037: $i,SY2038: $i] :
( ~ ( SV91 @ SY2037 )
| ~ ( SV91 @ SY2038 )
| ( SY2037 = SY2038 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2924]) ).
thf(3067,plain,
! [SV91: $i > $o,SV632: $i] :
( ( ( SV632
= ( sK62_SY3087 @ SV632 @ SV91 ) )
= $false )
| ( ( SV91 @ SV632 )
= $false )
| ( ( ! [SY2037: $i,SY2038: $i] :
( ~ ( SV91 @ SY2037 )
| ~ ( SV91 @ SY2038 )
| ( SY2037 = SY2038 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2924]) ).
thf(3068,plain,
! [SV95: $i,SV332: $i,SV516: $i,SV689: $i] :
( ( ( ~ ( in @ ( sK63_SY3141 @ SV689 @ SV516 @ SV332 @ SV95 ) @ SV95 ) )
= $false )
| ( ( subset @ SV516 @ SV689 )
= $true )
| ( ( subset @ SV689 @ ( cartprod @ SV95 @ SV332 ) )
= $false )
| ( ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2925]) ).
thf(3069,plain,
! [SV95: $i,SV516: $i,SV689: $i,SV332: $i] :
( ( ( ! [SY3197: $i] :
( ~ ( in @ SY3197 @ SV332 )
| ~ ( in @ ( kpair @ ( sK63_SY3141 @ SV689 @ SV516 @ SV332 @ SV95 ) @ SY3197 ) @ SV516 )
| ( in @ ( kpair @ ( sK63_SY3141 @ SV689 @ SV516 @ SV332 @ SV95 ) @ SY3197 ) @ SV689 ) ) )
= $false )
| ( ( subset @ SV516 @ SV689 )
= $true )
| ( ( subset @ SV689 @ ( cartprod @ SV95 @ SV332 ) )
= $false )
| ( ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2925]) ).
thf(3070,plain,
! [SV100: $i,SV337: $i > $o,SV518: $i] :
( ( ( in @ ( sK55_SY2926 @ SV518 @ SV337 @ SV100 ) @ SV100 )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV100
@ ^ [SY2618: $i] : ( SV337 @ SY2618 ) ) )
= $true )
| ( ( SV337 @ SV518 )
= $false )
| ( ( in @ SV518 @ SV100 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2926]) ).
thf(3071,plain,
! [SV100: $i,SV518: $i,SV337: $i > $o] :
( ( ( ~ ( SV337 @ ( sK55_SY2926 @ SV518 @ SV337 @ SV100 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV100
@ ^ [SY2618: $i] : ( SV337 @ SY2618 ) ) )
= $true )
| ( ( SV337 @ SV518 )
= $false )
| ( ( in @ SV518 @ SV100 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2927]) ).
thf(3072,plain,
! [SV100: $i,SV337: $i > $o,SV518: $i] :
( ( ( ( sK55_SY2926 @ SV518 @ SV337 @ SV100 )
= SV518 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV100
@ ^ [SY2618: $i] : ( SV337 @ SY2618 ) ) )
= $true )
| ( ( SV337 @ SV518 )
= $false )
| ( ( in @ SV518 @ SV100 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2927]) ).
thf(3073,plain,
( ( ~ ( in @ sK39_SY3168 @ sK2_SY2624 )
| sK33_SY3090 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2929]) ).
thf(3074,plain,
( ( ~ ( ~ ( in @ sK39_SY3168 @ sK9_SY2932 )
| sK33_SY3090 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2930]) ).
thf(3075,plain,
sK33_SY3090 = $false,
inference(extcnf_or_neg,[status(thm)],[2930]) ).
thf(3076,plain,
! [SV105: $i,SV342: $i,SV691: $i > $o,SV522: $i,SV778: $i] :
( ( ( ~ ( in @ SV778 @ SV522 )
| ( SV691 @ SV778 ) )
= $true )
| ( ( in @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ SV105 )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(3077,plain,
! [SV342: $i,SV691: $i > $o,SV522: $i,SV105: $i] :
( ( ( ~ ( in @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) @ SV342 ) )
= $false )
| ( ( ! [SY3145: $i] :
( ~ ( in @ SY3145 @ SV522 )
| ( SV691 @ SY3145 ) ) )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2932]) ).
thf(3078,plain,
! [SV105: $i,SV342: $i,SV522: $i,SV691: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) ) @ SV522 )
| ( SV691 @ ( kpair @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) ) ) )
= $false )
| ( ( ! [SY3145: $i] :
( ~ ( in @ SY3145 @ SV522 )
| ( SV691 @ SY3145 ) ) )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2932]) ).
thf(3079,plain,
! [SV635: $i,SV106: $i > $o] :
( ( ( ~ ( SV106 @ ( sK65_SY3092 @ SV635 @ SV106 ) ) )
= $false )
| ( ( SV106 @ SV635 )
= $false )
| ( ( ! [SY2086: $i,SY2087: $i] :
( ~ ( SV106 @ SY2086 )
| ~ ( SV106 @ SY2087 )
| ( SY2086 = SY2087 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2933]) ).
thf(3080,plain,
! [SV106: $i > $o,SV635: $i] :
( ( ( SV635
= ( sK65_SY3092 @ SV635 @ SV106 ) )
= $false )
| ( ( SV106 @ SV635 )
= $false )
| ( ( ! [SY2086: $i,SY2087: $i] :
( ~ ( SV106 @ SY2086 )
| ~ ( SV106 @ SY2087 )
| ( SY2086 = SY2087 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2933]) ).
thf(3081,plain,
! [SV636: $i,SV108: $i > $o] :
( ( ( ~ ( SV108 @ ( sK66_SY3093 @ SV636 @ SV108 ) ) )
= $false )
| ( ( SV108 @ SV636 )
= $false )
| ( ( SV108
@ ( descr
@ ^ [SY2093: $i] : ( SV108 @ SY2093 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2934]) ).
thf(3082,plain,
! [SV108: $i > $o,SV636: $i] :
( ( ( SV636
= ( sK66_SY3093 @ SV636 @ SV108 ) )
= $false )
| ( ( SV108 @ SV636 )
= $false )
| ( ( SV108
@ ( descr
@ ^ [SY2093: $i] : ( SV108 @ SY2093 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2934]) ).
thf(3083,plain,
! [SV638: $i,SV114: $i > $o] :
( ( ( ~ ( SV114 @ ( sK67_SY3096 @ SV638 @ SV114 ) ) )
= $false )
| ( ( SV114 @ SV638 )
= $false )
| ( ( ~ ! [SY2107: $i] :
~ ( SV114 @ SY2107 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2935]) ).
thf(3084,plain,
! [SV114: $i > $o,SV638: $i] :
( ( ( SV638
= ( sK67_SY3096 @ SV638 @ SV114 ) )
= $false )
| ( ( SV114 @ SV638 )
= $false )
| ( ( ~ ! [SY2107: $i] :
~ ( SV114 @ SY2107 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2935]) ).
thf(3085,plain,
! [SV741: $i,SV639: $i,SV348: $i,SV115: $i,SV767: $i] :
( ( ( ~ ( in @ SV767 @ SV115 ) )
= $true )
| ( ( ~ ( in @ SV767 @ ( binintersect @ SV348 @ SV639 ) )
| ( in @ SV767 @ ( binunion @ SV348 @ SV741 ) ) )
= $true )
| ( ( in @ SV741 @ ( powerset @ SV115 ) )
= $false )
| ( ( in @ SV639 @ ( powerset @ SV115 ) )
= $false )
| ( ( in @ SV348 @ ( powerset @ SV115 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2936]) ).
thf(3086,plain,
! [SV350: $i > $o,SV118: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ SV118 )
| ~ ( SV350 @ SV763 ) )
= $true )
| ( ( in @ ( sK10_SY2649 @ SV350 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2937]) ).
thf(3087,plain,
! [SV350: $i > $o,SV118: $i,SV764: $i] :
( ( ( ~ ( in @ SV764 @ SV118 )
| ~ ( SV350 @ SV764 ) )
= $true )
| ( ( SV350 @ ( sK10_SY2649 @ SV350 @ SV118 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2938]) ).
thf(3088,plain,
! [SV119: $i,SV351: $i > $o,SV692: $i] :
( ( ( ~ ( in @ ( sK56_SY2652 @ SV692 @ SV351 @ SV119 ) @ SV119 )
| ~ ~ ( SV351 @ ( sK56_SY2652 @ SV692 @ SV351 @ SV119 ) ) )
= $false )
| ( ( SV351 @ SV692 )
= $true )
| ( ( in @ SV692 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2939]) ).
thf(3089,plain,
! [SV120: $i,SV352: $i,SV641: $i,SV742: $i] :
( ( ( ~ ( in @ SV742 @ SV641 ) )
= $false )
| ( ( ~ ( in @ SV742 @ ( binintersect @ SV352 @ SV641 ) ) )
= $true )
| ( ( in @ SV742 @ SV120 )
= $false )
| ( ( in @ SV641 @ ( powerset @ SV120 ) )
= $false )
| ( ( in @ SV352 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2940]) ).
thf(3090,plain,
! [SV353: $i,SV642: $i,SV121: $i,SV765: $i] :
( ( ( in @ SV765 @ SV121 )
= $false )
| ( ( ~ ( in @ SV765 @ SV642 )
| ( in @ SV765 @ ( setminus @ SV121 @ SV353 ) ) )
= $true )
| ( ( subset @ SV353 @ ( setminus @ SV121 @ SV642 ) )
= $false )
| ( ( in @ SV642 @ ( powerset @ SV121 ) )
= $false )
| ( ( in @ SV353 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2941]) ).
thf(3091,plain,
! [SV126: $i,SV693: $o,SV358: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ SV358 )
| SV693 )
= $false )
| ( SV693 = $true )
| ( ( SV529 = SV126 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2942]) ).
thf(3092,plain,
! [SV126: $i,SV693: $o,SV358: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ SV358 ) )
= $false )
| ( SV693 = $true )
| ( SV693 = $false )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2943]) ).
thf(3093,plain,
! [SV358: $i,SV126: $i,SV529: $i,SV693: $o] :
( ( SV693 = $false )
| ( SV693 = $true )
| ( SV693 = $false )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2943]) ).
thf(3094,plain,
! [SV126: $i,SV358: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ SV358 )
| $true )
= $false )
| ( $true = $true )
| ( ( SV529 = SV126 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2944]) ).
thf(3095,plain,
! [SV126: $i,SV358: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ SV358 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2945]) ).
thf(3096,plain,
! [SV358: $i,SV126: $i,SV529: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2945]) ).
thf(3097,plain,
! [SV126: $i,SV358: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ SV358 )
| $false )
= $false )
| ( $false = $true )
| ( ( SV529 = SV126 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2946]) ).
thf(3098,plain,
! [SV126: $i,SV358: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ SV358 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2947]) ).
thf(3099,plain,
! [SV358: $i,SV126: $i,SV529: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2947]) ).
thf(3100,plain,
! [SV130: $i,SV644: $i,SV362: $i,SV743: $i] :
( ( ( ~ ( in @ SV743 @ SV362 ) )
= $false )
| ( ( ~ ( in @ SV743 @ ( binintersect @ SV362 @ SV644 ) ) )
= $true )
| ( ( in @ SV743 @ SV130 )
= $false )
| ( ( in @ SV644 @ ( powerset @ SV130 ) )
= $false )
| ( ( in @ SV362 @ ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2948]) ).
thf(3101,plain,
! [SV645: $i,SV363: $i,SV131: $i,SV744: $i] :
( ( ( in @ SV744 @ ( setminus @ SV131 @ SV363 ) )
= $false )
| ( ( in @ SV744 @ ( setminus @ SV131 @ ( binintersect @ SV363 @ SV645 ) ) )
= $true )
| ( ( in @ SV744 @ SV131 )
= $false )
| ( ( in @ SV645 @ ( powerset @ SV131 ) )
= $false )
| ( ( in @ SV363 @ ( powerset @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2949]) ).
thf(3102,plain,
! [SV135: $i,SV745: $i,SV647: $i,SV367: $i > $o] :
( ( ( SV367 @ SV647 )
= $false )
| ( ( ~ ( SV367 @ SV745 )
| ( SV647 = SV745 ) )
= $true )
| ( ( in @ SV745 @ SV135 )
= $false )
| ( ( in @ SV647 @ SV135 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV135
@ ^ [SY2676: $i] : ( SV367 @ SY2676 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2950]) ).
thf(3103,plain,
! [SV137: $i,SV746: $i,SV649: $i,SV369: $i] :
( ( ( subset @ SV369 @ SV649 )
= $false )
| ( ( ~ ~ ( in @ SV746 @ SV649 )
| ~ ( in @ SV746 @ SV369 ) )
= $true )
| ( ( in @ SV746 @ SV137 )
= $false )
| ( ( in @ SV649 @ ( powerset @ SV137 ) )
= $false )
| ( ( in @ SV369 @ ( powerset @ SV137 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2954]) ).
thf(3104,plain,
! [SV146: $i,SV377: $i,SV650: $i] :
( ( ( in @ ( sK57_SY3106 @ SV650 @ SV377 @ SV146 ) @ SV146 )
= $true )
| ( ( subset @ SV377 @ SV650 )
= $true )
| ( ( in @ SV650 @ ( powerset @ SV146 ) )
= $false )
| ( ( in @ SV377 @ ( powerset @ SV146 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2955]) ).
thf(3105,plain,
! [SV146: $i,SV377: $i,SV650: $i] :
( ( ( ~ ( in @ ( sK57_SY3106 @ SV650 @ SV377 @ SV146 ) @ SV377 ) )
= $false )
| ( ( subset @ SV377 @ SV650 )
= $true )
| ( ( in @ SV650 @ ( powerset @ SV146 ) )
= $false )
| ( ( in @ SV377 @ ( powerset @ SV146 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2956]) ).
thf(3106,plain,
! [SV146: $i,SV377: $i,SV650: $i] :
( ( ( in @ ( sK57_SY3106 @ SV650 @ SV377 @ SV146 ) @ SV650 )
= $false )
| ( ( subset @ SV377 @ SV650 )
= $true )
| ( ( in @ SV650 @ ( powerset @ SV146 ) )
= $false )
| ( ( in @ SV377 @ ( powerset @ SV146 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2956]) ).
thf(3107,plain,
! [SV147: $i] :
( ( ~ ! [SY2953: $i] :
( ~ ( in @ SY2953 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY2188: $i] :
( ~ ( in @ SY2188 @ SY2953 )
| ( in @ SY2188 @ SV147 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2957]) ).
thf(3108,plain,
! [SV147: $i] :
( ( ~ ! [SY2955: $i,SY2956: $i] :
( ~ ~ ( ~ ( in @ SY2955 @ SV147 )
| ~ ( in @ SY2956 @ SV147 ) )
| ~ ! [SY2957: $i] :
( ~ ( in @ SY2957 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SY2955 @ SY2957 )
| ( in @ SY2956 @ SY2957 ) )
| ~ ( ~ ( in @ SY2956 @ SY2957 )
| ( in @ SY2955 @ SY2957 ) ) ) )
| ( SY2955 = SY2956 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2957]) ).
thf(3109,plain,
! [SV779: $i,SV147: $i,SV768: $i] :
( ( ~ ~ ( ~ ( in @ SV768 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SV779 @ ( sK3_SY2186 @ SV147 ) ) )
| ! [SY3204: $i] :
( ~ ( in @ SY3204 @ SV768 )
| ( in @ SY3204 @ SV779 ) )
| ! [SY3205: $i] :
( ~ ( in @ SY3205 @ SV779 )
| ( in @ SY3205 @ SV768 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2958]) ).
thf(3110,plain,
! [SV147: $i,SV747: $i] :
( ( ( ~ ! [SY3176: $i] :
( ~ ( in @ SY3176 @ SV747 )
| ( in @ SY3176 @ SV147 ) ) )
= $true )
| ( ( ~ ~ ! [SY3177: $i] :
~ ( in @ SY3177 @ SV747 ) )
= $true )
| ( ( ~ ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2959]) ).
thf(3111,plain,
! [SV748: $i,SV651: $i,SV381: $i,SV151: $i,SV769: $i] :
( ( ( ~ ( in @ SV769 @ SV151 ) )
= $true )
| ( ( ~ ( in @ SV769 @ ( binintersect @ SV381 @ SV651 ) )
| ( in @ SV769 @ ( binunion @ SV651 @ SV748 ) ) )
= $true )
| ( ( in @ SV748 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV651 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV381 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2960]) ).
thf(3112,plain,
! [SV749: $i,SV652: $i,SV156: $i,SV386: $i] :
( ( ( subset @ SV386 @ ( setminus @ SV156 @ SV652 ) )
= $false )
| ( ( ~ ( in @ SV749 @ SV652 )
| ~ ( in @ SV749 @ SV386 ) )
= $true )
| ( ( in @ SV749 @ SV156 )
= $false )
| ( ( in @ SV652 @ ( powerset @ SV156 ) )
= $false )
| ( ( in @ SV386 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(3113,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( SV160 @ ( sK49_SY2231 @ SV653 @ SV160 ) )
= $true )
| ( ( ~ ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2962]) ).
thf(3114,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ( SV160 @ ( sK58_SY3190 @ SV653 @ SV160 ) ) )
= $false )
| ( ( ~ ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2963]) ).
thf(3115,plain,
! [SV160: $i > $o,SV653: $i] :
( ( ( ( sK49_SY2231 @ SV653 @ SV160 )
= ( sK58_SY3190 @ SV653 @ SV160 ) )
= $false )
| ( ( ~ ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2963]) ).
thf(3116,plain,
! [SV657: $i,SV395: $i,SV167: $i,SV750: $i] :
( ( ( in @ SV750 @ ( setminus @ SV167 @ ( binunion @ SV395 @ SV657 ) ) )
= $false )
| ( ( in @ SV750 @ ( setminus @ SV167 @ SV395 ) )
= $true )
| ( ( in @ SV750 @ SV167 )
= $false )
| ( ( in @ SV657 @ ( powerset @ SV167 ) )
= $false )
| ( ( in @ SV395 @ ( powerset @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(3117,plain,
! [SV168: $i,SV396: $i,SV548: $i,SV697: $i] :
( ( ( ~ ( in @ ( sK68_SY3146 @ SV697 @ SV548 @ SV396 @ SV168 ) @ SV168 ) )
= $false )
| ( ( SV548 = SV697 )
= $true )
| ( ( func @ SV168 @ SV396 @ SV697 )
= $false )
| ( ( func @ SV168 @ SV396 @ SV548 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2965]) ).
thf(3118,plain,
! [SV697: $i,SV548: $i,SV396: $i,SV168: $i] :
( ( ( ( ap @ SV168 @ SV396 @ SV548 @ ( sK68_SY3146 @ SV697 @ SV548 @ SV396 @ SV168 ) )
= ( ap @ SV168 @ SV396 @ SV697 @ ( sK68_SY3146 @ SV697 @ SV548 @ SV396 @ SV168 ) ) )
= $false )
| ( ( SV548 = SV697 )
= $true )
| ( ( func @ SV168 @ SV396 @ SV697 )
= $false )
| ( ( func @ SV168 @ SV396 @ SV548 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2965]) ).
thf(3119,plain,
! [SV706: $i,SV408: $i > $o,SV180: $i] :
( ( ( ( dsetconstr @ SV180
@ ^ [SY2739: $i] : ( SV408 @ SY2739 ) )
!= emptyset )
= $true )
| ( $false = $true )
| ( ( in @ SV706 @ SV180 )
= $false )
| ( ( SV408 @ SV706 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2969]) ).
thf(3120,plain,
! [SV409: $i > $o,SV181: $i,SV770: $i] :
( ( ( ~ ( ~ ( in @ SV770 @ SV181 )
| ~ ( SV409 @ SV770 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( in @ ( sK12_SY2740 @ SV409 @ SV181 ) @ SV181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2970]) ).
thf(3121,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ( ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( in @ ( sK34_SY3112 @ SV409 @ SV181 ) @ SV181 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2971]) ).
thf(3122,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ( ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( SV409 @ ( sK12_SY2740 @ SV409 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2972]) ).
thf(3123,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ( ~ ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( SV409 @ ( sK34_SY3112 @ SV409 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2973]) ).
thf(3124,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ( ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( ( sK12_SY2740 @ SV409 @ SV181 )
= ( sK34_SY3112 @ SV409 @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2974]) ).
thf(3125,plain,
! [SV411: $i > $o,SV780: $i,SV183: $i > $o] :
( ( ( ~ ~ ( ~ ( SV183 @ SV780 )
| ~ ! [SY3206: $i] :
( ~ ( SV183 @ SY3206 )
| ( SV780 = SY3206 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2975]) ).
thf(3126,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( ~ ( ~ ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
| ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2976]) ).
thf(3127,plain,
! [SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
| ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2977]) ).
thf(3128,plain,
! [SV413: $i,SV185: $i,SV561: $i,SV760: $i,SV707: $i] :
( ( ( ~ ( in @ ( kpair @ SV707 @ SV760 ) @ SV561 ) )
= $true )
| ( ( ( ap @ SV185 @ SV413 @ SV561 @ SV707 )
= SV760 )
= $true )
| ( ( in @ SV760 @ SV413 )
= $false )
| ( ( in @ SV707 @ SV185 )
= $false )
| ( ( in @ SV561 @ ( funcSet @ SV185 @ SV413 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2978]) ).
thf(3129,plain,
! [SV186: $i,SV414: $i,SV659: $i] :
( ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV186 )
= $true )
| ( ( ~ ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV186 )
| ~ ( in @ SY3115 @ SV659 )
| ( in @ SY3115 @ SV414 ) )
| ( SV414 = SV659 ) )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2979]) ).
thf(3130,plain,
! [SV186: $i,SV414: $i,SV659: $i] :
( ( ( ~ ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV414 ) )
= $false )
| ( ( ~ ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV186 )
| ~ ( in @ SY3115 @ SV659 )
| ( in @ SY3115 @ SV414 ) )
| ( SV414 = SV659 ) )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2980]) ).
thf(3131,plain,
! [SV186: $i,SV414: $i,SV659: $i] :
( ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV659 )
= $false )
| ( ( ~ ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV186 )
| ~ ( in @ SY3115 @ SV659 )
| ( in @ SY3115 @ SV414 ) )
| ( SV414 = SV659 ) )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2980]) ).
thf(3132,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK69_SY3116 @ SV660 @ SV188 ) ) )
= $false )
| ( ( SV188 @ SV660 )
= $false )
| ( ( ~ ! [SY2316: $i] :
~ ~ ( ~ ( SV188 @ SY2316 )
| ~ ! [SY2317: $i] :
( ~ ( SV188 @ SY2317 )
| ( SY2316 = SY2317 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2981]) ).
thf(3133,plain,
! [SV188: $i > $o,SV660: $i] :
( ( ( SV660
= ( sK69_SY3116 @ SV660 @ SV188 ) )
= $false )
| ( ( SV188 @ SV660 )
= $false )
| ( ( ~ ! [SY2316: $i] :
~ ~ ( ~ ( SV188 @ SY2316 )
| ~ ! [SY2317: $i] :
( ~ ( SV188 @ SY2317 )
| ( SY2316 = SY2317 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2981]) ).
thf(3134,plain,
! [SV752: $i,SV661: $i,SV418: $i,SV191: $i,SV771: $i] :
( ( ( ~ ( in @ SV771 @ SV191 ) )
= $true )
| ( ( ~ ( in @ SV771 @ ( binintersect @ SV418 @ SV661 ) )
| ( in @ SV771 @ ( binintersect @ ( binunion @ SV418 @ SV752 ) @ ( binunion @ SV661 @ SV752 ) ) ) )
= $true )
| ( ( in @ SV752 @ ( powerset @ SV191 ) )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV191 ) )
= $false )
| ( ( in @ SV418 @ ( powerset @ SV191 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2982]) ).
thf(3135,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2983]) ).
thf(3136,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2984]) ).
thf(3137,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( ~ ( ~ ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
| ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2985]) ).
thf(3138,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
| ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2986]) ).
thf(3139,plain,
! [SV196: $i,SV566: $i,SV424: $i] :
( ( ( ! [SY3169: $i] :
~ ~ ( ~ ( in @ SY3169 @ SV424 )
| ( SV566
!= ( kpair @ ( sK35_SY2993 @ SV566 @ SV424 @ SV196 ) @ SY3169 ) ) ) )
= $false )
| ( ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2988]) ).
thf(3140,plain,
! [SV198: $i,SV426: $i,SV570: $i,SV712: $i] :
( ( ( ~ ( in @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SV198 ) )
= $false )
| ( ( ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) )
| ( SV570 = SV712 ) )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2989]) ).
thf(3141,plain,
! [SV198: $i,SV570: $i,SV712: $i,SV426: $i] :
( ( ( ! [SY3201: $i] :
( ~ ( in @ SY3201 @ SV426 )
| ~ ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SY3201 ) @ SV570 )
| ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SY3201 ) @ SV712 ) ) )
= $false )
| ( ( ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) )
| ( SV570 = SV712 ) )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2989]) ).
thf(3142,plain,
! [SV200: $i,SV428: $i,SV713: $i > $o,SV571: $i,SV781: $i] :
( ( ( ~ ( in @ SV781 @ SV571 )
| ( SV713 @ SV781 ) )
= $true )
| ( ( in @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ SV200 )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2990]) ).
thf(3143,plain,
! [SV428: $i,SV713: $i > $o,SV571: $i,SV200: $i] :
( ( ( ~ ( in @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) @ SV428 ) )
= $false )
| ( ( ! [SY3157: $i] :
( ~ ( in @ SY3157 @ SV571 )
| ( SV713 @ SY3157 ) ) )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2991]) ).
thf(3144,plain,
! [SV200: $i,SV428: $i,SV571: $i,SV713: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) ) @ SV571 )
| ( SV713 @ ( kpair @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) ) ) )
= $false )
| ( ( ! [SY3157: $i] :
( ~ ( in @ SY3157 @ SV571 )
| ( SV713 @ SY3157 ) ) )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2991]) ).
thf(3145,plain,
! [SV201: $i,SV714: $i,SV429: $i > $o] :
( ( ( SV429 @ SV714 )
= $true )
| ( ( in @ SV714 @ SV201 )
= $false )
| ( ( ~ ! [SY2794: $i] :
( ~ ( in @ SY2794 @ SV201 )
| ( SV429 @ SY2794 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2992]) ).
thf(3146,plain,
! [SV436: $i > $o,SV212: $i,SV772: $i] :
( ( ( ~ ( ~ ( in @ SV772 @ SV212 )
| ~ ( SV436 @ SV772 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( in @ ( sK15_SY2806 @ SV436 @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2994]) ).
thf(3147,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ( ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( in @ ( sK36_SY3121 @ SV436 @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2995]) ).
thf(3148,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ( ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( SV436 @ ( sK15_SY2806 @ SV436 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2996]) ).
thf(3149,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ( ~ ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( SV436 @ ( sK36_SY3121 @ SV436 @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2997]) ).
thf(3150,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ( ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( ( sK15_SY2806 @ SV436 @ SV212 )
= ( sK36_SY3121 @ SV436 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2998]) ).
thf(3151,plain,
! [SV215: $i] :
( ( ( ~ ( in @ ( sK44_SY2395 @ SV215 ) @ omega ) )
= $false )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( ! [SY2396: $i] :
( ~ ( in @ SY2396 @ omega )
| ( in @ SY2396 @ SV215 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2999]) ).
thf(3152,plain,
! [SV215: $i] :
( ( ( ~ ( in @ ( sK44_SY2395 @ SV215 ) @ SV215 ) )
= $false )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( ! [SY2396: $i] :
( ~ ( in @ SY2396 @ omega )
| ( in @ SY2396 @ SV215 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2999]) ).
thf(3153,plain,
! [SV215: $i,SV766: $i] :
( ( ( in @ SV766 @ omega )
= $false )
| ( ( in @ SV766 @ SV215 )
= $true )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( in @ ( setadjoin @ ( sK44_SY2395 @ SV215 ) @ ( sK44_SY2395 @ SV215 ) ) @ SV215 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3000]) ).
thf(3154,plain,
! [SV219: $i,SV442: $i,SV581: $i,SV720: $i] :
( ( ( ~ ( in @ ( sK72_SY3158 @ SV720 @ SV581 @ SV442 @ SV219 ) @ SV219 ) )
= $false )
| ( ( SV581 = SV720 )
= $true )
| ( ( in @ SV720 @ ( funcSet @ SV219 @ SV442 ) )
= $false )
| ( ( in @ SV581 @ ( funcSet @ SV219 @ SV442 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3002]) ).
thf(3155,plain,
! [SV720: $i,SV581: $i,SV442: $i,SV219: $i] :
( ( ( ( ap @ SV219 @ SV442 @ SV581 @ ( sK72_SY3158 @ SV720 @ SV581 @ SV442 @ SV219 ) )
= ( ap @ SV219 @ SV442 @ SV720 @ ( sK72_SY3158 @ SV720 @ SV581 @ SV442 @ SV219 ) ) )
= $false )
| ( ( SV581 = SV720 )
= $true )
| ( ( in @ SV720 @ ( funcSet @ SV219 @ SV442 ) )
= $false )
| ( ( in @ SV581 @ ( funcSet @ SV219 @ SV442 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3002]) ).
thf(3156,plain,
! [SV225: $i,SV448: $i] :
( ( ( ~ ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 ) )
= $false )
| ( ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 )
= $true )
| ( ( SV225 = SV448 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3004]) ).
thf(3157,plain,
! [SV225: $i,SV448: $i] :
( ( ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 )
= $false )
| ( ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 )
= $true )
| ( ( SV225 = SV448 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3004]) ).
thf(3158,plain,
! [SV225: $i,SV448: $i] :
( ( ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 )
= $true )
| ( ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 )
= $false )
| ( ( SV225 = SV448 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3005]) ).
thf(3159,plain,
! [SV243: $i,SV756: $i,SV667: $i,SV465: $i] :
( ( ( in @ SV465 @ ( powerset @ SV667 ) )
= $false )
| ( ( ~ ( in @ SV756 @ SV465 )
| ( in @ SV756 @ SV667 ) )
= $true )
| ( ( in @ SV756 @ SV243 )
= $false )
| ( ( in @ SV667 @ ( powerset @ SV243 ) )
= $false )
| ( ( in @ SV465 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3010]) ).
thf(3160,plain,
! [SV247: $i,SV469: $i,SV600: $i,SV728: $i] :
( ( ( ~ ( in @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) @ SV247 ) )
= $false )
| ( ( ! [SY3166: $i] :
( ~ ( in @ SY3166 @ SV247 )
| ! [SY3167: $i] :
( ~ ( in @ SY3167 @ SV469 )
| ~ ( in @ ( kpair @ SY3166 @ SY3167 ) @ SV728 )
| ( in @ ( kpair @ SY3166 @ SY3167 ) @ SV600 ) ) ) )
= $true )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3014]) ).
thf(3161,plain,
! [SV728: $i,SV600: $i,SV469: $i,SV247: $i] :
( ( ( ( ap @ SV247 @ SV469 @ SV600 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) )
= ( ap @ SV247 @ SV469 @ SV728 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) ) )
= $false )
| ( ( ! [SY3166: $i] :
( ~ ( in @ SY3166 @ SV247 )
| ! [SY3167: $i] :
( ~ ( in @ SY3167 @ SV469 )
| ~ ( in @ ( kpair @ SY3166 @ SY3167 ) @ SV728 )
| ( in @ ( kpair @ SY3166 @ SY3167 ) @ SV600 ) ) ) )
= $true )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3014]) ).
thf(3162,plain,
! [SV471: $i,SV249: $i > $i > $o,SV773: $i] :
( ( ( ~ ( ~ ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
| ~ ! [SY3202: $i] :
~ ~ ( ~ ( in @ SY3202 @ SV471 )
| ~ ( SV249 @ SY3202 @ SV773 ) ) )
| ~ ( ~ ~ ! [SY3203: $i] :
~ ~ ( ~ ( in @ SY3203 @ SV471 )
| ~ ( SV249 @ SY3203 @ SV773 ) )
| ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) ) ) )
= $false )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3015]) ).
thf(3163,plain,
! [SV757: $i,SV471: $i,SV249: $i > $i > $o] :
( ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( ~ ! [SY3187: $i] :
( ~ ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SY3187 )
| ( SV757 = SY3187 ) ) )
= $true )
| ( ( ~ ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3016]) ).
thf(3164,plain,
! [SV476: $i,SV733: $i,SV254: $i,SV669: $i] :
( ( ( ~ ( in @ SV669 @ SV254 ) )
= $true )
| ( ( in @ SV733 @ SV476 )
= $true )
| ( ( SV669 = SV733 )
= $false )
| ( ( SV254 = SV476 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3020]) ).
thf(3165,plain,
! [SV254: $i,SV669: $i,SV476: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV476 ) )
= $true )
| ( ( in @ SV669 @ SV254 )
= $true )
| ( ( SV669 = SV733 )
= $false )
| ( ( SV254 = SV476 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3021]) ).
thf(3166,plain,
! [SV670: $i,SV256: $i > $o] :
( ( ( ~ ( SV256 @ ( sK74_SY3127 @ SV670 @ SV256 ) ) )
= $false )
| ( ( SV256 @ SV670 )
= $false )
| ( ( ~ ! [SY2511: $i] :
~ ! [SY2512: $i] :
~ ( ~ ( ~ ( SV256 @ SY2512 )
| ( SY2512 = SY2511 ) )
| ~ ( ( SY2512 != SY2511 )
| ( SV256 @ SY2512 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3022]) ).
thf(3167,plain,
! [SV256: $i > $o,SV670: $i] :
( ( ( SV670
= ( sK74_SY3127 @ SV670 @ SV256 ) )
= $false )
| ( ( SV256 @ SV670 )
= $false )
| ( ( ~ ! [SY2511: $i] :
~ ! [SY2512: $i] :
~ ( ~ ( ~ ( SV256 @ SY2512 )
| ( SY2512 = SY2511 ) )
| ~ ( ( SY2512 != SY2511 )
| ( SV256 @ SY2512 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3022]) ).
thf(3168,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( SV35 @ ( sK60_SY3073 @ SV621 @ SV35 ) )
= $true )
| ( ( SV35 @ SV621 )
= $false )
| ( ( ~ ! [SY1902: $i] :
~ ~ ( ~ ( SV35 @ SY1902 )
| ~ ! [SY1903: $i] :
( ~ ( SV35 @ SY1903 )
| ( SY1902 = SY1903 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3023]) ).
thf(3169,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ! [SY1902: $i] :
~ ~ ( ~ ( SV35 @ SY1902 )
| ~ ! [SY1903: $i] :
( ~ ( SV35 @ SY1903 )
| ( SY1902 = SY1903 ) ) ) )
= $false )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV621
= ( sK60_SY3073 @ SV621 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3024]) ).
thf(3170,plain,
! [SV284: $i,SV38: $i,SV484: $i,SV758: $i,SV672: $i] :
( ( ( in @ ( kpair @ SV672 @ SV758 ) @ SV484 )
= $false )
| ( ( ( ap @ SV38 @ SV284 @ SV484 @ SV672 )
= SV758 )
= $true )
| ( ( in @ SV758 @ SV284 )
= $false )
| ( ( in @ SV672 @ SV38 )
= $false )
| ( ( func @ SV38 @ SV284 @ SV484 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3025]) ).
thf(3171,plain,
! [SV286: $i,SV676: $i > $o,SV623: $i > $o,SV40: $i] :
( ( ( in @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) @ SV286 )
= $true )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3026]) ).
thf(3172,plain,
! [SV40: $i,SV286: $i,SV623: $i > $o,SV676: $i > $o] :
( ( ( ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 )
!= ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
= $false )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3027]) ).
thf(3173,plain,
! [SV40: $i,SV286: $i,SV676: $i > $o,SV623: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) )
| ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) ) )
| ~ ( ~ ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
| ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3027]) ).
thf(3174,plain,
! [SV287: $i > $o,SV41: $i,SV774: $i] :
( ( ( ~ ( in @ SV774 @ SV41 ) )
= $true )
| ( ( ~ ( SV287 @ SV774 ) )
= $true )
| ( ( in @ ( sK30_SY2541 @ SV287 @ SV41 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3028]) ).
thf(3175,plain,
! [SV287: $i > $o,SV41: $i,SV775: $i] :
( ( ( ~ ( in @ SV775 @ SV41 ) )
= $true )
| ( ( ~ ( SV287 @ SV775 ) )
= $true )
| ( ( SV287 @ ( sK30_SY2541 @ SV287 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3029]) ).
thf(3176,plain,
! [SV44: $i > $o,SV624: $i] :
( ( ( ( ( sK31_SY3079 @ SV624 @ SV44 )
!= SV624 )
| ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) ) )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3030]) ).
thf(3177,plain,
! [SV44: $i > $o,SV624: $i] :
( ( ( ( sK31_SY3079 @ SV624 @ SV44 )
!= SV624 )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3031]) ).
thf(3178,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3031]) ).
thf(3179,plain,
! [SV64: $i,SV625: $i,SV305: $i,SV737: $i] :
( ( ( in @ SV737 @ ( binintersect @ SV305 @ SV625 ) )
= $false )
| ( ( in @ SV737 @ ( setminus @ SV64 @ SV305 ) )
= $false )
| ( ( in @ SV737 @ SV64 )
= $false )
| ( ( in @ SV625 @ ( powerset @ SV64 ) )
= $false )
| ( ( in @ SV305 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3032]) ).
thf(3180,plain,
! [SV66: $i,SV626: $i,SV307: $i,SV738: $i] :
( ( ( in @ SV738 @ ( binunion @ SV307 @ SV626 ) )
= $true )
| ( ( ~ ( in @ SV738 @ SV626 ) )
= $true )
| ( ( in @ SV738 @ SV66 )
= $false )
| ( ( in @ SV626 @ ( powerset @ SV66 ) )
= $false )
| ( ( in @ SV307 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3033]) ).
thf(3181,plain,
! [SV69: $i,SV310: $i] :
( ( ( in @ SV310 @ ( sK46_SY2574 @ SV69 @ SV310 ) )
= $true )
| ( ( in @ SV310 @ ( setunion @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3034]) ).
thf(3182,plain,
! [SV310: $i,SV69: $i] :
( ( ( in @ ( sK46_SY2574 @ SV69 @ SV310 ) @ SV69 )
= $true )
| ( ( in @ SV310 @ ( setunion @ SV69 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3035]) ).
thf(3183,plain,
! [SV69: $i,SV759: $i,SV310: $i] :
( ( ( in @ SV310 @ SV759 )
= $false )
| ( ( ~ ( in @ SV759 @ SV69 ) )
= $true )
| ( ( in @ SV310 @ ( setunion @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3036]) ).
thf(3184,plain,
! [SV627: $i,SV70: $i,SV311: $i,SV739: $i] :
( ( ( in @ SV739 @ SV311 )
= $false )
| ( ( in @ SV739 @ ( setminus @ SV70 @ ( binunion @ SV311 @ SV627 ) ) )
= $false )
| ( ( in @ SV739 @ SV70 )
= $false )
| ( ( in @ SV627 @ ( powerset @ SV70 ) )
= $false )
| ( ( in @ SV311 @ ( powerset @ SV70 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3037]) ).
thf(3185,plain,
! [SV73: $i,SV314: $i,SV628: $i] :
( ( ( in @ ( sK52_SY3083 @ SV628 @ SV314 @ SV73 ) @ SV314 )
= $true )
| ( ( in @ SV314 @ ( powerset @ SV628 ) )
= $true )
| ( ( in @ SV628 @ ( powerset @ SV73 ) )
= $false )
| ( ( in @ SV314 @ ( powerset @ SV73 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3039]) ).
thf(3186,plain,
! [SV315: $i,SV686: $o,SV74: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV74 ) )
= $false )
| ( SV686 = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3041]) ).
thf(3187,plain,
! [SV74: $i,SV686: $o,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 )
| SV686 )
= $false )
| ( SV686 = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3041]) ).
thf(3188,plain,
! [SV686: $o,SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SV686 ) )
= $true )
| ( SV686 = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3042]) ).
thf(3189,plain,
! [SV315: $i,SV686: $o,SV74: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV74 ) )
= $false )
| ( SV686 = $true )
| ( SV686 = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3043]) ).
thf(3190,plain,
! [SV74: $i,SV686: $o,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 )
| SV686 )
= $false )
| ( SV686 = $true )
| ( SV686 = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3043]) ).
thf(3191,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV74 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3044]) ).
thf(3192,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3044]) ).
thf(3193,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3045]) ).
thf(3194,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV74 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3046]) ).
thf(3195,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3046]) ).
thf(3196,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV74 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3047]) ).
thf(3197,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3047]) ).
thf(3198,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3048]) ).
thf(3199,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV74 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3049]) ).
thf(3200,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3049]) ).
thf(3201,plain,
! [SV318: $i > $o,SV79: $i,SV776: $i] :
( ( ( ~ ( in @ SV776 @ SV79 ) )
= $true )
| ( ( ~ ( SV318 @ SV776 ) )
= $true )
| ( ( in @ ( sK32_SY2591 @ SV318 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3050]) ).
thf(3202,plain,
! [SV318: $i > $o,SV79: $i,SV777: $i] :
( ( ( ~ ( in @ SV777 @ SV79 ) )
= $true )
| ( ( ~ ( SV318 @ SV777 ) )
= $true )
| ( ( SV318 @ ( sK32_SY2591 @ SV318 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3051]) ).
thf(3203,plain,
! [SV82: $i,SV630: $i] :
( ( ( ~ ! [SY3174: $i] :
~ ~ ( ~ ( in @ SY3174 @ ( sK38_SY2017 @ SV630 @ SV82 ) )
| ~ ( in @ SY3174 @ SV82 ) ) )
= $false )
| ( ( in @ SV630 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3053]) ).
thf(3204,plain,
! [SV84: $i,SV607: $o,SV322: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV322 ) )
= $false )
| ( SV607 = $true )
| ( ( in @ SV513 @ SV84 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3054]) ).
thf(3205,plain,
! [SV322: $i,SV84: $i,SV513: $i,SV607: $o] :
( ( SV607 = $false )
| ( SV607 = $true )
| ( ( in @ SV513 @ SV84 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3054]) ).
thf(3206,plain,
! [SV84: $i,SV607: $o,SV322: $i,SV513: $i] :
( ( ( in @ SV513 @ SV322 )
= $true )
| ( SV607 = $true )
| ( SV607 = $false )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3055]) ).
thf(3207,plain,
! [SV84: $i,SV322: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV322 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV513 @ SV84 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3057]) ).
thf(3208,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV513 @ SV84 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3057]) ).
thf(3209,plain,
! [SV84: $i,SV322: $i,SV513: $i] :
( ( ( in @ SV513 @ SV322 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3058]) ).
thf(3210,plain,
! [SV84: $i,SV322: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV322 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV513 @ SV84 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3060]) ).
thf(3211,plain,
! [SV322: $i,SV84: $i,SV513: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV513 @ SV84 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3060]) ).
thf(3212,plain,
! [SV84: $i,SV322: $i,SV513: $i] :
( ( ( in @ SV513 @ SV322 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3061]) ).
thf(3213,plain,
! [SV85: $i,SV631: $i,SV323: $i,SV740: $i] :
( ( ( in @ SV740 @ ( binunion @ SV323 @ SV631 ) )
= $true )
| ( ( ~ ( in @ SV740 @ SV323 ) )
= $true )
| ( ( in @ SV740 @ SV85 )
= $false )
| ( ( in @ SV631 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV323 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3063]) ).
thf(3214,plain,
! [SV87: $i,SV325: $i > $o,SV687: $i] :
( ( ( ~ ( in @ ( sK53_SY2599 @ SV687 @ SV325 @ SV87 ) @ SV87 ) )
= $false )
| ( ( SV325 @ SV687 )
= $true )
| ( ( in @ SV687 @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3064]) ).
thf(3215,plain,
! [SV87: $i,SV687: $i,SV325: $i > $o] :
( ( ( ~ ~ ( SV325 @ ( sK53_SY2599 @ SV687 @ SV325 @ SV87 ) ) )
= $false )
| ( ( SV325 @ SV687 )
= $true )
| ( ( in @ SV687 @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3064]) ).
thf(3216,plain,
! [SV632: $i,SV91: $i > $o] :
( ( ( SV91 @ ( sK62_SY3087 @ SV632 @ SV91 ) )
= $true )
| ( ( SV91 @ SV632 )
= $false )
| ( ( ! [SY2037: $i,SY2038: $i] :
( ~ ( SV91 @ SY2037 )
| ~ ( SV91 @ SY2038 )
| ( SY2037 = SY2038 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3066]) ).
thf(3217,plain,
! [SV632: $i,SV782: $i,SV91: $i > $o] :
( ( ( ! [SY3207: $i] :
( ~ ( SV91 @ SV782 )
| ~ ( SV91 @ SY3207 )
| ( SV782 = SY3207 ) ) )
= $true )
| ( ( SV91 @ SV632 )
= $false )
| ( ( SV632
= ( sK62_SY3087 @ SV632 @ SV91 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3067]) ).
thf(3218,plain,
! [SV95: $i,SV332: $i,SV516: $i,SV689: $i] :
( ( ( in @ ( sK63_SY3141 @ SV689 @ SV516 @ SV332 @ SV95 ) @ SV95 )
= $true )
| ( ( subset @ SV516 @ SV689 )
= $true )
| ( ( subset @ SV689 @ ( cartprod @ SV95 @ SV332 ) )
= $false )
| ( ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3068]) ).
thf(3219,plain,
! [SV332: $i,SV689: $i,SV516: $i,SV95: $i] :
( ( ( ~ ( in @ ( sK75_SY3197 @ SV95 @ SV516 @ SV689 @ SV332 ) @ SV332 )
| ~ ( in @ ( kpair @ ( sK63_SY3141 @ SV689 @ SV516 @ SV332 @ SV95 ) @ ( sK75_SY3197 @ SV95 @ SV516 @ SV689 @ SV332 ) ) @ SV516 )
| ( in @ ( kpair @ ( sK63_SY3141 @ SV689 @ SV516 @ SV332 @ SV95 ) @ ( sK75_SY3197 @ SV95 @ SV516 @ SV689 @ SV332 ) ) @ SV689 ) )
= $false )
| ( ( subset @ SV516 @ SV689 )
= $true )
| ( ( subset @ SV689 @ ( cartprod @ SV95 @ SV332 ) )
= $false )
| ( ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3069]) ).
thf(3220,plain,
! [SV100: $i,SV518: $i,SV337: $i > $o] :
( ( ( SV337 @ ( sK55_SY2926 @ SV518 @ SV337 @ SV100 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV100
@ ^ [SY2618: $i] : ( SV337 @ SY2618 ) ) )
= $true )
| ( ( SV337 @ SV518 )
= $false )
| ( ( in @ SV518 @ SV100 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3071]) ).
thf(3221,plain,
( ( ( ~ ( in @ sK39_SY3168 @ sK2_SY2624 ) )
= $true )
| ( sK33_SY3090 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[3073]) ).
thf(3222,plain,
( ( ~ ( in @ sK39_SY3168 @ sK9_SY2932 )
| sK33_SY3090 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3074]) ).
thf(3223,plain,
! [SV105: $i,SV342: $i,SV691: $i > $o,SV522: $i,SV778: $i] :
( ( ( ~ ( in @ SV778 @ SV522 ) )
= $true )
| ( ( SV691 @ SV778 )
= $true )
| ( ( in @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ SV105 )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3076]) ).
thf(3224,plain,
! [SV342: $i,SV691: $i > $o,SV522: $i,SV105: $i] :
( ( ( in @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) @ SV342 )
= $true )
| ( ( ! [SY3145: $i] :
( ~ ( in @ SY3145 @ SV522 )
| ( SV691 @ SY3145 ) ) )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3077]) ).
thf(3225,plain,
! [SV105: $i,SV342: $i,SV522: $i,SV691: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) ) @ SV522 ) )
= $false )
| ( ( ! [SY3145: $i] :
( ~ ( in @ SY3145 @ SV522 )
| ( SV691 @ SY3145 ) ) )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3078]) ).
thf(3226,plain,
! [SV105: $i,SV342: $i,SV522: $i,SV691: $i > $o] :
( ( ( SV691 @ ( kpair @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) ) )
= $false )
| ( ( ! [SY3145: $i] :
( ~ ( in @ SY3145 @ SV522 )
| ( SV691 @ SY3145 ) ) )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3078]) ).
thf(3227,plain,
! [SV635: $i,SV106: $i > $o] :
( ( ( SV106 @ ( sK65_SY3092 @ SV635 @ SV106 ) )
= $true )
| ( ( SV106 @ SV635 )
= $false )
| ( ( ! [SY2086: $i,SY2087: $i] :
( ~ ( SV106 @ SY2086 )
| ~ ( SV106 @ SY2087 )
| ( SY2086 = SY2087 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3079]) ).
thf(3228,plain,
! [SV635: $i,SV783: $i,SV106: $i > $o] :
( ( ( ! [SY3208: $i] :
( ~ ( SV106 @ SV783 )
| ~ ( SV106 @ SY3208 )
| ( SV783 = SY3208 ) ) )
= $true )
| ( ( SV106 @ SV635 )
= $false )
| ( ( SV635
= ( sK65_SY3092 @ SV635 @ SV106 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3080]) ).
thf(3229,plain,
! [SV636: $i,SV108: $i > $o] :
( ( ( SV108 @ ( sK66_SY3093 @ SV636 @ SV108 ) )
= $true )
| ( ( SV108 @ SV636 )
= $false )
| ( ( SV108
@ ( descr
@ ^ [SY2093: $i] : ( SV108 @ SY2093 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3081]) ).
thf(3230,plain,
! [SV638: $i,SV114: $i > $o] :
( ( ( SV114 @ ( sK67_SY3096 @ SV638 @ SV114 ) )
= $true )
| ( ( SV114 @ SV638 )
= $false )
| ( ( ~ ! [SY2107: $i] :
~ ( SV114 @ SY2107 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3083]) ).
thf(3231,plain,
! [SV638: $i,SV114: $i > $o] :
( ( ( ! [SY2107: $i] :
~ ( SV114 @ SY2107 ) )
= $false )
| ( ( SV114 @ SV638 )
= $false )
| ( ( SV638
= ( sK67_SY3096 @ SV638 @ SV114 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3084]) ).
thf(3232,plain,
! [SV741: $i,SV639: $i,SV348: $i,SV115: $i,SV767: $i] :
( ( ( in @ SV767 @ SV115 )
= $false )
| ( ( ~ ( in @ SV767 @ ( binintersect @ SV348 @ SV639 ) )
| ( in @ SV767 @ ( binunion @ SV348 @ SV741 ) ) )
= $true )
| ( ( in @ SV741 @ ( powerset @ SV115 ) )
= $false )
| ( ( in @ SV639 @ ( powerset @ SV115 ) )
= $false )
| ( ( in @ SV348 @ ( powerset @ SV115 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3085]) ).
thf(3233,plain,
! [SV350: $i > $o,SV118: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ SV118 ) )
= $true )
| ( ( ~ ( SV350 @ SV763 ) )
= $true )
| ( ( in @ ( sK10_SY2649 @ SV350 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3086]) ).
thf(3234,plain,
! [SV350: $i > $o,SV118: $i,SV764: $i] :
( ( ( ~ ( in @ SV764 @ SV118 ) )
= $true )
| ( ( ~ ( SV350 @ SV764 ) )
= $true )
| ( ( SV350 @ ( sK10_SY2649 @ SV350 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3087]) ).
thf(3235,plain,
! [SV119: $i,SV351: $i > $o,SV692: $i] :
( ( ( ~ ( in @ ( sK56_SY2652 @ SV692 @ SV351 @ SV119 ) @ SV119 ) )
= $false )
| ( ( SV351 @ SV692 )
= $true )
| ( ( in @ SV692 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3088]) ).
thf(3236,plain,
! [SV119: $i,SV692: $i,SV351: $i > $o] :
( ( ( ~ ~ ( SV351 @ ( sK56_SY2652 @ SV692 @ SV351 @ SV119 ) ) )
= $false )
| ( ( SV351 @ SV692 )
= $true )
| ( ( in @ SV692 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3088]) ).
thf(3237,plain,
! [SV120: $i,SV352: $i,SV641: $i,SV742: $i] :
( ( ( in @ SV742 @ SV641 )
= $true )
| ( ( ~ ( in @ SV742 @ ( binintersect @ SV352 @ SV641 ) ) )
= $true )
| ( ( in @ SV742 @ SV120 )
= $false )
| ( ( in @ SV641 @ ( powerset @ SV120 ) )
= $false )
| ( ( in @ SV352 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3089]) ).
thf(3238,plain,
! [SV353: $i,SV121: $i,SV642: $i,SV765: $i] :
( ( ( ~ ( in @ SV765 @ SV642 ) )
= $true )
| ( ( in @ SV765 @ ( setminus @ SV121 @ SV353 ) )
= $true )
| ( ( in @ SV765 @ SV121 )
= $false )
| ( ( subset @ SV353 @ ( setminus @ SV121 @ SV642 ) )
= $false )
| ( ( in @ SV642 @ ( powerset @ SV121 ) )
= $false )
| ( ( in @ SV353 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3090]) ).
thf(3239,plain,
! [SV126: $i,SV693: $o,SV358: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ SV358 ) )
= $false )
| ( SV693 = $true )
| ( ( SV529 = SV126 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3091]) ).
thf(3240,plain,
! [SV358: $i,SV126: $i,SV529: $i,SV693: $o] :
( ( SV693 = $false )
| ( SV693 = $true )
| ( ( SV529 = SV126 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3091]) ).
thf(3241,plain,
! [SV126: $i,SV693: $o,SV358: $i,SV529: $i] :
( ( ( in @ SV529 @ SV358 )
= $true )
| ( SV693 = $true )
| ( SV693 = $false )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3092]) ).
thf(3242,plain,
! [SV126: $i,SV358: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ SV358 ) )
= $false )
| ( $true = $true )
| ( ( SV529 = SV126 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3094]) ).
thf(3243,plain,
! [SV358: $i,SV126: $i,SV529: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( SV529 = SV126 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3094]) ).
thf(3244,plain,
! [SV126: $i,SV358: $i,SV529: $i] :
( ( ( in @ SV529 @ SV358 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3095]) ).
thf(3245,plain,
! [SV126: $i,SV358: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ SV358 ) )
= $false )
| ( $false = $true )
| ( ( SV529 = SV126 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3097]) ).
thf(3246,plain,
! [SV358: $i,SV126: $i,SV529: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( SV529 = SV126 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3097]) ).
thf(3247,plain,
! [SV126: $i,SV358: $i,SV529: $i] :
( ( ( in @ SV529 @ SV358 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3098]) ).
thf(3248,plain,
! [SV130: $i,SV644: $i,SV362: $i,SV743: $i] :
( ( ( in @ SV743 @ SV362 )
= $true )
| ( ( ~ ( in @ SV743 @ ( binintersect @ SV362 @ SV644 ) ) )
= $true )
| ( ( in @ SV743 @ SV130 )
= $false )
| ( ( in @ SV644 @ ( powerset @ SV130 ) )
= $false )
| ( ( in @ SV362 @ ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3100]) ).
thf(3249,plain,
! [SV135: $i,SV647: $i,SV745: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ SV745 ) )
= $true )
| ( ( SV647 = SV745 )
= $true )
| ( ( SV367 @ SV647 )
= $false )
| ( ( in @ SV745 @ SV135 )
= $false )
| ( ( in @ SV647 @ SV135 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV135
@ ^ [SY2676: $i] : ( SV367 @ SY2676 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3102]) ).
thf(3250,plain,
! [SV137: $i,SV369: $i,SV649: $i,SV746: $i] :
( ( ( ~ ~ ( in @ SV746 @ SV649 ) )
= $true )
| ( ( ~ ( in @ SV746 @ SV369 ) )
= $true )
| ( ( subset @ SV369 @ SV649 )
= $false )
| ( ( in @ SV746 @ SV137 )
= $false )
| ( ( in @ SV649 @ ( powerset @ SV137 ) )
= $false )
| ( ( in @ SV369 @ ( powerset @ SV137 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3103]) ).
thf(3251,plain,
! [SV146: $i,SV377: $i,SV650: $i] :
( ( ( in @ ( sK57_SY3106 @ SV650 @ SV377 @ SV146 ) @ SV377 )
= $true )
| ( ( subset @ SV377 @ SV650 )
= $true )
| ( ( in @ SV650 @ ( powerset @ SV146 ) )
= $false )
| ( ( in @ SV377 @ ( powerset @ SV146 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3105]) ).
thf(3252,plain,
! [SV147: $i] :
( ( ! [SY2953: $i] :
( ~ ( in @ SY2953 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY2188: $i] :
( ~ ( in @ SY2188 @ SY2953 )
| ( in @ SY2188 @ SV147 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3107]) ).
thf(3253,plain,
! [SV147: $i] :
( ( ! [SY2955: $i,SY2956: $i] :
( ~ ~ ( ~ ( in @ SY2955 @ SV147 )
| ~ ( in @ SY2956 @ SV147 ) )
| ~ ! [SY2957: $i] :
( ~ ( in @ SY2957 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SY2955 @ SY2957 )
| ( in @ SY2956 @ SY2957 ) )
| ~ ( ~ ( in @ SY2956 @ SY2957 )
| ( in @ SY2955 @ SY2957 ) ) ) )
| ( SY2955 = SY2956 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3108]) ).
thf(3254,plain,
! [SV779: $i,SV147: $i,SV768: $i] :
( ( ( ~ ~ ( ~ ( in @ SV768 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SV779 @ ( sK3_SY2186 @ SV147 ) ) ) )
= $true )
| ( ( ! [SY3204: $i] :
( ~ ( in @ SY3204 @ SV768 )
| ( in @ SY3204 @ SV779 ) )
| ! [SY3205: $i] :
( ~ ( in @ SY3205 @ SV779 )
| ( in @ SY3205 @ SV768 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3109]) ).
thf(3255,plain,
! [SV147: $i,SV747: $i] :
( ( ( ! [SY3176: $i] :
( ~ ( in @ SY3176 @ SV747 )
| ( in @ SY3176 @ SV147 ) ) )
= $false )
| ( ( ~ ~ ! [SY3177: $i] :
~ ( in @ SY3177 @ SV747 ) )
= $true )
| ( ( ~ ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3110]) ).
thf(3256,plain,
! [SV748: $i,SV651: $i,SV381: $i,SV151: $i,SV769: $i] :
( ( ( in @ SV769 @ SV151 )
= $false )
| ( ( ~ ( in @ SV769 @ ( binintersect @ SV381 @ SV651 ) )
| ( in @ SV769 @ ( binunion @ SV651 @ SV748 ) ) )
= $true )
| ( ( in @ SV748 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV651 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV381 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3111]) ).
thf(3257,plain,
! [SV156: $i,SV386: $i,SV652: $i,SV749: $i] :
( ( ( ~ ( in @ SV749 @ SV652 ) )
= $true )
| ( ( ~ ( in @ SV749 @ SV386 ) )
= $true )
| ( ( subset @ SV386 @ ( setminus @ SV156 @ SV652 ) )
= $false )
| ( ( in @ SV749 @ SV156 )
= $false )
| ( ( in @ SV652 @ ( powerset @ SV156 ) )
= $false )
| ( ( in @ SV386 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3112]) ).
thf(3258,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $false )
| ( ( SV160 @ ( sK49_SY2231 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3113]) ).
thf(3259,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( SV160 @ ( sK58_SY3190 @ SV653 @ SV160 ) )
= $true )
| ( ( ~ ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3114]) ).
thf(3260,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $false )
| ( ( ( sK49_SY2231 @ SV653 @ SV160 )
= ( sK58_SY3190 @ SV653 @ SV160 ) )
= $false )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3115]) ).
thf(3261,plain,
! [SV168: $i,SV396: $i,SV548: $i,SV697: $i] :
( ( ( in @ ( sK68_SY3146 @ SV697 @ SV548 @ SV396 @ SV168 ) @ SV168 )
= $true )
| ( ( SV548 = SV697 )
= $true )
| ( ( func @ SV168 @ SV396 @ SV697 )
= $false )
| ( ( func @ SV168 @ SV396 @ SV548 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3117]) ).
thf(3262,plain,
! [SV706: $i,SV408: $i > $o,SV180: $i] :
( ( ( ( dsetconstr @ SV180
@ ^ [SY2739: $i] : ( SV408 @ SY2739 ) )
= emptyset )
= $false )
| ( $false = $true )
| ( ( in @ SV706 @ SV180 )
= $false )
| ( ( SV408 @ SV706 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3119]) ).
thf(3263,plain,
! [SV409: $i > $o,SV181: $i,SV770: $i] :
( ( ( ~ ( in @ SV770 @ SV181 )
| ~ ( SV409 @ SV770 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( in @ ( sK12_SY2740 @ SV409 @ SV181 ) @ SV181 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3120]) ).
thf(3264,plain,
! [SV409: $i > $o,SV181: $i,SV784: $i] :
( ( ( ~ ~ ( ~ ( in @ SV784 @ SV181 )
| ~ ( SV409 @ SV784 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( in @ ( sK34_SY3112 @ SV409 @ SV181 ) @ SV181 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3121]) ).
thf(3265,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ( ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( SV409 @ ( sK12_SY2740 @ SV409 @ SV181 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3122]) ).
thf(3266,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ( ~ ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( SV409 @ ( sK34_SY3112 @ SV409 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3123]) ).
thf(3267,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ( ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( ( sK12_SY2740 @ SV409 @ SV181 )
= ( sK34_SY3112 @ SV409 @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3124]) ).
thf(3268,plain,
! [SV411: $i > $o,SV780: $i,SV183: $i > $o] :
( ( ( ~ ( ~ ( SV183 @ SV780 )
| ~ ! [SY3206: $i] :
( ~ ( SV183 @ SY3206 )
| ( SV780 = SY3206 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3125]) ).
thf(3269,plain,
! [SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
| ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3126]) ).
thf(3270,plain,
! [SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3127]) ).
thf(3271,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3127]) ).
thf(3272,plain,
! [SV413: $i,SV185: $i,SV561: $i,SV760: $i,SV707: $i] :
( ( ( in @ ( kpair @ SV707 @ SV760 ) @ SV561 )
= $false )
| ( ( ( ap @ SV185 @ SV413 @ SV561 @ SV707 )
= SV760 )
= $true )
| ( ( in @ SV760 @ SV413 )
= $false )
| ( ( in @ SV707 @ SV185 )
= $false )
| ( ( in @ SV561 @ ( funcSet @ SV185 @ SV413 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3128]) ).
thf(3273,plain,
! [SV414: $i,SV659: $i,SV186: $i] :
( ( ( ~ ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV186 )
| ~ ( in @ SY3115 @ SV659 )
| ( in @ SY3115 @ SV414 ) ) )
= $true )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV186 )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3129]) ).
thf(3274,plain,
! [SV186: $i,SV414: $i,SV659: $i] :
( ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV414 )
= $true )
| ( ( ~ ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV186 )
| ~ ( in @ SY3115 @ SV659 )
| ( in @ SY3115 @ SV414 ) )
| ( SV414 = SV659 ) )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3130]) ).
thf(3275,plain,
! [SV414: $i,SV659: $i,SV186: $i] :
( ( ( ~ ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV186 )
| ~ ( in @ SY3115 @ SV659 )
| ( in @ SY3115 @ SV414 ) ) )
= $true )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV659 )
= $false )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3131]) ).
thf(3276,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( SV188 @ ( sK69_SY3116 @ SV660 @ SV188 ) )
= $true )
| ( ( SV188 @ SV660 )
= $false )
| ( ( ~ ! [SY2316: $i] :
~ ~ ( ~ ( SV188 @ SY2316 )
| ~ ! [SY2317: $i] :
( ~ ( SV188 @ SY2317 )
| ( SY2316 = SY2317 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3132]) ).
thf(3277,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ! [SY2316: $i] :
~ ~ ( ~ ( SV188 @ SY2316 )
| ~ ! [SY2317: $i] :
( ~ ( SV188 @ SY2317 )
| ( SY2316 = SY2317 ) ) ) )
= $false )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV660
= ( sK69_SY3116 @ SV660 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3133]) ).
thf(3278,plain,
! [SV752: $i,SV661: $i,SV418: $i,SV191: $i,SV771: $i] :
( ( ( in @ SV771 @ SV191 )
= $false )
| ( ( ~ ( in @ SV771 @ ( binintersect @ SV418 @ SV661 ) )
| ( in @ SV771 @ ( binintersect @ ( binunion @ SV418 @ SV752 ) @ ( binunion @ SV661 @ SV752 ) ) ) )
= $true )
| ( ( in @ SV752 @ ( powerset @ SV191 ) )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV191 ) )
= $false )
| ( ( in @ SV418 @ ( powerset @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3134]) ).
thf(3279,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) ) )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3135]) ).
thf(3280,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) ) )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3136]) ).
thf(3281,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
| ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3137]) ).
thf(3282,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3138]) ).
thf(3283,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3138]) ).
thf(3284,plain,
! [SV424: $i,SV566: $i,SV196: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK76_SY3169 @ SV196 @ SV566 @ SV424 ) @ SV424 )
| ( SV566
!= ( kpair @ ( sK35_SY2993 @ SV566 @ SV424 @ SV196 ) @ ( sK76_SY3169 @ SV196 @ SV566 @ SV424 ) ) ) ) )
= $false )
| ( ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3139]) ).
thf(3285,plain,
! [SV198: $i,SV426: $i,SV570: $i,SV712: $i] :
( ( ( in @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SV198 )
= $true )
| ( ( ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) )
| ( SV570 = SV712 ) )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3140]) ).
thf(3286,plain,
! [SV426: $i,SV712: $i,SV570: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) @ SV426 )
| ~ ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV570 )
| ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV712 ) )
= $false )
| ( ( ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) )
| ( SV570 = SV712 ) )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3141]) ).
thf(3287,plain,
! [SV200: $i,SV428: $i,SV713: $i > $o,SV571: $i,SV781: $i] :
( ( ( ~ ( in @ SV781 @ SV571 ) )
= $true )
| ( ( SV713 @ SV781 )
= $true )
| ( ( in @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ SV200 )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3142]) ).
thf(3288,plain,
! [SV428: $i,SV713: $i > $o,SV571: $i,SV200: $i] :
( ( ( in @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) @ SV428 )
= $true )
| ( ( ! [SY3157: $i] :
( ~ ( in @ SY3157 @ SV571 )
| ( SV713 @ SY3157 ) ) )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3143]) ).
thf(3289,plain,
! [SV200: $i,SV428: $i,SV571: $i,SV713: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) ) @ SV571 ) )
= $false )
| ( ( ! [SY3157: $i] :
( ~ ( in @ SY3157 @ SV571 )
| ( SV713 @ SY3157 ) ) )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3144]) ).
thf(3290,plain,
! [SV200: $i,SV428: $i,SV571: $i,SV713: $i > $o] :
( ( ( SV713 @ ( kpair @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) ) )
= $false )
| ( ( ! [SY3157: $i] :
( ~ ( in @ SY3157 @ SV571 )
| ( SV713 @ SY3157 ) ) )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3144]) ).
thf(3291,plain,
! [SV714: $i,SV429: $i > $o,SV201: $i] :
( ( ( ! [SY2794: $i] :
( ~ ( in @ SY2794 @ SV201 )
| ( SV429 @ SY2794 ) ) )
= $false )
| ( ( in @ SV714 @ SV201 )
= $false )
| ( ( SV429 @ SV714 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3145]) ).
thf(3292,plain,
! [SV436: $i > $o,SV212: $i,SV772: $i] :
( ( ( ~ ( in @ SV772 @ SV212 )
| ~ ( SV436 @ SV772 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( in @ ( sK15_SY2806 @ SV436 @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3146]) ).
thf(3293,plain,
! [SV436: $i > $o,SV212: $i,SV785: $i] :
( ( ( ~ ~ ( ~ ( in @ SV785 @ SV212 )
| ~ ( SV436 @ SV785 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( in @ ( sK36_SY3121 @ SV436 @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3147]) ).
thf(3294,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ( ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( SV436 @ ( sK15_SY2806 @ SV436 @ SV212 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3148]) ).
thf(3295,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ( ~ ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( SV436 @ ( sK36_SY3121 @ SV436 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3149]) ).
thf(3296,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ( ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( ( sK15_SY2806 @ SV436 @ SV212 )
= ( sK36_SY3121 @ SV436 @ SV212 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3150]) ).
thf(3297,plain,
! [SV215: $i] :
( ( ( in @ ( sK44_SY2395 @ SV215 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( ! [SY2396: $i] :
( ~ ( in @ SY2396 @ omega )
| ( in @ SY2396 @ SV215 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3151]) ).
thf(3298,plain,
! [SV215: $i] :
( ( ( in @ ( sK44_SY2395 @ SV215 ) @ SV215 )
= $true )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( ! [SY2396: $i] :
( ~ ( in @ SY2396 @ omega )
| ( in @ SY2396 @ SV215 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3152]) ).
thf(3299,plain,
! [SV219: $i,SV442: $i,SV581: $i,SV720: $i] :
( ( ( in @ ( sK72_SY3158 @ SV720 @ SV581 @ SV442 @ SV219 ) @ SV219 )
= $true )
| ( ( SV581 = SV720 )
= $true )
| ( ( in @ SV720 @ ( funcSet @ SV219 @ SV442 ) )
= $false )
| ( ( in @ SV581 @ ( funcSet @ SV219 @ SV442 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3154]) ).
thf(3300,plain,
! [SV225: $i,SV448: $i] :
( ( ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV448 )
= $true )
| ( ( in @ ( sK16_SY2834 @ SV448 @ SV225 ) @ SV225 )
= $true )
| ( ( SV225 = SV448 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3156]) ).
thf(3301,plain,
! [SV243: $i,SV667: $i,SV465: $i,SV756: $i] :
( ( ( ~ ( in @ SV756 @ SV465 ) )
= $true )
| ( ( in @ SV756 @ SV667 )
= $true )
| ( ( in @ SV465 @ ( powerset @ SV667 ) )
= $false )
| ( ( in @ SV756 @ SV243 )
= $false )
| ( ( in @ SV667 @ ( powerset @ SV243 ) )
= $false )
| ( ( in @ SV465 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3159]) ).
thf(3302,plain,
! [SV247: $i,SV469: $i,SV600: $i,SV728: $i] :
( ( ( in @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) @ SV247 )
= $true )
| ( ( ! [SY3166: $i] :
( ~ ( in @ SY3166 @ SV247 )
| ! [SY3167: $i] :
( ~ ( in @ SY3167 @ SV469 )
| ~ ( in @ ( kpair @ SY3166 @ SY3167 ) @ SV728 )
| ( in @ ( kpair @ SY3166 @ SY3167 ) @ SV600 ) ) ) )
= $true )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3160]) ).
thf(3303,plain,
! [SV600: $i,SV728: $i,SV469: $i,SV247: $i,SV786: $i] :
( ( ( ~ ( in @ SV786 @ SV247 )
| ! [SY3209: $i] :
( ~ ( in @ SY3209 @ SV469 )
| ~ ( in @ ( kpair @ SV786 @ SY3209 ) @ SV728 )
| ( in @ ( kpair @ SV786 @ SY3209 ) @ SV600 ) ) )
= $true )
| ( ( ( ap @ SV247 @ SV469 @ SV600 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) )
= ( ap @ SV247 @ SV469 @ SV728 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) ) )
= $false )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3161]) ).
thf(3304,plain,
! [SV471: $i,SV249: $i > $i > $o,SV773: $i] :
( ( ( ~ ( ~ ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
| ~ ! [SY3202: $i] :
~ ~ ( ~ ( in @ SY3202 @ SV471 )
| ~ ( SV249 @ SY3202 @ SV773 ) ) ) )
= $false )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3162]) ).
thf(3305,plain,
! [SV773: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ~ ( ~ ~ ! [SY3203: $i] :
~ ~ ( ~ ( in @ SY3203 @ SV471 )
| ~ ( SV249 @ SY3203 @ SV773 ) )
| ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) ) ) )
= $false )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3162]) ).
thf(3306,plain,
! [SV757: $i,SV471: $i,SV249: $i > $i > $o] :
( ( ( ! [SY3187: $i] :
( ~ ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SY3187 )
| ( SV757 = SY3187 ) ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( ~ ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3163]) ).
thf(3307,plain,
! [SV476: $i,SV733: $i,SV254: $i,SV669: $i] :
( ( ( in @ SV669 @ SV254 )
= $false )
| ( ( in @ SV733 @ SV476 )
= $true )
| ( ( SV669 = SV733 )
= $false )
| ( ( SV254 = SV476 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3164]) ).
thf(3308,plain,
! [SV254: $i,SV669: $i,SV476: $i,SV733: $i] :
( ( ( in @ SV733 @ SV476 )
= $false )
| ( ( in @ SV669 @ SV254 )
= $true )
| ( ( SV669 = SV733 )
= $false )
| ( ( SV254 = SV476 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3165]) ).
thf(3309,plain,
! [SV670: $i,SV256: $i > $o] :
( ( ( SV256 @ ( sK74_SY3127 @ SV670 @ SV256 ) )
= $true )
| ( ( SV256 @ SV670 )
= $false )
| ( ( ~ ! [SY2511: $i] :
~ ! [SY2512: $i] :
~ ( ~ ( ~ ( SV256 @ SY2512 )
| ( SY2512 = SY2511 ) )
| ~ ( ( SY2512 != SY2511 )
| ( SV256 @ SY2512 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3166]) ).
thf(3310,plain,
! [SV670: $i,SV256: $i > $o] :
( ( ( ! [SY2511: $i] :
~ ! [SY2512: $i] :
~ ( ~ ( ~ ( SV256 @ SY2512 )
| ( SY2512 = SY2511 ) )
| ~ ( ( SY2512 != SY2511 )
| ( SV256 @ SY2512 ) ) ) )
= $false )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV670
= ( sK74_SY3127 @ SV670 @ SV256 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3167]) ).
thf(3311,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ! [SY1902: $i] :
~ ~ ( ~ ( SV35 @ SY1902 )
| ~ ! [SY1903: $i] :
( ~ ( SV35 @ SY1903 )
| ( SY1902 = SY1903 ) ) ) )
= $false )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV35 @ ( sK60_SY3073 @ SV621 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3168]) ).
thf(3312,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ~ ~ ( ~ ( SV35 @ ( sK78_SY1902 @ SV621 @ SV35 ) )
| ~ ! [SY3210: $i] :
( ~ ( SV35 @ SY3210 )
| ( ( sK78_SY1902 @ SV621 @ SV35 )
= SY3210 ) ) ) )
= $false )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV621
= ( sK60_SY3073 @ SV621 @ SV35 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3169]) ).
thf(3313,plain,
! [SV40: $i,SV286: $i,SV623: $i > $o,SV676: $i > $o] :
( ( ( ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 )
= ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
= $true )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3172]) ).
thf(3314,plain,
! [SV40: $i,SV286: $i,SV676: $i > $o,SV623: $i > $o] :
( ( ( ~ ( ~ ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) )
| ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) ) )
| ~ ( ~ ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
| ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3173]) ).
thf(3315,plain,
! [SV287: $i > $o,SV41: $i,SV774: $i] :
( ( ( in @ SV774 @ SV41 )
= $false )
| ( ( ~ ( SV287 @ SV774 ) )
= $true )
| ( ( in @ ( sK30_SY2541 @ SV287 @ SV41 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3174]) ).
thf(3316,plain,
! [SV287: $i > $o,SV41: $i,SV775: $i] :
( ( ( in @ SV775 @ SV41 )
= $false )
| ( ( ~ ( SV287 @ SV775 ) )
= $true )
| ( ( SV287 @ ( sK30_SY2541 @ SV287 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3175]) ).
thf(3317,plain,
! [SV44: $i > $o,SV624: $i] :
( ( ( ( sK31_SY3079 @ SV624 @ SV44 )
!= SV624 )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3176]) ).
thf(3318,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3176]) ).
thf(3319,plain,
! [SV44: $i > $o,SV624: $i] :
( ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3177]) ).
thf(3320,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3178]) ).
thf(3321,plain,
! [SV66: $i,SV307: $i,SV626: $i,SV738: $i] :
( ( ( in @ SV738 @ SV626 )
= $false )
| ( ( in @ SV738 @ ( binunion @ SV307 @ SV626 ) )
= $true )
| ( ( in @ SV738 @ SV66 )
= $false )
| ( ( in @ SV626 @ ( powerset @ SV66 ) )
= $false )
| ( ( in @ SV307 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3180]) ).
thf(3322,plain,
! [SV310: $i,SV69: $i,SV759: $i] :
( ( ( in @ SV759 @ SV69 )
= $false )
| ( ( in @ SV310 @ SV759 )
= $false )
| ( ( in @ SV310 @ ( setunion @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3183]) ).
thf(3323,plain,
! [SV315: $i,SV686: $o,SV74: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV74 ) )
= $true )
| ( SV686 = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3186]) ).
thf(3324,plain,
! [SV74: $i,SV686: $o,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 ) )
= $false )
| ( SV686 = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3187]) ).
thf(3325,plain,
! [SV315: $i,SV74: $i,SV509: $i,SV686: $o] :
( ( SV686 = $false )
| ( SV686 = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3187]) ).
thf(3326,plain,
! [SV686: $o,SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| SV686 )
= $false )
| ( SV686 = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3188]) ).
thf(3327,plain,
! [SV315: $i,SV686: $o,SV74: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV74 ) )
= $true )
| ( SV686 = $true )
| ( SV686 = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3189]) ).
thf(3328,plain,
! [SV74: $i,SV686: $o,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 ) )
= $false )
| ( SV686 = $true )
| ( SV686 = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3190]) ).
thf(3329,plain,
! [SV315: $i,SV74: $i,SV509: $i,SV686: $o] :
( ( SV686 = $false )
| ( SV686 = $true )
| ( SV686 = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3190]) ).
thf(3330,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV74 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3191]) ).
thf(3331,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3192]) ).
thf(3332,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3192]) ).
thf(3333,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3193]) ).
thf(3334,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV74 ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3194]) ).
thf(3335,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3195]) ).
thf(3336,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3195]) ).
thf(3337,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV74 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3196]) ).
thf(3338,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3197]) ).
thf(3339,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3197]) ).
thf(3340,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV74 )
| ~ ( in @ SV509 @ SV315 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3198]) ).
thf(3341,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV74 ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3199]) ).
thf(3342,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3200]) ).
thf(3343,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3200]) ).
thf(3344,plain,
! [SV318: $i > $o,SV79: $i,SV776: $i] :
( ( ( in @ SV776 @ SV79 )
= $false )
| ( ( ~ ( SV318 @ SV776 ) )
= $true )
| ( ( in @ ( sK32_SY2591 @ SV318 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3201]) ).
thf(3345,plain,
! [SV318: $i > $o,SV79: $i,SV777: $i] :
( ( ( in @ SV777 @ SV79 )
= $false )
| ( ( ~ ( SV318 @ SV777 ) )
= $true )
| ( ( SV318 @ ( sK32_SY2591 @ SV318 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3202]) ).
thf(3346,plain,
! [SV82: $i,SV630: $i] :
( ( ( ! [SY3174: $i] :
~ ~ ( ~ ( in @ SY3174 @ ( sK38_SY2017 @ SV630 @ SV82 ) )
| ~ ( in @ SY3174 @ SV82 ) ) )
= $true )
| ( ( in @ SV630 @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3203]) ).
thf(3347,plain,
! [SV84: $i,SV607: $o,SV322: $i,SV513: $i] :
( ( ( in @ SV513 @ SV322 )
= $true )
| ( SV607 = $true )
| ( ( in @ SV513 @ SV84 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3204]) ).
thf(3348,plain,
! [SV84: $i,SV322: $i,SV513: $i] :
( ( ( in @ SV513 @ SV322 )
= $true )
| ( $true = $true )
| ( ( in @ SV513 @ SV84 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3207]) ).
thf(3349,plain,
! [SV84: $i,SV322: $i,SV513: $i] :
( ( ( in @ SV513 @ SV322 )
= $true )
| ( $false = $true )
| ( ( in @ SV513 @ SV84 )
= $true )
| ( ( in @ SV513 @ ( binunion @ SV84 @ SV322 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3210]) ).
thf(3350,plain,
! [SV85: $i,SV631: $i,SV323: $i,SV740: $i] :
( ( ( in @ SV740 @ SV323 )
= $false )
| ( ( in @ SV740 @ ( binunion @ SV323 @ SV631 ) )
= $true )
| ( ( in @ SV740 @ SV85 )
= $false )
| ( ( in @ SV631 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV323 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3213]) ).
thf(3351,plain,
! [SV87: $i,SV325: $i > $o,SV687: $i] :
( ( ( in @ ( sK53_SY2599 @ SV687 @ SV325 @ SV87 ) @ SV87 )
= $true )
| ( ( SV325 @ SV687 )
= $true )
| ( ( in @ SV687 @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3214]) ).
thf(3352,plain,
! [SV87: $i,SV687: $i,SV325: $i > $o] :
( ( ( ~ ( SV325 @ ( sK53_SY2599 @ SV687 @ SV325 @ SV87 ) ) )
= $true )
| ( ( SV325 @ SV687 )
= $true )
| ( ( in @ SV687 @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3215]) ).
thf(3353,plain,
! [SV632: $i,SV787: $i,SV91: $i > $o] :
( ( ( ! [SY3211: $i] :
( ~ ( SV91 @ SV787 )
| ~ ( SV91 @ SY3211 )
| ( SV787 = SY3211 ) ) )
= $true )
| ( ( SV91 @ SV632 )
= $false )
| ( ( SV91 @ ( sK62_SY3087 @ SV632 @ SV91 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3216]) ).
thf(3354,plain,
! [SV632: $i,SV788: $i,SV782: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV782 )
| ~ ( SV91 @ SV788 )
| ( SV782 = SV788 ) )
= $true )
| ( ( SV91 @ SV632 )
= $false )
| ( ( SV632
= ( sK62_SY3087 @ SV632 @ SV91 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3217]) ).
thf(3355,plain,
! [SV332: $i,SV689: $i,SV516: $i,SV95: $i] :
( ( ( ~ ( in @ ( sK75_SY3197 @ SV95 @ SV516 @ SV689 @ SV332 ) @ SV332 ) )
= $false )
| ( ( subset @ SV516 @ SV689 )
= $true )
| ( ( subset @ SV689 @ ( cartprod @ SV95 @ SV332 ) )
= $false )
| ( ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3219]) ).
thf(3356,plain,
! [SV95: $i,SV332: $i,SV516: $i,SV689: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK63_SY3141 @ SV689 @ SV516 @ SV332 @ SV95 ) @ ( sK75_SY3197 @ SV95 @ SV516 @ SV689 @ SV332 ) ) @ SV516 )
| ( in @ ( kpair @ ( sK63_SY3141 @ SV689 @ SV516 @ SV332 @ SV95 ) @ ( sK75_SY3197 @ SV95 @ SV516 @ SV689 @ SV332 ) ) @ SV689 ) )
= $false )
| ( ( subset @ SV516 @ SV689 )
= $true )
| ( ( subset @ SV689 @ ( cartprod @ SV95 @ SV332 ) )
= $false )
| ( ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3219]) ).
thf(3357,plain,
( ( ( in @ sK39_SY3168 @ sK2_SY2624 )
= $false )
| ( sK33_SY3090 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[3221]) ).
thf(3358,plain,
( ( ( ~ ( in @ sK39_SY3168 @ sK9_SY2932 ) )
= $true )
| ( sK33_SY3090 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[3222]) ).
thf(3359,plain,
! [SV105: $i,SV342: $i,SV691: $i > $o,SV522: $i,SV778: $i] :
( ( ( in @ SV778 @ SV522 )
= $false )
| ( ( SV691 @ SV778 )
= $true )
| ( ( in @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ SV105 )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3223]) ).
thf(3360,plain,
! [SV342: $i,SV105: $i,SV691: $i > $o,SV522: $i,SV789: $i] :
( ( ( ~ ( in @ SV789 @ SV522 )
| ( SV691 @ SV789 ) )
= $true )
| ( ( in @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) @ SV342 )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3224]) ).
thf(3361,plain,
! [SV105: $i,SV342: $i,SV522: $i,SV691: $i > $o] :
( ( ( in @ ( kpair @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) ) @ SV522 )
= $true )
| ( ( ! [SY3145: $i] :
( ~ ( in @ SY3145 @ SV522 )
| ( SV691 @ SY3145 ) ) )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3225]) ).
thf(3362,plain,
! [SV105: $i,SV342: $i,SV691: $i > $o,SV522: $i,SV790: $i] :
( ( ( ~ ( in @ SV790 @ SV522 )
| ( SV691 @ SV790 ) )
= $true )
| ( ( SV691 @ ( kpair @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) ) )
= $false )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3226]) ).
thf(3363,plain,
! [SV635: $i,SV791: $i,SV106: $i > $o] :
( ( ( ! [SY3212: $i] :
( ~ ( SV106 @ SV791 )
| ~ ( SV106 @ SY3212 )
| ( SV791 = SY3212 ) ) )
= $true )
| ( ( SV106 @ SV635 )
= $false )
| ( ( SV106 @ ( sK65_SY3092 @ SV635 @ SV106 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3227]) ).
thf(3364,plain,
! [SV635: $i,SV792: $i,SV783: $i,SV106: $i > $o] :
( ( ( ~ ( SV106 @ SV783 )
| ~ ( SV106 @ SV792 )
| ( SV783 = SV792 ) )
= $true )
| ( ( SV106 @ SV635 )
= $false )
| ( ( SV635
= ( sK65_SY3092 @ SV635 @ SV106 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3228]) ).
thf(3365,plain,
! [SV638: $i,SV114: $i > $o] :
( ( ( ! [SY2107: $i] :
~ ( SV114 @ SY2107 ) )
= $false )
| ( ( SV114 @ SV638 )
= $false )
| ( ( SV114 @ ( sK67_SY3096 @ SV638 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3230]) ).
thf(3366,plain,
! [SV638: $i,SV114: $i > $o] :
( ( ( ~ ( SV114 @ ( sK79_SY2107 @ SV638 @ SV114 ) ) )
= $false )
| ( ( SV114 @ SV638 )
= $false )
| ( ( SV638
= ( sK67_SY3096 @ SV638 @ SV114 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3231]) ).
thf(3367,plain,
! [SV115: $i,SV741: $i,SV639: $i,SV348: $i,SV767: $i] :
( ( ( ~ ( in @ SV767 @ ( binintersect @ SV348 @ SV639 ) ) )
= $true )
| ( ( in @ SV767 @ ( binunion @ SV348 @ SV741 ) )
= $true )
| ( ( in @ SV767 @ SV115 )
= $false )
| ( ( in @ SV741 @ ( powerset @ SV115 ) )
= $false )
| ( ( in @ SV639 @ ( powerset @ SV115 ) )
= $false )
| ( ( in @ SV348 @ ( powerset @ SV115 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3232]) ).
thf(3368,plain,
! [SV350: $i > $o,SV118: $i,SV763: $i] :
( ( ( in @ SV763 @ SV118 )
= $false )
| ( ( ~ ( SV350 @ SV763 ) )
= $true )
| ( ( in @ ( sK10_SY2649 @ SV350 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3233]) ).
thf(3369,plain,
! [SV350: $i > $o,SV118: $i,SV764: $i] :
( ( ( in @ SV764 @ SV118 )
= $false )
| ( ( ~ ( SV350 @ SV764 ) )
= $true )
| ( ( SV350 @ ( sK10_SY2649 @ SV350 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3234]) ).
thf(3370,plain,
! [SV119: $i,SV351: $i > $o,SV692: $i] :
( ( ( in @ ( sK56_SY2652 @ SV692 @ SV351 @ SV119 ) @ SV119 )
= $true )
| ( ( SV351 @ SV692 )
= $true )
| ( ( in @ SV692 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3235]) ).
thf(3371,plain,
! [SV119: $i,SV692: $i,SV351: $i > $o] :
( ( ( ~ ( SV351 @ ( sK56_SY2652 @ SV692 @ SV351 @ SV119 ) ) )
= $true )
| ( ( SV351 @ SV692 )
= $true )
| ( ( in @ SV692 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3236]) ).
thf(3372,plain,
! [SV120: $i,SV641: $i,SV352: $i,SV742: $i] :
( ( ( in @ SV742 @ ( binintersect @ SV352 @ SV641 ) )
= $false )
| ( ( in @ SV742 @ SV641 )
= $true )
| ( ( in @ SV742 @ SV120 )
= $false )
| ( ( in @ SV641 @ ( powerset @ SV120 ) )
= $false )
| ( ( in @ SV352 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3237]) ).
thf(3373,plain,
! [SV353: $i,SV121: $i,SV642: $i,SV765: $i] :
( ( ( in @ SV765 @ SV642 )
= $false )
| ( ( in @ SV765 @ ( setminus @ SV121 @ SV353 ) )
= $true )
| ( ( in @ SV765 @ SV121 )
= $false )
| ( ( subset @ SV353 @ ( setminus @ SV121 @ SV642 ) )
= $false )
| ( ( in @ SV642 @ ( powerset @ SV121 ) )
= $false )
| ( ( in @ SV353 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3238]) ).
thf(3374,plain,
! [SV126: $i,SV693: $o,SV358: $i,SV529: $i] :
( ( ( in @ SV529 @ SV358 )
= $true )
| ( SV693 = $true )
| ( ( SV529 = SV126 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3239]) ).
thf(3375,plain,
! [SV126: $i,SV358: $i,SV529: $i] :
( ( ( in @ SV529 @ SV358 )
= $true )
| ( $true = $true )
| ( ( SV529 = SV126 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3242]) ).
thf(3376,plain,
! [SV126: $i,SV358: $i,SV529: $i] :
( ( ( in @ SV529 @ SV358 )
= $true )
| ( $false = $true )
| ( ( SV529 = SV126 )
= $true )
| ( ( in @ SV529 @ ( setadjoin @ SV126 @ SV358 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3245]) ).
thf(3377,plain,
! [SV130: $i,SV644: $i,SV362: $i,SV743: $i] :
( ( ( in @ SV743 @ ( binintersect @ SV362 @ SV644 ) )
= $false )
| ( ( in @ SV743 @ SV362 )
= $true )
| ( ( in @ SV743 @ SV130 )
= $false )
| ( ( in @ SV644 @ ( powerset @ SV130 ) )
= $false )
| ( ( in @ SV362 @ ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3248]) ).
thf(3378,plain,
! [SV135: $i,SV647: $i,SV745: $i,SV367: $i > $o] :
( ( ( SV367 @ SV745 )
= $false )
| ( ( SV647 = SV745 )
= $true )
| ( ( SV367 @ SV647 )
= $false )
| ( ( in @ SV745 @ SV135 )
= $false )
| ( ( in @ SV647 @ SV135 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV135
@ ^ [SY2676: $i] : ( SV367 @ SY2676 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3249]) ).
thf(3379,plain,
! [SV137: $i,SV369: $i,SV649: $i,SV746: $i] :
( ( ( ~ ( in @ SV746 @ SV649 ) )
= $false )
| ( ( ~ ( in @ SV746 @ SV369 ) )
= $true )
| ( ( subset @ SV369 @ SV649 )
= $false )
| ( ( in @ SV746 @ SV137 )
= $false )
| ( ( in @ SV649 @ ( powerset @ SV137 ) )
= $false )
| ( ( in @ SV369 @ ( powerset @ SV137 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3250]) ).
thf(3380,plain,
! [SV147: $i,SV793: $i] :
( ( ~ ( in @ SV793 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3213: $i] :
( ~ ( in @ SY3213 @ SV793 )
| ( in @ SY3213 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3252]) ).
thf(3381,plain,
! [SV147: $i,SV794: $i] :
( ( ! [SY3214: $i] :
( ~ ~ ( ~ ( in @ SV794 @ SV147 )
| ~ ( in @ SY3214 @ SV147 ) )
| ~ ! [SY3215: $i] :
( ~ ( in @ SY3215 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SV794 @ SY3215 )
| ( in @ SY3214 @ SY3215 ) )
| ~ ( ~ ( in @ SY3214 @ SY3215 )
| ( in @ SV794 @ SY3215 ) ) ) )
| ( SV794 = SY3214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3253]) ).
thf(3382,plain,
! [SV779: $i,SV147: $i,SV768: $i] :
( ( ( ~ ( ~ ( in @ SV768 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SV779 @ ( sK3_SY2186 @ SV147 ) ) ) )
= $false )
| ( ( ! [SY3204: $i] :
( ~ ( in @ SY3204 @ SV768 )
| ( in @ SY3204 @ SV779 ) )
| ! [SY3205: $i] :
( ~ ( in @ SY3205 @ SV779 )
| ( in @ SY3205 @ SV768 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3254]) ).
thf(3383,plain,
! [SV747: $i,SV147: $i] :
( ( ( ~ ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
| ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 ) )
= $false )
| ( ( ~ ~ ! [SY3177: $i] :
~ ( in @ SY3177 @ SV747 ) )
= $true )
| ( ( ~ ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3255]) ).
thf(3384,plain,
! [SV151: $i,SV748: $i,SV651: $i,SV381: $i,SV769: $i] :
( ( ( ~ ( in @ SV769 @ ( binintersect @ SV381 @ SV651 ) ) )
= $true )
| ( ( in @ SV769 @ ( binunion @ SV651 @ SV748 ) )
= $true )
| ( ( in @ SV769 @ SV151 )
= $false )
| ( ( in @ SV748 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV651 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV381 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3256]) ).
thf(3385,plain,
! [SV156: $i,SV386: $i,SV652: $i,SV749: $i] :
( ( ( in @ SV749 @ SV652 )
= $false )
| ( ( ~ ( in @ SV749 @ SV386 ) )
= $true )
| ( ( subset @ SV386 @ ( setminus @ SV156 @ SV652 ) )
= $false )
| ( ( in @ SV749 @ SV156 )
= $false )
| ( ( in @ SV652 @ ( powerset @ SV156 ) )
= $false )
| ( ( in @ SV386 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3257]) ).
thf(3386,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ~ ( ~ ( SV160 @ ( sK81_SY2233 @ SV653 @ SV160 ) )
| ~ ! [SY3216: $i] :
( ~ ( SV160 @ SY3216 )
| ( ( sK81_SY2233 @ SV653 @ SV160 )
= SY3216 ) ) ) )
= $false )
| ( ( SV160 @ ( sK49_SY2231 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3258]) ).
thf(3387,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ! [SY2233: $i] :
~ ~ ( ~ ( SV160 @ SY2233 )
| ~ ! [SY2234: $i] :
( ~ ( SV160 @ SY2234 )
| ( SY2233 = SY2234 ) ) ) )
= $false )
| ( ( SV160 @ ( sK58_SY3190 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3259]) ).
thf(3388,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ~ ( ~ ( SV160 @ ( sK82_SY2233 @ SV653 @ SV160 ) )
| ~ ! [SY3217: $i] :
( ~ ( SV160 @ SY3217 )
| ( ( sK82_SY2233 @ SV653 @ SV160 )
= SY3217 ) ) ) )
= $false )
| ( ( ( sK49_SY2231 @ SV653 @ SV160 )
= ( sK58_SY3190 @ SV653 @ SV160 ) )
= $false )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3260]) ).
thf(3389,plain,
! [SV409: $i > $o,SV181: $i,SV770: $i] :
( ( ( ~ ( in @ SV770 @ SV181 ) )
= $true )
| ( ( ~ ( SV409 @ SV770 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( in @ ( sK12_SY2740 @ SV409 @ SV181 ) @ SV181 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3263]) ).
thf(3390,plain,
! [SV409: $i > $o,SV181: $i,SV784: $i] :
( ( ( ~ ( ~ ( in @ SV784 @ SV181 )
| ~ ( SV409 @ SV784 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( in @ ( sK34_SY3112 @ SV409 @ SV181 ) @ SV181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3264]) ).
thf(3391,plain,
! [SV409: $i > $o,SV181: $i,SV795: $i] :
( ( ( ~ ~ ( ~ ( in @ SV795 @ SV181 )
| ~ ( SV409 @ SV795 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( SV409 @ ( sK12_SY2740 @ SV409 @ SV181 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3265]) ).
thf(3392,plain,
! [SV409: $i > $o,SV181: $i] :
( ( ( ! [SY2742: $i] :
~ ~ ( ~ ( in @ SY2742 @ SV181 )
| ~ ( SV409 @ SY2742 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( SV409 @ ( sK34_SY3112 @ SV409 @ SV181 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3266]) ).
thf(3393,plain,
! [SV409: $i > $o,SV181: $i,SV796: $i] :
( ( ( ~ ~ ( ~ ( in @ SV796 @ SV181 )
| ~ ( SV409 @ SV796 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( ( sK12_SY2740 @ SV409 @ SV181 )
= ( sK34_SY3112 @ SV409 @ SV181 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3267]) ).
thf(3394,plain,
! [SV411: $i > $o,SV780: $i,SV183: $i > $o] :
( ( ( ~ ( SV183 @ SV780 )
| ~ ! [SY3206: $i] :
( ~ ( SV183 @ SY3206 )
| ( SV780 = SY3206 ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3268]) ).
thf(3395,plain,
! [SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3269]) ).
thf(3396,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3269]) ).
thf(3397,plain,
! [SV183: $i > $o,SV411: $i > $o] :
( ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3270]) ).
thf(3398,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3271]) ).
thf(3399,plain,
! [SV414: $i,SV659: $i,SV186: $i] :
( ( ( ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV186 )
| ~ ( in @ SY3115 @ SV659 )
| ( in @ SY3115 @ SV414 ) ) )
= $false )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV186 )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3273]) ).
thf(3400,plain,
! [SV414: $i,SV659: $i,SV186: $i] :
( ( ( ~ ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV186 )
| ~ ( in @ SY3115 @ SV659 )
| ( in @ SY3115 @ SV414 ) ) )
= $true )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV414 )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3274]) ).
thf(3401,plain,
! [SV414: $i,SV659: $i,SV186: $i] :
( ( ( ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV186 )
| ~ ( in @ SY3115 @ SV659 )
| ( in @ SY3115 @ SV414 ) ) )
= $false )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV659 )
= $false )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3275]) ).
thf(3402,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ! [SY2316: $i] :
~ ~ ( ~ ( SV188 @ SY2316 )
| ~ ! [SY2317: $i] :
( ~ ( SV188 @ SY2317 )
| ( SY2316 = SY2317 ) ) ) )
= $false )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV188 @ ( sK69_SY3116 @ SV660 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3276]) ).
thf(3403,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ~ ~ ( ~ ( SV188 @ ( sK83_SY2316 @ SV660 @ SV188 ) )
| ~ ! [SY3218: $i] :
( ~ ( SV188 @ SY3218 )
| ( ( sK83_SY2316 @ SV660 @ SV188 )
= SY3218 ) ) ) )
= $false )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV660
= ( sK69_SY3116 @ SV660 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3277]) ).
thf(3404,plain,
! [SV191: $i,SV752: $i,SV661: $i,SV418: $i,SV771: $i] :
( ( ( ~ ( in @ SV771 @ ( binintersect @ SV418 @ SV661 ) ) )
= $true )
| ( ( in @ SV771 @ ( binintersect @ ( binunion @ SV418 @ SV752 ) @ ( binunion @ SV661 @ SV752 ) ) )
= $true )
| ( ( in @ SV771 @ SV191 )
= $false )
| ( ( in @ SV752 @ ( powerset @ SV191 ) )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV191 ) )
= $false )
| ( ( in @ SV418 @ ( powerset @ SV191 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3278]) ).
thf(3405,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3279]) ).
thf(3406,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3280]) ).
thf(3407,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3281]) ).
thf(3408,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3281]) ).
thf(3409,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3282]) ).
thf(3410,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3283]) ).
thf(3411,plain,
! [SV424: $i,SV566: $i,SV196: $i] :
( ( ( ~ ( ~ ( in @ ( sK76_SY3169 @ SV196 @ SV566 @ SV424 ) @ SV424 )
| ( SV566
!= ( kpair @ ( sK35_SY2993 @ SV566 @ SV424 @ SV196 ) @ ( sK76_SY3169 @ SV196 @ SV566 @ SV424 ) ) ) ) )
= $true )
| ( ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3284]) ).
thf(3412,plain,
! [SV570: $i,SV712: $i,SV426: $i,SV198: $i] :
( ( ( ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) ) )
= $true )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SV198 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3285]) ).
thf(3413,plain,
! [SV426: $i,SV712: $i,SV570: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) @ SV426 ) )
= $false )
| ( ( ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) )
| ( SV570 = SV712 ) )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3286]) ).
thf(3414,plain,
! [SV198: $i,SV426: $i,SV570: $i,SV712: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV570 )
| ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV712 ) )
= $false )
| ( ( ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) )
| ( SV570 = SV712 ) )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3286]) ).
thf(3415,plain,
! [SV200: $i,SV428: $i,SV713: $i > $o,SV571: $i,SV781: $i] :
( ( ( in @ SV781 @ SV571 )
= $false )
| ( ( SV713 @ SV781 )
= $true )
| ( ( in @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ SV200 )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3287]) ).
thf(3416,plain,
! [SV428: $i,SV200: $i,SV713: $i > $o,SV571: $i,SV797: $i] :
( ( ( ~ ( in @ SV797 @ SV571 )
| ( SV713 @ SV797 ) )
= $true )
| ( ( in @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) @ SV428 )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3288]) ).
thf(3417,plain,
! [SV200: $i,SV428: $i,SV571: $i,SV713: $i > $o] :
( ( ( in @ ( kpair @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) ) @ SV571 )
= $true )
| ( ( ! [SY3157: $i] :
( ~ ( in @ SY3157 @ SV571 )
| ( SV713 @ SY3157 ) ) )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3289]) ).
thf(3418,plain,
! [SV200: $i,SV428: $i,SV713: $i > $o,SV571: $i,SV798: $i] :
( ( ( ~ ( in @ SV798 @ SV571 )
| ( SV713 @ SV798 ) )
= $true )
| ( ( SV713 @ ( kpair @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) ) )
= $false )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3290]) ).
thf(3419,plain,
! [SV201: $i,SV429: $i > $o,SV714: $i] :
( ( ( ~ ( in @ ( sK84_SY2794 @ SV714 @ SV429 @ SV201 ) @ SV201 )
| ( SV429 @ ( sK84_SY2794 @ SV714 @ SV429 @ SV201 ) ) )
= $false )
| ( ( in @ SV714 @ SV201 )
= $false )
| ( ( SV429 @ SV714 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3291]) ).
thf(3420,plain,
! [SV436: $i > $o,SV212: $i,SV772: $i] :
( ( ( ~ ( in @ SV772 @ SV212 ) )
= $true )
| ( ( ~ ( SV436 @ SV772 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( in @ ( sK15_SY2806 @ SV436 @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3292]) ).
thf(3421,plain,
! [SV436: $i > $o,SV212: $i,SV785: $i] :
( ( ( ~ ( ~ ( in @ SV785 @ SV212 )
| ~ ( SV436 @ SV785 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( in @ ( sK36_SY3121 @ SV436 @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3293]) ).
thf(3422,plain,
! [SV436: $i > $o,SV212: $i,SV799: $i] :
( ( ( ~ ~ ( ~ ( in @ SV799 @ SV212 )
| ~ ( SV436 @ SV799 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( SV436 @ ( sK15_SY2806 @ SV436 @ SV212 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3294]) ).
thf(3423,plain,
! [SV436: $i > $o,SV212: $i] :
( ( ( ! [SY2808: $i] :
~ ~ ( ~ ( in @ SY2808 @ SV212 )
| ~ ( SV436 @ SY2808 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( SV436 @ ( sK36_SY3121 @ SV436 @ SV212 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3295]) ).
thf(3424,plain,
! [SV436: $i > $o,SV212: $i,SV800: $i] :
( ( ( ~ ~ ( ~ ( in @ SV800 @ SV212 )
| ~ ( SV436 @ SV800 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( ( sK15_SY2806 @ SV436 @ SV212 )
= ( sK36_SY3121 @ SV436 @ SV212 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3296]) ).
thf(3425,plain,
! [SV215: $i,SV801: $i] :
( ( ( ~ ( in @ SV801 @ omega )
| ( in @ SV801 @ SV215 ) )
= $true )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( in @ ( sK44_SY2395 @ SV215 ) @ omega )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3297]) ).
thf(3426,plain,
! [SV215: $i,SV802: $i] :
( ( ( ~ ( in @ SV802 @ omega )
| ( in @ SV802 @ SV215 ) )
= $true )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( in @ ( sK44_SY2395 @ SV215 ) @ SV215 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3298]) ).
thf(3427,plain,
! [SV243: $i,SV667: $i,SV465: $i,SV756: $i] :
( ( ( in @ SV756 @ SV465 )
= $false )
| ( ( in @ SV756 @ SV667 )
= $true )
| ( ( in @ SV465 @ ( powerset @ SV667 ) )
= $false )
| ( ( in @ SV756 @ SV243 )
= $false )
| ( ( in @ SV667 @ ( powerset @ SV243 ) )
= $false )
| ( ( in @ SV465 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3301]) ).
thf(3428,plain,
! [SV600: $i,SV728: $i,SV469: $i,SV247: $i,SV803: $i] :
( ( ( ~ ( in @ SV803 @ SV247 )
| ! [SY3219: $i] :
( ~ ( in @ SY3219 @ SV469 )
| ~ ( in @ ( kpair @ SV803 @ SY3219 ) @ SV728 )
| ( in @ ( kpair @ SV803 @ SY3219 ) @ SV600 ) ) )
= $true )
| ( ( in @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) @ SV247 )
= $true )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3302]) ).
thf(3429,plain,
! [SV600: $i,SV728: $i,SV469: $i,SV247: $i,SV786: $i] :
( ( ( ~ ( in @ SV786 @ SV247 ) )
= $true )
| ( ( ! [SY3209: $i] :
( ~ ( in @ SY3209 @ SV469 )
| ~ ( in @ ( kpair @ SV786 @ SY3209 ) @ SV728 )
| ( in @ ( kpair @ SV786 @ SY3209 ) @ SV600 ) ) )
= $true )
| ( ( ( ap @ SV247 @ SV469 @ SV600 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) )
= ( ap @ SV247 @ SV469 @ SV728 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) ) )
= $false )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3303]) ).
thf(3430,plain,
! [SV471: $i,SV249: $i > $i > $o,SV773: $i] :
( ( ( ~ ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
| ~ ! [SY3202: $i] :
~ ~ ( ~ ( in @ SY3202 @ SV471 )
| ~ ( SV249 @ SY3202 @ SV773 ) ) )
= $true )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3304]) ).
thf(3431,plain,
! [SV773: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ~ ~ ! [SY3203: $i] :
~ ~ ( ~ ( in @ SY3203 @ SV471 )
| ~ ( SV249 @ SY3203 @ SV773 ) )
| ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) ) )
= $true )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3305]) ).
thf(3432,plain,
! [SV757: $i,SV471: $i,SV249: $i > $i > $o] :
( ( ( ~ ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
| ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( ~ ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3306]) ).
thf(3433,plain,
! [SV670: $i,SV256: $i > $o] :
( ( ( ! [SY2511: $i] :
~ ! [SY2512: $i] :
~ ( ~ ( ~ ( SV256 @ SY2512 )
| ( SY2512 = SY2511 ) )
| ~ ( ( SY2512 != SY2511 )
| ( SV256 @ SY2512 ) ) ) )
= $false )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV256 @ ( sK74_SY3127 @ SV670 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3309]) ).
thf(3434,plain,
! [SV670: $i,SV256: $i > $o] :
( ( ( ~ ! [SY3220: $i] :
~ ( ~ ( ~ ( SV256 @ SY3220 )
| ( SY3220
= ( sK86_SY2511 @ SV670 @ SV256 ) ) )
| ~ ( ( SY3220
!= ( sK86_SY2511 @ SV670 @ SV256 ) )
| ( SV256 @ SY3220 ) ) ) )
= $false )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV670
= ( sK74_SY3127 @ SV670 @ SV256 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3310]) ).
thf(3435,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ~ ~ ( ~ ( SV35 @ ( sK87_SY1902 @ SV621 @ SV35 ) )
| ~ ! [SY3221: $i] :
( ~ ( SV35 @ SY3221 )
| ( ( sK87_SY1902 @ SV621 @ SV35 )
= SY3221 ) ) ) )
= $false )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV35 @ ( sK60_SY3073 @ SV621 @ SV35 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3311]) ).
thf(3436,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ~ ( ~ ( SV35 @ ( sK78_SY1902 @ SV621 @ SV35 ) )
| ~ ! [SY3210: $i] :
( ~ ( SV35 @ SY3210 )
| ( ( sK78_SY1902 @ SV621 @ SV35 )
= SY3210 ) ) ) )
= $true )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV621
= ( sK60_SY3073 @ SV621 @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3312]) ).
thf(3437,plain,
! [SV40: $i,SV286: $i,SV676: $i > $o,SV623: $i > $o] :
( ( ( ~ ( ~ ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) )
| ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
| ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3314]) ).
thf(3438,plain,
! [SV41: $i,SV774: $i,SV287: $i > $o] :
( ( ( SV287 @ SV774 )
= $false )
| ( ( in @ SV774 @ SV41 )
= $false )
| ( ( in @ ( sK30_SY2541 @ SV287 @ SV41 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3315]) ).
thf(3439,plain,
! [SV41: $i,SV775: $i,SV287: $i > $o] :
( ( ( SV287 @ SV775 )
= $false )
| ( ( in @ SV775 @ SV41 )
= $false )
| ( ( SV287 @ ( sK30_SY2541 @ SV287 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3316]) ).
thf(3440,plain,
! [SV44: $i > $o,SV624: $i] :
( ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( ~ ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3317]) ).
thf(3441,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3318]) ).
thf(3442,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3319]) ).
thf(3443,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ~ ( ~ ( SV44 @ ( sK88_SY1929 @ SV624 @ SV44 ) )
| ~ ! [SY3222: $i] :
( ~ ( SV44 @ SY3222 )
| ( ( sK88_SY1929 @ SV624 @ SV44 )
= SY3222 ) ) ) )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3320]) ).
thf(3444,plain,
! [SV315: $i,SV686: $o,SV74: $i,SV509: $i] :
( ( ( in @ SV509 @ SV74 )
= $false )
| ( SV686 = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3323]) ).
thf(3445,plain,
! [SV74: $i,SV686: $o,SV315: $i,SV509: $i] :
( ( ( in @ SV509 @ SV315 )
= $true )
| ( SV686 = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3324]) ).
thf(3446,plain,
! [SV315: $i,SV686: $o,SV74: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV74 ) )
= $false )
| ( SV686 = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3326]) ).
thf(3447,plain,
! [SV74: $i,SV686: $o,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 )
| SV686 )
= $false )
| ( SV686 = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3326]) ).
thf(3448,plain,
! [SV315: $i,SV686: $o,SV74: $i,SV509: $i] :
( ( ( in @ SV509 @ SV74 )
= $false )
| ( SV686 = $true )
| ( SV686 = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3327]) ).
thf(3449,plain,
! [SV74: $i,SV686: $o,SV315: $i,SV509: $i] :
( ( ( in @ SV509 @ SV315 )
= $true )
| ( SV686 = $true )
| ( SV686 = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3328]) ).
thf(3450,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( in @ SV509 @ SV74 )
= $false )
| ( $true = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3330]) ).
thf(3451,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( in @ SV509 @ SV315 )
= $true )
| ( $true = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3331]) ).
thf(3452,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV74 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3333]) ).
thf(3453,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3333]) ).
thf(3454,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( in @ SV509 @ SV74 )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3334]) ).
thf(3455,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( in @ SV509 @ SV315 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3335]) ).
thf(3456,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( in @ SV509 @ SV74 )
= $false )
| ( $false = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3337]) ).
thf(3457,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( in @ SV509 @ SV315 )
= $true )
| ( $false = $true )
| ( ( in @ SV509 @ SV74 )
= $true )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3338]) ).
thf(3458,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ SV74 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3340]) ).
thf(3459,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3340]) ).
thf(3460,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( in @ SV509 @ SV74 )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3341]) ).
thf(3461,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( in @ SV509 @ SV315 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3342]) ).
thf(3462,plain,
! [SV79: $i,SV776: $i,SV318: $i > $o] :
( ( ( SV318 @ SV776 )
= $false )
| ( ( in @ SV776 @ SV79 )
= $false )
| ( ( in @ ( sK32_SY2591 @ SV318 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3344]) ).
thf(3463,plain,
! [SV79: $i,SV777: $i,SV318: $i > $o] :
( ( ( SV318 @ SV777 )
= $false )
| ( ( in @ SV777 @ SV79 )
= $false )
| ( ( SV318 @ ( sK32_SY2591 @ SV318 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3345]) ).
thf(3464,plain,
! [SV82: $i,SV630: $i,SV804: $i] :
( ( ( ~ ~ ( ~ ( in @ SV804 @ ( sK38_SY2017 @ SV630 @ SV82 ) )
| ~ ( in @ SV804 @ SV82 ) ) )
= $true )
| ( ( in @ SV630 @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3346]) ).
thf(3465,plain,
! [SV87: $i,SV687: $i,SV325: $i > $o] :
( ( ( SV325 @ ( sK53_SY2599 @ SV687 @ SV325 @ SV87 ) )
= $false )
| ( ( SV325 @ SV687 )
= $true )
| ( ( in @ SV687 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3352]) ).
thf(3466,plain,
! [SV632: $i,SV805: $i,SV787: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV787 )
| ~ ( SV91 @ SV805 )
| ( SV787 = SV805 ) )
= $true )
| ( ( SV91 @ SV632 )
= $false )
| ( ( SV91 @ ( sK62_SY3087 @ SV632 @ SV91 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3353]) ).
thf(3467,plain,
! [SV632: $i,SV788: $i,SV782: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV782 ) )
= $true )
| ( ( ~ ( SV91 @ SV788 )
| ( SV782 = SV788 ) )
= $true )
| ( ( SV91 @ SV632 )
= $false )
| ( ( SV632
= ( sK62_SY3087 @ SV632 @ SV91 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3354]) ).
thf(3468,plain,
! [SV332: $i,SV689: $i,SV516: $i,SV95: $i] :
( ( ( in @ ( sK75_SY3197 @ SV95 @ SV516 @ SV689 @ SV332 ) @ SV332 )
= $true )
| ( ( subset @ SV516 @ SV689 )
= $true )
| ( ( subset @ SV689 @ ( cartprod @ SV95 @ SV332 ) )
= $false )
| ( ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3355]) ).
thf(3469,plain,
! [SV95: $i,SV332: $i,SV516: $i,SV689: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK63_SY3141 @ SV689 @ SV516 @ SV332 @ SV95 ) @ ( sK75_SY3197 @ SV95 @ SV516 @ SV689 @ SV332 ) ) @ SV516 ) )
= $false )
| ( ( subset @ SV516 @ SV689 )
= $true )
| ( ( subset @ SV689 @ ( cartprod @ SV95 @ SV332 ) )
= $false )
| ( ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3356]) ).
thf(3470,plain,
! [SV95: $i,SV332: $i,SV516: $i,SV689: $i] :
( ( ( in @ ( kpair @ ( sK63_SY3141 @ SV689 @ SV516 @ SV332 @ SV95 ) @ ( sK75_SY3197 @ SV95 @ SV516 @ SV689 @ SV332 ) ) @ SV689 )
= $false )
| ( ( subset @ SV516 @ SV689 )
= $true )
| ( ( subset @ SV689 @ ( cartprod @ SV95 @ SV332 ) )
= $false )
| ( ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3356]) ).
thf(3471,plain,
( ( ( in @ sK39_SY3168 @ sK9_SY2932 )
= $false )
| ( sK33_SY3090 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[3358]) ).
thf(3472,plain,
! [SV342: $i,SV105: $i,SV691: $i > $o,SV522: $i,SV789: $i] :
( ( ( ~ ( in @ SV789 @ SV522 ) )
= $true )
| ( ( SV691 @ SV789 )
= $true )
| ( ( in @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) @ SV342 )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3360]) ).
thf(3473,plain,
! [SV105: $i,SV342: $i,SV691: $i > $o,SV522: $i,SV806: $i] :
( ( ( ~ ( in @ SV806 @ SV522 )
| ( SV691 @ SV806 ) )
= $true )
| ( ( in @ ( kpair @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) ) @ SV522 )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3361]) ).
thf(3474,plain,
! [SV105: $i,SV342: $i,SV691: $i > $o,SV522: $i,SV790: $i] :
( ( ( ~ ( in @ SV790 @ SV522 ) )
= $true )
| ( ( SV691 @ SV790 )
= $true )
| ( ( SV691 @ ( kpair @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) ) )
= $false )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3362]) ).
thf(3475,plain,
! [SV635: $i,SV807: $i,SV791: $i,SV106: $i > $o] :
( ( ( ~ ( SV106 @ SV791 )
| ~ ( SV106 @ SV807 )
| ( SV791 = SV807 ) )
= $true )
| ( ( SV106 @ SV635 )
= $false )
| ( ( SV106 @ ( sK65_SY3092 @ SV635 @ SV106 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3363]) ).
thf(3476,plain,
! [SV635: $i,SV792: $i,SV783: $i,SV106: $i > $o] :
( ( ( ~ ( SV106 @ SV783 ) )
= $true )
| ( ( ~ ( SV106 @ SV792 )
| ( SV783 = SV792 ) )
= $true )
| ( ( SV106 @ SV635 )
= $false )
| ( ( SV635
= ( sK65_SY3092 @ SV635 @ SV106 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3364]) ).
thf(3477,plain,
! [SV638: $i,SV114: $i > $o] :
( ( ( ~ ( SV114 @ ( sK89_SY2107 @ SV638 @ SV114 ) ) )
= $false )
| ( ( SV114 @ SV638 )
= $false )
| ( ( SV114 @ ( sK67_SY3096 @ SV638 @ SV114 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3365]) ).
thf(3478,plain,
! [SV638: $i,SV114: $i > $o] :
( ( ( SV114 @ ( sK79_SY2107 @ SV638 @ SV114 ) )
= $true )
| ( ( SV114 @ SV638 )
= $false )
| ( ( SV638
= ( sK67_SY3096 @ SV638 @ SV114 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3366]) ).
thf(3479,plain,
! [SV115: $i,SV741: $i,SV639: $i,SV348: $i,SV767: $i] :
( ( ( in @ SV767 @ ( binintersect @ SV348 @ SV639 ) )
= $false )
| ( ( in @ SV767 @ ( binunion @ SV348 @ SV741 ) )
= $true )
| ( ( in @ SV767 @ SV115 )
= $false )
| ( ( in @ SV741 @ ( powerset @ SV115 ) )
= $false )
| ( ( in @ SV639 @ ( powerset @ SV115 ) )
= $false )
| ( ( in @ SV348 @ ( powerset @ SV115 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3367]) ).
thf(3480,plain,
! [SV118: $i,SV763: $i,SV350: $i > $o] :
( ( ( SV350 @ SV763 )
= $false )
| ( ( in @ SV763 @ SV118 )
= $false )
| ( ( in @ ( sK10_SY2649 @ SV350 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3368]) ).
thf(3481,plain,
! [SV118: $i,SV764: $i,SV350: $i > $o] :
( ( ( SV350 @ SV764 )
= $false )
| ( ( in @ SV764 @ SV118 )
= $false )
| ( ( SV350 @ ( sK10_SY2649 @ SV350 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3369]) ).
thf(3482,plain,
! [SV119: $i,SV692: $i,SV351: $i > $o] :
( ( ( SV351 @ ( sK56_SY2652 @ SV692 @ SV351 @ SV119 ) )
= $false )
| ( ( SV351 @ SV692 )
= $true )
| ( ( in @ SV692 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3371]) ).
thf(3483,plain,
! [SV137: $i,SV369: $i,SV649: $i,SV746: $i] :
( ( ( in @ SV746 @ SV649 )
= $true )
| ( ( ~ ( in @ SV746 @ SV369 ) )
= $true )
| ( ( subset @ SV369 @ SV649 )
= $false )
| ( ( in @ SV746 @ SV137 )
= $false )
| ( ( in @ SV649 @ ( powerset @ SV137 ) )
= $false )
| ( ( in @ SV369 @ ( powerset @ SV137 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3379]) ).
thf(3484,plain,
! [SV147: $i,SV793: $i] :
( ( ( ~ ( in @ SV793 @ ( sK3_SY2186 @ SV147 ) ) )
= $true )
| ( ( ! [SY3213: $i] :
( ~ ( in @ SY3213 @ SV793 )
| ( in @ SY3213 @ SV147 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3380]) ).
thf(3485,plain,
! [SV808: $i,SV147: $i,SV794: $i] :
( ( ~ ~ ( ~ ( in @ SV794 @ SV147 )
| ~ ( in @ SV808 @ SV147 ) )
| ~ ! [SY3223: $i] :
( ~ ( in @ SY3223 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SV794 @ SY3223 )
| ( in @ SV808 @ SY3223 ) )
| ~ ( ~ ( in @ SV808 @ SY3223 )
| ( in @ SV794 @ SY3223 ) ) ) )
| ( SV794 = SV808 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3381]) ).
thf(3486,plain,
! [SV779: $i,SV147: $i,SV768: $i] :
( ( ( ~ ( in @ SV768 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SV779 @ ( sK3_SY2186 @ SV147 ) ) )
= $true )
| ( ( ! [SY3204: $i] :
( ~ ( in @ SY3204 @ SV768 )
| ( in @ SY3204 @ SV779 ) )
| ! [SY3205: $i] :
( ~ ( in @ SY3205 @ SV779 )
| ( in @ SY3205 @ SV768 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3382]) ).
thf(3487,plain,
! [SV747: $i,SV147: $i] :
( ( ( ~ ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 ) )
= $false )
| ( ( ~ ~ ! [SY3177: $i] :
~ ( in @ SY3177 @ SV747 ) )
= $true )
| ( ( ~ ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3383]) ).
thf(3488,plain,
! [SV747: $i,SV147: $i] :
( ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( ~ ~ ! [SY3177: $i] :
~ ( in @ SY3177 @ SV747 ) )
= $true )
| ( ( ~ ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3383]) ).
thf(3489,plain,
! [SV151: $i,SV748: $i,SV651: $i,SV381: $i,SV769: $i] :
( ( ( in @ SV769 @ ( binintersect @ SV381 @ SV651 ) )
= $false )
| ( ( in @ SV769 @ ( binunion @ SV651 @ SV748 ) )
= $true )
| ( ( in @ SV769 @ SV151 )
= $false )
| ( ( in @ SV748 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV651 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV381 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3384]) ).
thf(3490,plain,
! [SV156: $i,SV652: $i,SV386: $i,SV749: $i] :
( ( ( in @ SV749 @ SV386 )
= $false )
| ( ( in @ SV749 @ SV652 )
= $false )
| ( ( subset @ SV386 @ ( setminus @ SV156 @ SV652 ) )
= $false )
| ( ( in @ SV749 @ SV156 )
= $false )
| ( ( in @ SV652 @ ( powerset @ SV156 ) )
= $false )
| ( ( in @ SV386 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3385]) ).
thf(3491,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ( ~ ( SV160 @ ( sK81_SY2233 @ SV653 @ SV160 ) )
| ~ ! [SY3216: $i] :
( ~ ( SV160 @ SY3216 )
| ( ( sK81_SY2233 @ SV653 @ SV160 )
= SY3216 ) ) ) )
= $true )
| ( ( SV160 @ ( sK49_SY2231 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3386]) ).
thf(3492,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ~ ( ~ ( SV160 @ ( sK90_SY2233 @ SV653 @ SV160 ) )
| ~ ! [SY3224: $i] :
( ~ ( SV160 @ SY3224 )
| ( ( sK90_SY2233 @ SV653 @ SV160 )
= SY3224 ) ) ) )
= $false )
| ( ( SV160 @ ( sK58_SY3190 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3387]) ).
thf(3493,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ( ~ ( SV160 @ ( sK82_SY2233 @ SV653 @ SV160 ) )
| ~ ! [SY3217: $i] :
( ~ ( SV160 @ SY3217 )
| ( ( sK82_SY2233 @ SV653 @ SV160 )
= SY3217 ) ) ) )
= $true )
| ( ( ( sK49_SY2231 @ SV653 @ SV160 )
= ( sK58_SY3190 @ SV653 @ SV160 ) )
= $false )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3388]) ).
thf(3494,plain,
! [SV409: $i > $o,SV181: $i,SV770: $i] :
( ( ( in @ SV770 @ SV181 )
= $false )
| ( ( ~ ( SV409 @ SV770 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( in @ ( sK12_SY2740 @ SV409 @ SV181 ) @ SV181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3389]) ).
thf(3495,plain,
! [SV409: $i > $o,SV181: $i,SV784: $i] :
( ( ( ~ ( in @ SV784 @ SV181 )
| ~ ( SV409 @ SV784 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( in @ ( sK34_SY3112 @ SV409 @ SV181 ) @ SV181 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3390]) ).
thf(3496,plain,
! [SV409: $i > $o,SV181: $i,SV795: $i] :
( ( ( ~ ( ~ ( in @ SV795 @ SV181 )
| ~ ( SV409 @ SV795 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( SV409 @ ( sK12_SY2740 @ SV409 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3391]) ).
thf(3497,plain,
! [SV409: $i > $o,SV181: $i,SV809: $i] :
( ( ( ~ ~ ( ~ ( in @ SV809 @ SV181 )
| ~ ( SV409 @ SV809 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( SV409 @ ( sK34_SY3112 @ SV409 @ SV181 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3392]) ).
thf(3498,plain,
! [SV409: $i > $o,SV181: $i,SV796: $i] :
( ( ( ~ ( ~ ( in @ SV796 @ SV181 )
| ~ ( SV409 @ SV796 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( ( sK12_SY2740 @ SV409 @ SV181 )
= ( sK34_SY3112 @ SV409 @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3393]) ).
thf(3499,plain,
! [SV411: $i > $o,SV780: $i,SV183: $i > $o] :
( ( ( ~ ( SV183 @ SV780 ) )
= $true )
| ( ( ~ ! [SY3206: $i] :
( ~ ( SV183 @ SY3206 )
| ( SV780 = SY3206 ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3394]) ).
thf(3500,plain,
! [SV183: $i > $o,SV411: $i > $o] :
( ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) )
| ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3395]) ).
thf(3501,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3396]) ).
thf(3502,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3397]) ).
thf(3503,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3398]) ).
thf(3504,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( ~ ( in @ ( sK91_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV186 )
| ~ ( in @ ( sK91_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV659 )
| ( in @ ( sK91_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV414 ) )
= $false )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV186 )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3399]) ).
thf(3505,plain,
! [SV414: $i,SV659: $i,SV186: $i] :
( ( ( ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV186 )
| ~ ( in @ SY3115 @ SV659 )
| ( in @ SY3115 @ SV414 ) ) )
= $false )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV414 )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3400]) ).
thf(3506,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( ~ ( in @ ( sK92_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV186 )
| ~ ( in @ ( sK92_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV659 )
| ( in @ ( sK92_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV414 ) )
= $false )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV659 )
= $false )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3401]) ).
thf(3507,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ~ ~ ( ~ ( SV188 @ ( sK93_SY2316 @ SV660 @ SV188 ) )
| ~ ! [SY3225: $i] :
( ~ ( SV188 @ SY3225 )
| ( ( sK93_SY2316 @ SV660 @ SV188 )
= SY3225 ) ) ) )
= $false )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV188 @ ( sK69_SY3116 @ SV660 @ SV188 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3402]) ).
thf(3508,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ ( sK83_SY2316 @ SV660 @ SV188 ) )
| ~ ! [SY3218: $i] :
( ~ ( SV188 @ SY3218 )
| ( ( sK83_SY2316 @ SV660 @ SV188 )
= SY3218 ) ) ) )
= $true )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV660
= ( sK69_SY3116 @ SV660 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3403]) ).
thf(3509,plain,
! [SV191: $i,SV752: $i,SV661: $i,SV418: $i,SV771: $i] :
( ( ( in @ SV771 @ ( binintersect @ SV418 @ SV661 ) )
= $false )
| ( ( in @ SV771 @ ( binintersect @ ( binunion @ SV418 @ SV752 ) @ ( binunion @ SV661 @ SV752 ) ) )
= $true )
| ( ( in @ SV771 @ SV191 )
= $false )
| ( ( in @ SV752 @ ( powerset @ SV191 ) )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV191 ) )
= $false )
| ( ( in @ SV418 @ ( powerset @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3404]) ).
thf(3510,plain,
! [SV422: $i > $o,SV810: $i,SV193: $i > $o] :
( ( ( ~ ~ ( ~ ( SV193 @ SV810 )
| ~ ! [SY3226: $i] :
( ~ ( SV193 @ SY3226 )
| ( SV810 = SY3226 ) ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3405]) ).
thf(3511,plain,
! [SV193: $i > $o,SV811: $i,SV422: $i > $o] :
( ( ( ~ ~ ( ~ ( SV422 @ SV811 )
| ~ ! [SY3227: $i] :
( ~ ( SV422 @ SY3227 )
| ( SV811 = SY3227 ) ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3406]) ).
thf(3512,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3407]) ).
thf(3513,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3408]) ).
thf(3514,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3409]) ).
thf(3515,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3410]) ).
thf(3516,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3410]) ).
thf(3517,plain,
! [SV424: $i,SV566: $i,SV196: $i] :
( ( ( ~ ( in @ ( sK76_SY3169 @ SV196 @ SV566 @ SV424 ) @ SV424 )
| ( SV566
!= ( kpair @ ( sK35_SY2993 @ SV566 @ SV424 @ SV196 ) @ ( sK76_SY3169 @ SV196 @ SV566 @ SV424 ) ) ) )
= $false )
| ( ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3411]) ).
thf(3518,plain,
! [SV570: $i,SV712: $i,SV426: $i,SV198: $i] :
( ( ( ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SV198 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3412]) ).
thf(3519,plain,
! [SV426: $i,SV712: $i,SV570: $i,SV198: $i] :
( ( ( in @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) @ SV426 )
= $true )
| ( ( ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) )
| ( SV570 = SV712 ) )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3413]) ).
thf(3520,plain,
! [SV198: $i,SV426: $i,SV570: $i,SV712: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV570 ) )
= $false )
| ( ( ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) )
| ( SV570 = SV712 ) )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3414]) ).
thf(3521,plain,
! [SV198: $i,SV426: $i,SV570: $i,SV712: $i] :
( ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV712 )
= $false )
| ( ( ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) )
| ( SV570 = SV712 ) )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3414]) ).
thf(3522,plain,
! [SV428: $i,SV200: $i,SV713: $i > $o,SV571: $i,SV797: $i] :
( ( ( ~ ( in @ SV797 @ SV571 ) )
= $true )
| ( ( SV713 @ SV797 )
= $true )
| ( ( in @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) @ SV428 )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3416]) ).
thf(3523,plain,
! [SV200: $i,SV428: $i,SV713: $i > $o,SV571: $i,SV812: $i] :
( ( ( ~ ( in @ SV812 @ SV571 )
| ( SV713 @ SV812 ) )
= $true )
| ( ( in @ ( kpair @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) ) @ SV571 )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3417]) ).
thf(3524,plain,
! [SV200: $i,SV428: $i,SV713: $i > $o,SV571: $i,SV798: $i] :
( ( ( ~ ( in @ SV798 @ SV571 ) )
= $true )
| ( ( SV713 @ SV798 )
= $true )
| ( ( SV713 @ ( kpair @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) ) )
= $false )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3418]) ).
thf(3525,plain,
! [SV201: $i,SV429: $i > $o,SV714: $i] :
( ( ( ~ ( in @ ( sK84_SY2794 @ SV714 @ SV429 @ SV201 ) @ SV201 ) )
= $false )
| ( ( in @ SV714 @ SV201 )
= $false )
| ( ( SV429 @ SV714 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3419]) ).
thf(3526,plain,
! [SV201: $i,SV714: $i,SV429: $i > $o] :
( ( ( SV429 @ ( sK84_SY2794 @ SV714 @ SV429 @ SV201 ) )
= $false )
| ( ( in @ SV714 @ SV201 )
= $false )
| ( ( SV429 @ SV714 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3419]) ).
thf(3527,plain,
! [SV436: $i > $o,SV212: $i,SV772: $i] :
( ( ( in @ SV772 @ SV212 )
= $false )
| ( ( ~ ( SV436 @ SV772 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( in @ ( sK15_SY2806 @ SV436 @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3420]) ).
thf(3528,plain,
! [SV436: $i > $o,SV212: $i,SV785: $i] :
( ( ( ~ ( in @ SV785 @ SV212 )
| ~ ( SV436 @ SV785 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( in @ ( sK36_SY3121 @ SV436 @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3421]) ).
thf(3529,plain,
! [SV436: $i > $o,SV212: $i,SV799: $i] :
( ( ( ~ ( ~ ( in @ SV799 @ SV212 )
| ~ ( SV436 @ SV799 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( SV436 @ ( sK15_SY2806 @ SV436 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3422]) ).
thf(3530,plain,
! [SV436: $i > $o,SV212: $i,SV813: $i] :
( ( ( ~ ~ ( ~ ( in @ SV813 @ SV212 )
| ~ ( SV436 @ SV813 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( SV436 @ ( sK36_SY3121 @ SV436 @ SV212 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3423]) ).
thf(3531,plain,
! [SV436: $i > $o,SV212: $i,SV800: $i] :
( ( ( ~ ( ~ ( in @ SV800 @ SV212 )
| ~ ( SV436 @ SV800 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( ( sK15_SY2806 @ SV436 @ SV212 )
= ( sK36_SY3121 @ SV436 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3424]) ).
thf(3532,plain,
! [SV215: $i,SV801: $i] :
( ( ( ~ ( in @ SV801 @ omega ) )
= $true )
| ( ( in @ SV801 @ SV215 )
= $true )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( in @ ( sK44_SY2395 @ SV215 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3425]) ).
thf(3533,plain,
! [SV215: $i,SV802: $i] :
( ( ( ~ ( in @ SV802 @ omega ) )
= $true )
| ( ( in @ SV802 @ SV215 )
= $true )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( in @ ( sK44_SY2395 @ SV215 ) @ SV215 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3426]) ).
thf(3534,plain,
! [SV600: $i,SV728: $i,SV469: $i,SV247: $i,SV803: $i] :
( ( ( ~ ( in @ SV803 @ SV247 ) )
= $true )
| ( ( ! [SY3219: $i] :
( ~ ( in @ SY3219 @ SV469 )
| ~ ( in @ ( kpair @ SV803 @ SY3219 ) @ SV728 )
| ( in @ ( kpair @ SV803 @ SY3219 ) @ SV600 ) ) )
= $true )
| ( ( in @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) @ SV247 )
= $true )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3428]) ).
thf(3535,plain,
! [SV600: $i,SV728: $i,SV469: $i,SV247: $i,SV786: $i] :
( ( ( in @ SV786 @ SV247 )
= $false )
| ( ( ! [SY3209: $i] :
( ~ ( in @ SY3209 @ SV469 )
| ~ ( in @ ( kpair @ SV786 @ SY3209 ) @ SV728 )
| ( in @ ( kpair @ SV786 @ SY3209 ) @ SV600 ) ) )
= $true )
| ( ( ( ap @ SV247 @ SV469 @ SV600 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) )
= ( ap @ SV247 @ SV469 @ SV728 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) ) )
= $false )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3429]) ).
thf(3536,plain,
! [SV471: $i,SV249: $i > $i > $o,SV773: $i] :
( ( ( ~ ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) ) )
= $true )
| ( ( ~ ! [SY3202: $i] :
~ ~ ( ~ ( in @ SY3202 @ SV471 )
| ~ ( SV249 @ SY3202 @ SV773 ) ) )
= $true )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3430]) ).
thf(3537,plain,
! [SV773: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ~ ~ ! [SY3203: $i] :
~ ~ ( ~ ( in @ SY3203 @ SV471 )
| ~ ( SV249 @ SY3203 @ SV773 ) ) )
= $true )
| ( ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
= $true )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3431]) ).
thf(3538,plain,
! [SV757: $i,SV471: $i,SV249: $i > $i > $o] :
( ( ( ~ ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( ~ ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3432]) ).
thf(3539,plain,
! [SV249: $i > $i > $o,SV471: $i,SV757: $i] :
( ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( ~ ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3432]) ).
thf(3540,plain,
! [SV670: $i,SV256: $i > $o] :
( ( ( ~ ! [SY3228: $i] :
~ ( ~ ( ~ ( SV256 @ SY3228 )
| ( SY3228
= ( sK94_SY2511 @ SV670 @ SV256 ) ) )
| ~ ( ( SY3228
!= ( sK94_SY2511 @ SV670 @ SV256 ) )
| ( SV256 @ SY3228 ) ) ) )
= $false )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV256 @ ( sK74_SY3127 @ SV670 @ SV256 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3433]) ).
thf(3541,plain,
! [SV670: $i,SV256: $i > $o] :
( ( ( ! [SY3220: $i] :
~ ( ~ ( ~ ( SV256 @ SY3220 )
| ( SY3220
= ( sK86_SY2511 @ SV670 @ SV256 ) ) )
| ~ ( ( SY3220
!= ( sK86_SY2511 @ SV670 @ SV256 ) )
| ( SV256 @ SY3220 ) ) ) )
= $true )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV670
= ( sK74_SY3127 @ SV670 @ SV256 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3434]) ).
thf(3542,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ~ ( ~ ( SV35 @ ( sK87_SY1902 @ SV621 @ SV35 ) )
| ~ ! [SY3221: $i] :
( ~ ( SV35 @ SY3221 )
| ( ( sK87_SY1902 @ SV621 @ SV35 )
= SY3221 ) ) ) )
= $true )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV35 @ ( sK60_SY3073 @ SV621 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3435]) ).
thf(3543,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ~ ( SV35 @ ( sK78_SY1902 @ SV621 @ SV35 ) )
| ~ ! [SY3210: $i] :
( ~ ( SV35 @ SY3210 )
| ( ( sK78_SY1902 @ SV621 @ SV35 )
= SY3210 ) ) )
= $false )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV621
= ( sK60_SY3073 @ SV621 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3436]) ).
thf(3544,plain,
! [SV40: $i,SV286: $i,SV676: $i > $o,SV623: $i > $o] :
( ( ( ~ ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) )
| ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) ) )
= $false )
| ( ( ~ ( ~ ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
| ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3437]) ).
thf(3545,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ! [SY1929: $i] :
~ ~ ( ~ ( SV44 @ SY1929 )
| ~ ! [SY1930: $i] :
( ~ ( SV44 @ SY1930 )
| ( SY1929 = SY1930 ) ) ) )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3440]) ).
thf(3546,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ~ ( ~ ( SV44 @ ( sK95_SY1929 @ SV624 @ SV44 ) )
| ~ ! [SY3229: $i] :
( ~ ( SV44 @ SY3229 )
| ( ( sK95_SY1929 @ SV624 @ SV44 )
= SY3229 ) ) ) )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3441]) ).
thf(3547,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ~ ( ~ ( SV44 @ ( sK96_SY1929 @ SV624 @ SV44 ) )
| ~ ! [SY3230: $i] :
( ~ ( SV44 @ SY3230 )
| ( ( sK96_SY1929 @ SV624 @ SV44 )
= SY3230 ) ) ) )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3442]) ).
thf(3548,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ( ~ ( SV44 @ ( sK88_SY1929 @ SV624 @ SV44 ) )
| ~ ! [SY3222: $i] :
( ~ ( SV44 @ SY3222 )
| ( ( sK88_SY1929 @ SV624 @ SV44 )
= SY3222 ) ) ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3443]) ).
thf(3549,plain,
! [SV315: $i,SV686: $o,SV74: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV74 ) )
= $true )
| ( SV686 = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3446]) ).
thf(3550,plain,
! [SV74: $i,SV686: $o,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 ) )
= $false )
| ( SV686 = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3447]) ).
thf(3551,plain,
! [SV74: $i,SV315: $i,SV509: $i,SV686: $o] :
( ( SV686 = $false )
| ( SV686 = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3447]) ).
thf(3552,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV74 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3452]) ).
thf(3553,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3453]) ).
thf(3554,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3453]) ).
thf(3555,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV74 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3458]) ).
thf(3556,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV315 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3459]) ).
thf(3557,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3459]) ).
thf(3558,plain,
! [SV82: $i,SV630: $i,SV804: $i] :
( ( ( ~ ( ~ ( in @ SV804 @ ( sK38_SY2017 @ SV630 @ SV82 ) )
| ~ ( in @ SV804 @ SV82 ) ) )
= $false )
| ( ( in @ SV630 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3464]) ).
thf(3559,plain,
! [SV632: $i,SV805: $i,SV787: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV787 ) )
= $true )
| ( ( ~ ( SV91 @ SV805 )
| ( SV787 = SV805 ) )
= $true )
| ( ( SV91 @ SV632 )
= $false )
| ( ( SV91 @ ( sK62_SY3087 @ SV632 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3466]) ).
thf(3560,plain,
! [SV632: $i,SV788: $i,SV782: $i,SV91: $i > $o] :
( ( ( SV91 @ SV782 )
= $false )
| ( ( ~ ( SV91 @ SV788 )
| ( SV782 = SV788 ) )
= $true )
| ( ( SV91 @ SV632 )
= $false )
| ( ( SV632
= ( sK62_SY3087 @ SV632 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3467]) ).
thf(3561,plain,
! [SV95: $i,SV332: $i,SV516: $i,SV689: $i] :
( ( ( in @ ( kpair @ ( sK63_SY3141 @ SV689 @ SV516 @ SV332 @ SV95 ) @ ( sK75_SY3197 @ SV95 @ SV516 @ SV689 @ SV332 ) ) @ SV516 )
= $true )
| ( ( subset @ SV516 @ SV689 )
= $true )
| ( ( subset @ SV689 @ ( cartprod @ SV95 @ SV332 ) )
= $false )
| ( ( subset @ SV516 @ ( cartprod @ SV95 @ SV332 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3469]) ).
thf(3562,plain,
! [SV342: $i,SV105: $i,SV691: $i > $o,SV522: $i,SV789: $i] :
( ( ( in @ SV789 @ SV522 )
= $false )
| ( ( SV691 @ SV789 )
= $true )
| ( ( in @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) @ SV342 )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3472]) ).
thf(3563,plain,
! [SV105: $i,SV342: $i,SV691: $i > $o,SV522: $i,SV806: $i] :
( ( ( ~ ( in @ SV806 @ SV522 ) )
= $true )
| ( ( SV691 @ SV806 )
= $true )
| ( ( in @ ( kpair @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) ) @ SV522 )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3473]) ).
thf(3564,plain,
! [SV105: $i,SV342: $i,SV691: $i > $o,SV522: $i,SV790: $i] :
( ( ( in @ SV790 @ SV522 )
= $false )
| ( ( SV691 @ SV790 )
= $true )
| ( ( SV691 @ ( kpair @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) ) )
= $false )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3474]) ).
thf(3565,plain,
! [SV635: $i,SV807: $i,SV791: $i,SV106: $i > $o] :
( ( ( ~ ( SV106 @ SV791 ) )
= $true )
| ( ( ~ ( SV106 @ SV807 )
| ( SV791 = SV807 ) )
= $true )
| ( ( SV106 @ SV635 )
= $false )
| ( ( SV106 @ ( sK65_SY3092 @ SV635 @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3475]) ).
thf(3566,plain,
! [SV635: $i,SV792: $i,SV783: $i,SV106: $i > $o] :
( ( ( SV106 @ SV783 )
= $false )
| ( ( ~ ( SV106 @ SV792 )
| ( SV783 = SV792 ) )
= $true )
| ( ( SV106 @ SV635 )
= $false )
| ( ( SV635
= ( sK65_SY3092 @ SV635 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3476]) ).
thf(3567,plain,
! [SV638: $i,SV114: $i > $o] :
( ( ( SV114 @ ( sK89_SY2107 @ SV638 @ SV114 ) )
= $true )
| ( ( SV114 @ SV638 )
= $false )
| ( ( SV114 @ ( sK67_SY3096 @ SV638 @ SV114 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3477]) ).
thf(3568,plain,
! [SV137: $i,SV649: $i,SV369: $i,SV746: $i] :
( ( ( in @ SV746 @ SV369 )
= $false )
| ( ( in @ SV746 @ SV649 )
= $true )
| ( ( subset @ SV369 @ SV649 )
= $false )
| ( ( in @ SV746 @ SV137 )
= $false )
| ( ( in @ SV649 @ ( powerset @ SV137 ) )
= $false )
| ( ( in @ SV369 @ ( powerset @ SV137 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3483]) ).
thf(3569,plain,
! [SV147: $i,SV793: $i] :
( ( ( in @ SV793 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( ! [SY3213: $i] :
( ~ ( in @ SY3213 @ SV793 )
| ( in @ SY3213 @ SV147 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3484]) ).
thf(3570,plain,
! [SV808: $i,SV147: $i,SV794: $i] :
( ( ( ~ ~ ( ~ ( in @ SV794 @ SV147 )
| ~ ( in @ SV808 @ SV147 ) ) )
= $true )
| ( ( ~ ! [SY3223: $i] :
( ~ ( in @ SY3223 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SV794 @ SY3223 )
| ( in @ SV808 @ SY3223 ) )
| ~ ( ~ ( in @ SV808 @ SY3223 )
| ( in @ SV794 @ SY3223 ) ) ) )
| ( SV794 = SV808 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3485]) ).
thf(3571,plain,
! [SV779: $i,SV147: $i,SV768: $i] :
( ( ( ~ ( in @ SV768 @ ( sK3_SY2186 @ SV147 ) ) )
= $true )
| ( ( ~ ( in @ SV779 @ ( sK3_SY2186 @ SV147 ) ) )
= $true )
| ( ( ! [SY3204: $i] :
( ~ ( in @ SY3204 @ SV768 )
| ( in @ SY3204 @ SV779 ) )
| ! [SY3205: $i] :
( ~ ( in @ SY3205 @ SV779 )
| ( in @ SY3205 @ SV768 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3486]) ).
thf(3572,plain,
! [SV747: $i,SV147: $i] :
( ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( ~ ~ ! [SY3177: $i] :
~ ( in @ SY3177 @ SV747 ) )
= $true )
| ( ( ~ ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3487]) ).
thf(3573,plain,
! [SV147: $i,SV747: $i] :
( ( ( ~ ! [SY3177: $i] :
~ ( in @ SY3177 @ SV747 ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( ~ ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3488]) ).
thf(3574,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ( SV160 @ ( sK81_SY2233 @ SV653 @ SV160 ) )
| ~ ! [SY3216: $i] :
( ~ ( SV160 @ SY3216 )
| ( ( sK81_SY2233 @ SV653 @ SV160 )
= SY3216 ) ) )
= $false )
| ( ( SV160 @ ( sK49_SY2231 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3491]) ).
thf(3575,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ( ~ ( SV160 @ ( sK90_SY2233 @ SV653 @ SV160 ) )
| ~ ! [SY3224: $i] :
( ~ ( SV160 @ SY3224 )
| ( ( sK90_SY2233 @ SV653 @ SV160 )
= SY3224 ) ) ) )
= $true )
| ( ( SV160 @ ( sK58_SY3190 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3492]) ).
thf(3576,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ( SV160 @ ( sK82_SY2233 @ SV653 @ SV160 ) )
| ~ ! [SY3217: $i] :
( ~ ( SV160 @ SY3217 )
| ( ( sK82_SY2233 @ SV653 @ SV160 )
= SY3217 ) ) )
= $false )
| ( ( ( sK49_SY2231 @ SV653 @ SV160 )
= ( sK58_SY3190 @ SV653 @ SV160 ) )
= $false )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3493]) ).
thf(3577,plain,
! [SV181: $i,SV770: $i,SV409: $i > $o] :
( ( ( SV409 @ SV770 )
= $false )
| ( ( in @ SV770 @ SV181 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( in @ ( sK12_SY2740 @ SV409 @ SV181 ) @ SV181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3494]) ).
thf(3578,plain,
! [SV409: $i > $o,SV181: $i,SV784: $i] :
( ( ( ~ ( in @ SV784 @ SV181 ) )
= $true )
| ( ( ~ ( SV409 @ SV784 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( in @ ( sK34_SY3112 @ SV409 @ SV181 ) @ SV181 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3495]) ).
thf(3579,plain,
! [SV409: $i > $o,SV181: $i,SV795: $i] :
( ( ( ~ ( in @ SV795 @ SV181 )
| ~ ( SV409 @ SV795 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( SV409 @ ( sK12_SY2740 @ SV409 @ SV181 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3496]) ).
thf(3580,plain,
! [SV409: $i > $o,SV181: $i,SV809: $i] :
( ( ( ~ ( ~ ( in @ SV809 @ SV181 )
| ~ ( SV409 @ SV809 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( SV409 @ ( sK34_SY3112 @ SV409 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3497]) ).
thf(3581,plain,
! [SV409: $i > $o,SV181: $i,SV796: $i] :
( ( ( ~ ( in @ SV796 @ SV181 )
| ~ ( SV409 @ SV796 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( ( sK12_SY2740 @ SV409 @ SV181 )
= ( sK34_SY3112 @ SV409 @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3498]) ).
thf(3582,plain,
! [SV411: $i > $o,SV780: $i,SV183: $i > $o] :
( ( ( SV183 @ SV780 )
= $false )
| ( ( ~ ! [SY3206: $i] :
( ~ ( SV183 @ SY3206 )
| ( SV780 = SY3206 ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3499]) ).
thf(3583,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3500]) ).
thf(3584,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3501]) ).
thf(3585,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3502]) ).
thf(3586,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3503]) ).
thf(3587,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( ~ ( in @ ( sK91_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV186 ) )
= $false )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV186 )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3504]) ).
thf(3588,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( ~ ( in @ ( sK91_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV659 )
| ( in @ ( sK91_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV414 ) )
= $false )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV186 )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3504]) ).
thf(3589,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( ~ ( in @ ( sK97_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV186 )
| ~ ( in @ ( sK97_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV659 )
| ( in @ ( sK97_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV414 ) )
= $false )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV414 )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3505]) ).
thf(3590,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( ~ ( in @ ( sK92_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV186 ) )
= $false )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV659 )
= $false )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3506]) ).
thf(3591,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( ~ ( in @ ( sK92_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV659 )
| ( in @ ( sK92_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV414 ) )
= $false )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV659 )
= $false )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3506]) ).
thf(3592,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ ( sK93_SY2316 @ SV660 @ SV188 ) )
| ~ ! [SY3225: $i] :
( ~ ( SV188 @ SY3225 )
| ( ( sK93_SY2316 @ SV660 @ SV188 )
= SY3225 ) ) ) )
= $true )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV188 @ ( sK69_SY3116 @ SV660 @ SV188 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3507]) ).
thf(3593,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK83_SY2316 @ SV660 @ SV188 ) )
| ~ ! [SY3218: $i] :
( ~ ( SV188 @ SY3218 )
| ( ( sK83_SY2316 @ SV660 @ SV188 )
= SY3218 ) ) )
= $false )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV660
= ( sK69_SY3116 @ SV660 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3508]) ).
thf(3594,plain,
! [SV422: $i > $o,SV810: $i,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ SV810 )
| ~ ! [SY3226: $i] :
( ~ ( SV193 @ SY3226 )
| ( SV810 = SY3226 ) ) ) )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3510]) ).
thf(3595,plain,
! [SV193: $i > $o,SV811: $i,SV422: $i > $o] :
( ( ( ~ ( ~ ( SV422 @ SV811 )
| ~ ! [SY3227: $i] :
( ~ ( SV422 @ SY3227 )
| ( SV811 = SY3227 ) ) ) )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3511]) ).
thf(3596,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
| ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3512]) ).
thf(3597,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3513]) ).
thf(3598,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3513]) ).
thf(3599,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3514]) ).
thf(3600,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3514]) ).
thf(3601,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3515]) ).
thf(3602,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3516]) ).
thf(3603,plain,
! [SV424: $i,SV566: $i,SV196: $i] :
( ( ( ~ ( in @ ( sK76_SY3169 @ SV196 @ SV566 @ SV424 ) @ SV424 ) )
= $false )
| ( ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3517]) ).
thf(3604,plain,
! [SV196: $i,SV424: $i,SV566: $i] :
( ( ( SV566
!= ( kpair @ ( sK35_SY2993 @ SV566 @ SV424 @ SV196 ) @ ( sK76_SY3169 @ SV196 @ SV566 @ SV424 ) ) )
= $false )
| ( ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3517]) ).
thf(3605,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( ~ ( in @ ( sK98_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SV198 )
| ! [SY3231: $i] :
( ~ ( in @ SY3231 @ SV426 )
| ~ ( in @ ( kpair @ ( sK98_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SY3231 ) @ SV712 )
| ( in @ ( kpair @ ( sK98_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SY3231 ) @ SV570 ) ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SV198 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3518]) ).
thf(3606,plain,
! [SV570: $i,SV712: $i,SV426: $i,SV198: $i] :
( ( ( ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) ) )
= $true )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) @ SV426 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3519]) ).
thf(3607,plain,
! [SV198: $i,SV426: $i,SV570: $i,SV712: $i] :
( ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV570 )
= $true )
| ( ( ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) )
| ( SV570 = SV712 ) )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3520]) ).
thf(3608,plain,
! [SV570: $i,SV712: $i,SV426: $i,SV198: $i] :
( ( ( ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) ) )
= $true )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV712 )
= $false )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3521]) ).
thf(3609,plain,
! [SV428: $i,SV200: $i,SV713: $i > $o,SV571: $i,SV797: $i] :
( ( ( in @ SV797 @ SV571 )
= $false )
| ( ( SV713 @ SV797 )
= $true )
| ( ( in @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) @ SV428 )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3522]) ).
thf(3610,plain,
! [SV200: $i,SV428: $i,SV713: $i > $o,SV571: $i,SV812: $i] :
( ( ( ~ ( in @ SV812 @ SV571 ) )
= $true )
| ( ( SV713 @ SV812 )
= $true )
| ( ( in @ ( kpair @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) ) @ SV571 )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3523]) ).
thf(3611,plain,
! [SV200: $i,SV428: $i,SV713: $i > $o,SV571: $i,SV798: $i] :
( ( ( in @ SV798 @ SV571 )
= $false )
| ( ( SV713 @ SV798 )
= $true )
| ( ( SV713 @ ( kpair @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) ) )
= $false )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3524]) ).
thf(3612,plain,
! [SV201: $i,SV429: $i > $o,SV714: $i] :
( ( ( in @ ( sK84_SY2794 @ SV714 @ SV429 @ SV201 ) @ SV201 )
= $true )
| ( ( in @ SV714 @ SV201 )
= $false )
| ( ( SV429 @ SV714 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3525]) ).
thf(3613,plain,
! [SV212: $i,SV772: $i,SV436: $i > $o] :
( ( ( SV436 @ SV772 )
= $false )
| ( ( in @ SV772 @ SV212 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( in @ ( sK15_SY2806 @ SV436 @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3527]) ).
thf(3614,plain,
! [SV436: $i > $o,SV212: $i,SV785: $i] :
( ( ( ~ ( in @ SV785 @ SV212 ) )
= $true )
| ( ( ~ ( SV436 @ SV785 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( in @ ( sK36_SY3121 @ SV436 @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3528]) ).
thf(3615,plain,
! [SV436: $i > $o,SV212: $i,SV799: $i] :
( ( ( ~ ( in @ SV799 @ SV212 )
| ~ ( SV436 @ SV799 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( SV436 @ ( sK15_SY2806 @ SV436 @ SV212 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3529]) ).
thf(3616,plain,
! [SV436: $i > $o,SV212: $i,SV813: $i] :
( ( ( ~ ( ~ ( in @ SV813 @ SV212 )
| ~ ( SV436 @ SV813 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( SV436 @ ( sK36_SY3121 @ SV436 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3530]) ).
thf(3617,plain,
! [SV436: $i > $o,SV212: $i,SV800: $i] :
( ( ( ~ ( in @ SV800 @ SV212 )
| ~ ( SV436 @ SV800 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( ( sK15_SY2806 @ SV436 @ SV212 )
= ( sK36_SY3121 @ SV436 @ SV212 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3531]) ).
thf(3618,plain,
! [SV215: $i,SV801: $i] :
( ( ( in @ SV801 @ omega )
= $false )
| ( ( in @ SV801 @ SV215 )
= $true )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( in @ ( sK44_SY2395 @ SV215 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3532]) ).
thf(3619,plain,
! [SV215: $i,SV802: $i] :
( ( ( in @ SV802 @ omega )
= $false )
| ( ( in @ SV802 @ SV215 )
= $true )
| ( ( in @ emptyset @ SV215 )
= $false )
| ( ( in @ ( sK44_SY2395 @ SV215 ) @ SV215 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3533]) ).
thf(3620,plain,
! [SV600: $i,SV728: $i,SV469: $i,SV247: $i,SV803: $i] :
( ( ( in @ SV803 @ SV247 )
= $false )
| ( ( ! [SY3219: $i] :
( ~ ( in @ SY3219 @ SV469 )
| ~ ( in @ ( kpair @ SV803 @ SY3219 ) @ SV728 )
| ( in @ ( kpair @ SV803 @ SY3219 ) @ SV600 ) ) )
= $true )
| ( ( in @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) @ SV247 )
= $true )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3534]) ).
thf(3621,plain,
! [SV247: $i,SV600: $i,SV728: $i,SV786: $i,SV469: $i,SV814: $i] :
( ( ( ~ ( in @ SV814 @ SV469 )
| ~ ( in @ ( kpair @ SV786 @ SV814 ) @ SV728 )
| ( in @ ( kpair @ SV786 @ SV814 ) @ SV600 ) )
= $true )
| ( ( in @ SV786 @ SV247 )
= $false )
| ( ( ( ap @ SV247 @ SV469 @ SV600 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) )
= ( ap @ SV247 @ SV469 @ SV728 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) ) )
= $false )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3535]) ).
thf(3622,plain,
! [SV471: $i,SV249: $i > $i > $o,SV773: $i] :
( ( ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
= $false )
| ( ( ~ ! [SY3202: $i] :
~ ~ ( ~ ( in @ SY3202 @ SV471 )
| ~ ( SV249 @ SY3202 @ SV773 ) ) )
= $true )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3536]) ).
thf(3623,plain,
! [SV773: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ~ ! [SY3203: $i] :
~ ~ ( ~ ( in @ SY3203 @ SV471 )
| ~ ( SV249 @ SY3203 @ SV773 ) ) )
= $false )
| ( ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
= $true )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3537]) ).
thf(3624,plain,
! [SV757: $i,SV471: $i,SV249: $i > $i > $o] :
( ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( ~ ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3538]) ).
thf(3625,plain,
! [SV757: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3539]) ).
thf(3626,plain,
! [SV670: $i,SV256: $i > $o] :
( ( ( ! [SY3228: $i] :
~ ( ~ ( ~ ( SV256 @ SY3228 )
| ( SY3228
= ( sK94_SY2511 @ SV670 @ SV256 ) ) )
| ~ ( ( SY3228
!= ( sK94_SY2511 @ SV670 @ SV256 ) )
| ( SV256 @ SY3228 ) ) ) )
= $true )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV256 @ ( sK74_SY3127 @ SV670 @ SV256 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3540]) ).
thf(3627,plain,
! [SV670: $i,SV815: $i,SV256: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV256 @ SV815 )
| ( SV815
= ( sK86_SY2511 @ SV670 @ SV256 ) ) )
| ~ ( ( SV815
!= ( sK86_SY2511 @ SV670 @ SV256 ) )
| ( SV256 @ SV815 ) ) ) )
= $true )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV670
= ( sK74_SY3127 @ SV670 @ SV256 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3541]) ).
thf(3628,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ~ ( SV35 @ ( sK87_SY1902 @ SV621 @ SV35 ) )
| ~ ! [SY3221: $i] :
( ~ ( SV35 @ SY3221 )
| ( ( sK87_SY1902 @ SV621 @ SV35 )
= SY3221 ) ) )
= $false )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV35 @ ( sK60_SY3073 @ SV621 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3542]) ).
thf(3629,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ~ ( SV35 @ ( sK78_SY1902 @ SV621 @ SV35 ) ) )
= $false )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV621
= ( sK60_SY3073 @ SV621 @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3543]) ).
thf(3630,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ~ ! [SY3210: $i] :
( ~ ( SV35 @ SY3210 )
| ( ( sK78_SY1902 @ SV621 @ SV35 )
= SY3210 ) ) )
= $false )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV621
= ( sK60_SY3073 @ SV621 @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3543]) ).
thf(3631,plain,
! [SV40: $i,SV286: $i,SV676: $i > $o,SV623: $i > $o] :
( ( ( ~ ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) ) )
= $false )
| ( ( ~ ( ~ ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
| ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3544]) ).
thf(3632,plain,
! [SV286: $i,SV623: $i > $o,SV40: $i,SV676: $i > $o] :
( ( ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
= $false )
| ( ( ~ ( ~ ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
| ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3544]) ).
thf(3633,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ~ ( ~ ( SV44 @ ( sK99_SY1929 @ SV624 @ SV44 ) )
| ~ ! [SY3232: $i] :
( ~ ( SV44 @ SY3232 )
| ( ( sK99_SY1929 @ SV624 @ SV44 )
= SY3232 ) ) ) )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3545]) ).
thf(3634,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ( ~ ( SV44 @ ( sK95_SY1929 @ SV624 @ SV44 ) )
| ~ ! [SY3229: $i] :
( ~ ( SV44 @ SY3229 )
| ( ( sK95_SY1929 @ SV624 @ SV44 )
= SY3229 ) ) ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3546]) ).
thf(3635,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ( ~ ( SV44 @ ( sK96_SY1929 @ SV624 @ SV44 ) )
| ~ ! [SY3230: $i] :
( ~ ( SV44 @ SY3230 )
| ( ( sK96_SY1929 @ SV624 @ SV44 )
= SY3230 ) ) ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3547]) ).
thf(3636,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ( SV44 @ ( sK88_SY1929 @ SV624 @ SV44 ) )
| ~ ! [SY3222: $i] :
( ~ ( SV44 @ SY3222 )
| ( ( sK88_SY1929 @ SV624 @ SV44 )
= SY3222 ) ) )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3548]) ).
thf(3637,plain,
! [SV315: $i,SV686: $o,SV74: $i,SV509: $i] :
( ( ( in @ SV509 @ SV74 )
= $false )
| ( SV686 = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3549]) ).
thf(3638,plain,
! [SV74: $i,SV686: $o,SV315: $i,SV509: $i] :
( ( ( in @ SV509 @ SV315 )
= $true )
| ( SV686 = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3550]) ).
thf(3639,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( in @ SV509 @ SV74 )
= $false )
| ( $true = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3552]) ).
thf(3640,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( in @ SV509 @ SV315 )
= $true )
| ( $true = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3553]) ).
thf(3641,plain,
! [SV315: $i,SV74: $i,SV509: $i] :
( ( ( in @ SV509 @ SV74 )
= $false )
| ( $false = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3555]) ).
thf(3642,plain,
! [SV74: $i,SV315: $i,SV509: $i] :
( ( ( in @ SV509 @ SV315 )
= $true )
| ( $false = $true )
| ( ( in @ SV509 @ SV315 )
= $false )
| ( ( in @ SV509 @ ( symdiff @ SV74 @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3556]) ).
thf(3643,plain,
! [SV82: $i,SV630: $i,SV804: $i] :
( ( ( ~ ( in @ SV804 @ ( sK38_SY2017 @ SV630 @ SV82 ) )
| ~ ( in @ SV804 @ SV82 ) )
= $true )
| ( ( in @ SV630 @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3558]) ).
thf(3644,plain,
! [SV632: $i,SV805: $i,SV787: $i,SV91: $i > $o] :
( ( ( SV91 @ SV787 )
= $false )
| ( ( ~ ( SV91 @ SV805 )
| ( SV787 = SV805 ) )
= $true )
| ( ( SV91 @ SV632 )
= $false )
| ( ( SV91 @ ( sK62_SY3087 @ SV632 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3559]) ).
thf(3645,plain,
! [SV632: $i,SV782: $i,SV788: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV788 ) )
= $true )
| ( ( SV782 = SV788 )
= $true )
| ( ( SV91 @ SV782 )
= $false )
| ( ( SV91 @ SV632 )
= $false )
| ( ( SV632
= ( sK62_SY3087 @ SV632 @ SV91 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3560]) ).
thf(3646,plain,
! [SV105: $i,SV342: $i,SV691: $i > $o,SV522: $i,SV806: $i] :
( ( ( in @ SV806 @ SV522 )
= $false )
| ( ( SV691 @ SV806 )
= $true )
| ( ( in @ ( kpair @ ( sK48_SY3143 @ SV691 @ SV522 @ SV342 @ SV105 ) @ ( sK64_SY3189 @ SV105 @ SV522 @ SV691 @ SV342 ) ) @ SV522 )
= $true )
| ( ( subset @ SV522 @ ( cartprod @ SV105 @ SV342 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3563]) ).
thf(3647,plain,
! [SV635: $i,SV807: $i,SV791: $i,SV106: $i > $o] :
( ( ( SV106 @ SV791 )
= $false )
| ( ( ~ ( SV106 @ SV807 )
| ( SV791 = SV807 ) )
= $true )
| ( ( SV106 @ SV635 )
= $false )
| ( ( SV106 @ ( sK65_SY3092 @ SV635 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3565]) ).
thf(3648,plain,
! [SV635: $i,SV783: $i,SV792: $i,SV106: $i > $o] :
( ( ( ~ ( SV106 @ SV792 ) )
= $true )
| ( ( SV783 = SV792 )
= $true )
| ( ( SV106 @ SV783 )
= $false )
| ( ( SV106 @ SV635 )
= $false )
| ( ( SV635
= ( sK65_SY3092 @ SV635 @ SV106 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3566]) ).
thf(3649,plain,
! [SV147: $i,SV793: $i,SV816: $i] :
( ( ( ~ ( in @ SV816 @ SV793 )
| ( in @ SV816 @ SV147 ) )
= $true )
| ( ( in @ SV793 @ ( sK3_SY2186 @ SV147 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3569]) ).
thf(3650,plain,
! [SV808: $i,SV147: $i,SV794: $i] :
( ( ( ~ ( ~ ( in @ SV794 @ SV147 )
| ~ ( in @ SV808 @ SV147 ) ) )
= $false )
| ( ( ~ ! [SY3223: $i] :
( ~ ( in @ SY3223 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SV794 @ SY3223 )
| ( in @ SV808 @ SY3223 ) )
| ~ ( ~ ( in @ SV808 @ SY3223 )
| ( in @ SV794 @ SY3223 ) ) ) )
| ( SV794 = SV808 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3570]) ).
thf(3651,plain,
! [SV779: $i,SV147: $i,SV768: $i] :
( ( ( in @ SV768 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( ~ ( in @ SV779 @ ( sK3_SY2186 @ SV147 ) ) )
= $true )
| ( ( ! [SY3204: $i] :
( ~ ( in @ SY3204 @ SV768 )
| ( in @ SY3204 @ SV779 ) )
| ! [SY3205: $i] :
( ~ ( in @ SY3205 @ SV779 )
| ( in @ SY3205 @ SV768 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3571]) ).
thf(3652,plain,
! [SV147: $i,SV747: $i] :
( ( ( ~ ! [SY3177: $i] :
~ ( in @ SY3177 @ SV747 ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( ~ ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3572]) ).
thf(3653,plain,
! [SV147: $i,SV747: $i] :
( ( ( ! [SY3177: $i] :
~ ( in @ SY3177 @ SV747 ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( ~ ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3573]) ).
thf(3654,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ( SV160 @ ( sK81_SY2233 @ SV653 @ SV160 ) ) )
= $false )
| ( ( SV160 @ ( sK49_SY2231 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3574]) ).
thf(3655,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ! [SY3216: $i] :
( ~ ( SV160 @ SY3216 )
| ( ( sK81_SY2233 @ SV653 @ SV160 )
= SY3216 ) ) )
= $false )
| ( ( SV160 @ ( sK49_SY2231 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3574]) ).
thf(3656,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ( SV160 @ ( sK90_SY2233 @ SV653 @ SV160 ) )
| ~ ! [SY3224: $i] :
( ~ ( SV160 @ SY3224 )
| ( ( sK90_SY2233 @ SV653 @ SV160 )
= SY3224 ) ) )
= $false )
| ( ( SV160 @ ( sK58_SY3190 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3575]) ).
thf(3657,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ( SV160 @ ( sK82_SY2233 @ SV653 @ SV160 ) ) )
= $false )
| ( ( ( sK49_SY2231 @ SV653 @ SV160 )
= ( sK58_SY3190 @ SV653 @ SV160 ) )
= $false )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3576]) ).
thf(3658,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ! [SY3217: $i] :
( ~ ( SV160 @ SY3217 )
| ( ( sK82_SY2233 @ SV653 @ SV160 )
= SY3217 ) ) )
= $false )
| ( ( ( sK49_SY2231 @ SV653 @ SV160 )
= ( sK58_SY3190 @ SV653 @ SV160 ) )
= $false )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3576]) ).
thf(3659,plain,
! [SV409: $i > $o,SV181: $i,SV784: $i] :
( ( ( in @ SV784 @ SV181 )
= $false )
| ( ( ~ ( SV409 @ SV784 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( in @ ( sK34_SY3112 @ SV409 @ SV181 ) @ SV181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3578]) ).
thf(3660,plain,
! [SV409: $i > $o,SV181: $i,SV795: $i] :
( ( ( ~ ( in @ SV795 @ SV181 ) )
= $true )
| ( ( ~ ( SV409 @ SV795 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( SV409 @ ( sK12_SY2740 @ SV409 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3579]) ).
thf(3661,plain,
! [SV409: $i > $o,SV181: $i,SV809: $i] :
( ( ( ~ ( in @ SV809 @ SV181 )
| ~ ( SV409 @ SV809 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( SV409 @ ( sK34_SY3112 @ SV409 @ SV181 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3580]) ).
thf(3662,plain,
! [SV409: $i > $o,SV181: $i,SV796: $i] :
( ( ( ~ ( in @ SV796 @ SV181 ) )
= $true )
| ( ( ~ ( SV409 @ SV796 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( ( sK12_SY2740 @ SV409 @ SV181 )
= ( sK34_SY3112 @ SV409 @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3581]) ).
thf(3663,plain,
! [SV411: $i > $o,SV780: $i,SV183: $i > $o] :
( ( ( ! [SY3206: $i] :
( ~ ( SV183 @ SY3206 )
| ( SV780 = SY3206 ) ) )
= $false )
| ( ( SV183 @ SV780 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3582]) ).
thf(3664,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3583]) ).
thf(3665,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3584]) ).
thf(3666,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3585]) ).
thf(3667,plain,
! [SV411: $i > $o,SV817: $i,SV183: $i > $o] :
( ( ( ~ ~ ( ~ ( SV183 @ SV817 )
| ~ ! [SY3233: $i] :
( ~ ( SV183 @ SY3233 )
| ( SV817 = SY3233 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3586]) ).
thf(3668,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( in @ ( sK91_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV186 )
= $true )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV186 )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3587]) ).
thf(3669,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( ~ ( in @ ( sK91_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV659 ) )
= $false )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV186 )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3588]) ).
thf(3670,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( in @ ( sK91_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV414 )
= $false )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV186 )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3588]) ).
thf(3671,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( ~ ( in @ ( sK97_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV186 ) )
= $false )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV414 )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3589]) ).
thf(3672,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( ~ ( in @ ( sK97_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV659 )
| ( in @ ( sK97_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV414 ) )
= $false )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV414 )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3589]) ).
thf(3673,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( in @ ( sK92_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV186 )
= $true )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV659 )
= $false )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3590]) ).
thf(3674,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( ~ ( in @ ( sK92_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV659 ) )
= $false )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV659 )
= $false )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3591]) ).
thf(3675,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( in @ ( sK92_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV414 )
= $false )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV659 )
= $false )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3591]) ).
thf(3676,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK93_SY2316 @ SV660 @ SV188 ) )
| ~ ! [SY3225: $i] :
( ~ ( SV188 @ SY3225 )
| ( ( sK93_SY2316 @ SV660 @ SV188 )
= SY3225 ) ) )
= $false )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV188 @ ( sK69_SY3116 @ SV660 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3592]) ).
thf(3677,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK83_SY2316 @ SV660 @ SV188 ) ) )
= $false )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV660
= ( sK69_SY3116 @ SV660 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3593]) ).
thf(3678,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ~ ! [SY3218: $i] :
( ~ ( SV188 @ SY3218 )
| ( ( sK83_SY2316 @ SV660 @ SV188 )
= SY3218 ) ) )
= $false )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV660
= ( sK69_SY3116 @ SV660 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3593]) ).
thf(3679,plain,
! [SV422: $i > $o,SV810: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV810 )
| ~ ! [SY3226: $i] :
( ~ ( SV193 @ SY3226 )
| ( SV810 = SY3226 ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3594]) ).
thf(3680,plain,
! [SV193: $i > $o,SV811: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV811 )
| ~ ! [SY3227: $i] :
( ~ ( SV422 @ SY3227 )
| ( SV811 = SY3227 ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3595]) ).
thf(3681,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3596]) ).
thf(3682,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3596]) ).
thf(3683,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3597]) ).
thf(3684,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3598]) ).
thf(3685,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3599]) ).
thf(3686,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3600]) ).
thf(3687,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3601]) ).
thf(3688,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3602]) ).
thf(3689,plain,
! [SV424: $i,SV566: $i,SV196: $i] :
( ( ( in @ ( sK76_SY3169 @ SV196 @ SV566 @ SV424 ) @ SV424 )
= $true )
| ( ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3603]) ).
thf(3690,plain,
! [SV196: $i,SV424: $i,SV566: $i] :
( ( ( SV566
= ( kpair @ ( sK35_SY2993 @ SV566 @ SV424 @ SV196 ) @ ( sK76_SY3169 @ SV196 @ SV566 @ SV424 ) ) )
= $true )
| ( ( in @ SV566 @ ( cartprod @ SV196 @ SV424 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3604]) ).
thf(3691,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( ~ ( in @ ( sK98_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SV198 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SV198 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3605]) ).
thf(3692,plain,
! [SV198: $i,SV712: $i,SV570: $i,SV426: $i] :
( ( ( ! [SY3231: $i] :
( ~ ( in @ SY3231 @ SV426 )
| ~ ( in @ ( kpair @ ( sK98_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SY3231 ) @ SV712 )
| ( in @ ( kpair @ ( sK98_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SY3231 ) @ SV570 ) ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SV198 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3605]) ).
thf(3693,plain,
! [SV570: $i,SV712: $i,SV426: $i,SV198: $i] :
( ( ( ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) @ SV426 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3606]) ).
thf(3694,plain,
! [SV570: $i,SV712: $i,SV426: $i,SV198: $i] :
( ( ( ~ ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) ) )
= $true )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV570 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3607]) ).
thf(3695,plain,
! [SV570: $i,SV712: $i,SV426: $i,SV198: $i] :
( ( ( ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV712 )
= $false )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3608]) ).
thf(3696,plain,
! [SV200: $i,SV428: $i,SV713: $i > $o,SV571: $i,SV812: $i] :
( ( ( in @ SV812 @ SV571 )
= $false )
| ( ( SV713 @ SV812 )
= $true )
| ( ( in @ ( kpair @ ( sK50_SY3155 @ SV713 @ SV571 @ SV428 @ SV200 ) @ ( sK71_SY3191 @ SV200 @ SV571 @ SV713 @ SV428 ) ) @ SV571 )
= $true )
| ( ( subset @ SV571 @ ( cartprod @ SV200 @ SV428 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3610]) ).
thf(3697,plain,
! [SV436: $i > $o,SV212: $i,SV785: $i] :
( ( ( in @ SV785 @ SV212 )
= $false )
| ( ( ~ ( SV436 @ SV785 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( in @ ( sK36_SY3121 @ SV436 @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3614]) ).
thf(3698,plain,
! [SV436: $i > $o,SV212: $i,SV799: $i] :
( ( ( ~ ( in @ SV799 @ SV212 ) )
= $true )
| ( ( ~ ( SV436 @ SV799 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( SV436 @ ( sK15_SY2806 @ SV436 @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3615]) ).
thf(3699,plain,
! [SV436: $i > $o,SV212: $i,SV813: $i] :
( ( ( ~ ( in @ SV813 @ SV212 )
| ~ ( SV436 @ SV813 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( SV436 @ ( sK36_SY3121 @ SV436 @ SV212 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3616]) ).
thf(3700,plain,
! [SV436: $i > $o,SV212: $i,SV800: $i] :
( ( ( ~ ( in @ SV800 @ SV212 ) )
= $true )
| ( ( ~ ( SV436 @ SV800 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( ( sK15_SY2806 @ SV436 @ SV212 )
= ( sK36_SY3121 @ SV436 @ SV212 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3617]) ).
thf(3701,plain,
! [SV247: $i,SV600: $i,SV728: $i,SV803: $i,SV469: $i,SV818: $i] :
( ( ( ~ ( in @ SV818 @ SV469 )
| ~ ( in @ ( kpair @ SV803 @ SV818 ) @ SV728 )
| ( in @ ( kpair @ SV803 @ SV818 ) @ SV600 ) )
= $true )
| ( ( in @ SV803 @ SV247 )
= $false )
| ( ( in @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) @ SV247 )
= $true )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3620]) ).
thf(3702,plain,
! [SV247: $i,SV600: $i,SV728: $i,SV786: $i,SV469: $i,SV814: $i] :
( ( ( ~ ( in @ SV814 @ SV469 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV786 @ SV814 ) @ SV728 )
| ( in @ ( kpair @ SV786 @ SV814 ) @ SV600 ) )
= $true )
| ( ( in @ SV786 @ SV247 )
= $false )
| ( ( ( ap @ SV247 @ SV469 @ SV600 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) )
= ( ap @ SV247 @ SV469 @ SV728 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) ) )
= $false )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3621]) ).
thf(3703,plain,
! [SV773: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ! [SY3202: $i] :
~ ~ ( ~ ( in @ SY3202 @ SV471 )
| ~ ( SV249 @ SY3202 @ SV773 ) ) )
= $false )
| ( ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
= $false )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3622]) ).
thf(3704,plain,
! [SV773: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ! [SY3203: $i] :
~ ~ ( ~ ( in @ SY3203 @ SV471 )
| ~ ( SV249 @ SY3203 @ SV773 ) ) )
= $true )
| ( ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
= $true )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3623]) ).
thf(3705,plain,
! [SV757: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ! [SY2874: $i] :
~ ! [SY2875: $i] :
~ ( ~ ( ~ ( in @ SY2875 @ SY2874 )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY2875 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY2875 ) )
| ( in @ SY2875 @ SY2874 ) ) ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3624]) ).
thf(3706,plain,
! [SV471: $i,SV249: $i > $i > $o,SV757: $i] :
( ( ( ~ ! [SY3234: $i] :
~ ( ~ ( ~ ( in @ SY3234 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY3234 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY3234 ) )
| ( in @ SY3234 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) ) ) ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3625]) ).
thf(3707,plain,
! [SV670: $i,SV819: $i,SV256: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV256 @ SV819 )
| ( SV819
= ( sK94_SY2511 @ SV670 @ SV256 ) ) )
| ~ ( ( SV819
!= ( sK94_SY2511 @ SV670 @ SV256 ) )
| ( SV256 @ SV819 ) ) ) )
= $true )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV256 @ ( sK74_SY3127 @ SV670 @ SV256 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3626]) ).
thf(3708,plain,
! [SV670: $i,SV815: $i,SV256: $i > $o] :
( ( ( ~ ( ~ ( SV256 @ SV815 )
| ( SV815
= ( sK86_SY2511 @ SV670 @ SV256 ) ) )
| ~ ( ( SV815
!= ( sK86_SY2511 @ SV670 @ SV256 ) )
| ( SV256 @ SV815 ) ) )
= $false )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV670
= ( sK74_SY3127 @ SV670 @ SV256 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3627]) ).
thf(3709,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ~ ( SV35 @ ( sK87_SY1902 @ SV621 @ SV35 ) ) )
= $false )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV35 @ ( sK60_SY3073 @ SV621 @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3628]) ).
thf(3710,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ~ ! [SY3221: $i] :
( ~ ( SV35 @ SY3221 )
| ( ( sK87_SY1902 @ SV621 @ SV35 )
= SY3221 ) ) )
= $false )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV35 @ ( sK60_SY3073 @ SV621 @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3628]) ).
thf(3711,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( SV35 @ ( sK78_SY1902 @ SV621 @ SV35 ) )
= $true )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV621
= ( sK60_SY3073 @ SV621 @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3629]) ).
thf(3712,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ! [SY3210: $i] :
( ~ ( SV35 @ SY3210 )
| ( ( sK78_SY1902 @ SV621 @ SV35 )
= SY3210 ) ) )
= $true )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV621
= ( sK60_SY3073 @ SV621 @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3630]) ).
thf(3713,plain,
! [SV40: $i,SV286: $i,SV676: $i > $o,SV623: $i > $o] :
( ( ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) )
= $true )
| ( ( ~ ( ~ ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
| ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3631]) ).
thf(3714,plain,
! [SV286: $i,SV623: $i > $o,SV40: $i,SV676: $i > $o] :
( ( ( ~ ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
| ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) ) )
= $false )
| ( ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
= $false )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3632]) ).
thf(3715,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ( ~ ( SV44 @ ( sK99_SY1929 @ SV624 @ SV44 ) )
| ~ ! [SY3232: $i] :
( ~ ( SV44 @ SY3232 )
| ( ( sK99_SY1929 @ SV624 @ SV44 )
= SY3232 ) ) ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3633]) ).
thf(3716,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ( SV44 @ ( sK95_SY1929 @ SV624 @ SV44 ) )
| ~ ! [SY3229: $i] :
( ~ ( SV44 @ SY3229 )
| ( ( sK95_SY1929 @ SV624 @ SV44 )
= SY3229 ) ) )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3634]) ).
thf(3717,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ( SV44 @ ( sK96_SY1929 @ SV624 @ SV44 ) )
| ~ ! [SY3230: $i] :
( ~ ( SV44 @ SY3230 )
| ( ( sK96_SY1929 @ SV624 @ SV44 )
= SY3230 ) ) )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3635]) ).
thf(3718,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ( SV44 @ ( sK88_SY1929 @ SV624 @ SV44 ) ) )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3636]) ).
thf(3719,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ! [SY3222: $i] :
( ~ ( SV44 @ SY3222 )
| ( ( sK88_SY1929 @ SV624 @ SV44 )
= SY3222 ) ) )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3636]) ).
thf(3720,plain,
! [SV82: $i,SV630: $i,SV804: $i] :
( ( ( ~ ( in @ SV804 @ ( sK38_SY2017 @ SV630 @ SV82 ) ) )
= $true )
| ( ( ~ ( in @ SV804 @ SV82 ) )
= $true )
| ( ( in @ SV630 @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3643]) ).
thf(3721,plain,
! [SV632: $i,SV787: $i,SV805: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV805 ) )
= $true )
| ( ( SV787 = SV805 )
= $true )
| ( ( SV91 @ SV787 )
= $false )
| ( ( SV91 @ SV632 )
= $false )
| ( ( SV91 @ ( sK62_SY3087 @ SV632 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3644]) ).
thf(3722,plain,
! [SV632: $i,SV782: $i,SV788: $i,SV91: $i > $o] :
( ( ( SV91 @ SV788 )
= $false )
| ( ( SV782 = SV788 )
= $true )
| ( ( SV91 @ SV782 )
= $false )
| ( ( SV91 @ SV632 )
= $false )
| ( ( SV632
= ( sK62_SY3087 @ SV632 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3645]) ).
thf(3723,plain,
! [SV635: $i,SV791: $i,SV807: $i,SV106: $i > $o] :
( ( ( ~ ( SV106 @ SV807 ) )
= $true )
| ( ( SV791 = SV807 )
= $true )
| ( ( SV106 @ SV791 )
= $false )
| ( ( SV106 @ SV635 )
= $false )
| ( ( SV106 @ ( sK65_SY3092 @ SV635 @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3647]) ).
thf(3724,plain,
! [SV635: $i,SV783: $i,SV792: $i,SV106: $i > $o] :
( ( ( SV106 @ SV792 )
= $false )
| ( ( SV783 = SV792 )
= $true )
| ( ( SV106 @ SV783 )
= $false )
| ( ( SV106 @ SV635 )
= $false )
| ( ( SV635
= ( sK65_SY3092 @ SV635 @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3648]) ).
thf(3725,plain,
! [SV147: $i,SV793: $i,SV816: $i] :
( ( ( ~ ( in @ SV816 @ SV793 ) )
= $true )
| ( ( in @ SV816 @ SV147 )
= $true )
| ( ( in @ SV793 @ ( sK3_SY2186 @ SV147 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3649]) ).
thf(3726,plain,
! [SV808: $i,SV147: $i,SV794: $i] :
( ( ( ~ ( in @ SV794 @ SV147 )
| ~ ( in @ SV808 @ SV147 ) )
= $true )
| ( ( ~ ! [SY3223: $i] :
( ~ ( in @ SY3223 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SV794 @ SY3223 )
| ( in @ SV808 @ SY3223 ) )
| ~ ( ~ ( in @ SV808 @ SY3223 )
| ( in @ SV794 @ SY3223 ) ) ) )
| ( SV794 = SV808 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3650]) ).
thf(3727,plain,
! [SV768: $i,SV147: $i,SV779: $i] :
( ( ( in @ SV779 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( in @ SV768 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( ! [SY3204: $i] :
( ~ ( in @ SY3204 @ SV768 )
| ( in @ SY3204 @ SV779 ) )
| ! [SY3205: $i] :
( ~ ( in @ SY3205 @ SV779 )
| ( in @ SY3205 @ SV768 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3651]) ).
thf(3728,plain,
! [SV147: $i,SV747: $i] :
( ( ( ! [SY3177: $i] :
~ ( in @ SY3177 @ SV747 ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( ~ ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3652]) ).
thf(3729,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( ~ ( in @ SV820 @ SV747 ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( ~ ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3653]) ).
thf(3730,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( SV160 @ ( sK81_SY2233 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ ( sK49_SY2231 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3654]) ).
thf(3731,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ! [SY3216: $i] :
( ~ ( SV160 @ SY3216 )
| ( ( sK81_SY2233 @ SV653 @ SV160 )
= SY3216 ) ) )
= $true )
| ( ( SV160 @ ( sK49_SY2231 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3655]) ).
thf(3732,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ( SV160 @ ( sK90_SY2233 @ SV653 @ SV160 ) ) )
= $false )
| ( ( SV160 @ ( sK58_SY3190 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3656]) ).
thf(3733,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ~ ! [SY3224: $i] :
( ~ ( SV160 @ SY3224 )
| ( ( sK90_SY2233 @ SV653 @ SV160 )
= SY3224 ) ) )
= $false )
| ( ( SV160 @ ( sK58_SY3190 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3656]) ).
thf(3734,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( SV160 @ ( sK82_SY2233 @ SV653 @ SV160 ) )
= $true )
| ( ( ( sK49_SY2231 @ SV653 @ SV160 )
= ( sK58_SY3190 @ SV653 @ SV160 ) )
= $false )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3657]) ).
thf(3735,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ! [SY3217: $i] :
( ~ ( SV160 @ SY3217 )
| ( ( sK82_SY2233 @ SV653 @ SV160 )
= SY3217 ) ) )
= $true )
| ( ( ( sK49_SY2231 @ SV653 @ SV160 )
= ( sK58_SY3190 @ SV653 @ SV160 ) )
= $false )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3658]) ).
thf(3736,plain,
! [SV181: $i,SV784: $i,SV409: $i > $o] :
( ( ( SV409 @ SV784 )
= $false )
| ( ( in @ SV784 @ SV181 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( in @ ( sK34_SY3112 @ SV409 @ SV181 ) @ SV181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3659]) ).
thf(3737,plain,
! [SV409: $i > $o,SV181: $i,SV795: $i] :
( ( ( in @ SV795 @ SV181 )
= $false )
| ( ( ~ ( SV409 @ SV795 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( SV409 @ ( sK12_SY2740 @ SV409 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3660]) ).
thf(3738,plain,
! [SV409: $i > $o,SV181: $i,SV809: $i] :
( ( ( ~ ( in @ SV809 @ SV181 ) )
= $true )
| ( ( ~ ( SV409 @ SV809 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( SV409 @ ( sK34_SY3112 @ SV409 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3661]) ).
thf(3739,plain,
! [SV409: $i > $o,SV181: $i,SV796: $i] :
( ( ( in @ SV796 @ SV181 )
= $false )
| ( ( ~ ( SV409 @ SV796 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( ( sK12_SY2740 @ SV409 @ SV181 )
= ( sK34_SY3112 @ SV409 @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3662]) ).
thf(3740,plain,
! [SV780: $i,SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ( SV183 @ ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
| ( SV780
= ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) ) )
= $false )
| ( ( SV183 @ SV780 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3663]) ).
thf(3741,plain,
! [SV411: $i > $o,SV183: $i > $o] :
( ( ( ! [SY2296: $i] :
~ ~ ( ~ ( SV183 @ SY2296 )
| ~ ! [SY2297: $i] :
( ~ ( SV183 @ SY2297 )
| ( SY2296 = SY2297 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3664]) ).
thf(3742,plain,
! [SV411: $i > $o,SV821: $i,SV183: $i > $o] :
( ( ( ~ ~ ( ~ ( SV183 @ SV821 )
| ~ ! [SY3237: $i] :
( ~ ( SV183 @ SY3237 )
| ( SV821 = SY3237 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3665]) ).
thf(3743,plain,
! [SV411: $i > $o,SV822: $i,SV183: $i > $o] :
( ( ( ~ ~ ( ~ ( SV183 @ SV822 )
| ~ ! [SY3238: $i] :
( ~ ( SV183 @ SY3238 )
| ( SV822 = SY3238 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3666]) ).
thf(3744,plain,
! [SV411: $i > $o,SV817: $i,SV183: $i > $o] :
( ( ( ~ ( ~ ( SV183 @ SV817 )
| ~ ! [SY3233: $i] :
( ~ ( SV183 @ SY3233 )
| ( SV817 = SY3233 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3667]) ).
thf(3745,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( in @ ( sK91_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV659 )
= $true )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV186 )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3669]) ).
thf(3746,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( in @ ( sK97_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV186 )
= $true )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV414 )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3671]) ).
thf(3747,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( ~ ( in @ ( sK97_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV659 ) )
= $false )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV414 )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3672]) ).
thf(3748,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( in @ ( sK97_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV414 )
= $false )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV414 )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3672]) ).
thf(3749,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( in @ ( sK92_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV659 )
= $true )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV659 )
= $false )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3674]) ).
thf(3750,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK93_SY2316 @ SV660 @ SV188 ) ) )
= $false )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV188 @ ( sK69_SY3116 @ SV660 @ SV188 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3676]) ).
thf(3751,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ~ ! [SY3225: $i] :
( ~ ( SV188 @ SY3225 )
| ( ( sK93_SY2316 @ SV660 @ SV188 )
= SY3225 ) ) )
= $false )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV188 @ ( sK69_SY3116 @ SV660 @ SV188 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3676]) ).
thf(3752,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( SV188 @ ( sK83_SY2316 @ SV660 @ SV188 ) )
= $true )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV660
= ( sK69_SY3116 @ SV660 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3677]) ).
thf(3753,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ! [SY3218: $i] :
( ~ ( SV188 @ SY3218 )
| ( ( sK83_SY2316 @ SV660 @ SV188 )
= SY3218 ) ) )
= $true )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV660
= ( sK69_SY3116 @ SV660 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3678]) ).
thf(3754,plain,
! [SV422: $i > $o,SV810: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV810 ) )
= $true )
| ( ( ~ ! [SY3226: $i] :
( ~ ( SV193 @ SY3226 )
| ( SV810 = SY3226 ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3679]) ).
thf(3755,plain,
! [SV193: $i > $o,SV811: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV811 ) )
= $true )
| ( ( ~ ! [SY3227: $i] :
( ~ ( SV422 @ SY3227 )
| ( SV811 = SY3227 ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3680]) ).
thf(3756,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) )
| ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3681]) ).
thf(3757,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) )
| ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3682]) ).
thf(3758,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3683]) ).
thf(3759,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3684]) ).
thf(3760,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3685]) ).
thf(3761,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3686]) ).
thf(3762,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) ) )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3687]) ).
thf(3763,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) ) )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3688]) ).
thf(3764,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( in @ ( sK98_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SV198 )
= $true )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SV198 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3691]) ).
thf(3765,plain,
! [SV426: $i,SV570: $i,SV712: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK102_SY3231 @ SV198 @ SV712 @ SV570 @ SV426 ) @ SV426 )
| ~ ( in @ ( kpair @ ( sK98_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK102_SY3231 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV712 )
| ( in @ ( kpair @ ( sK98_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK102_SY3231 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV570 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SV198 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3692]) ).
thf(3766,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( ~ ( in @ ( sK103_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SV198 )
| ! [SY3239: $i] :
( ~ ( in @ SY3239 @ SV426 )
| ~ ( in @ ( kpair @ ( sK103_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SY3239 ) @ SV712 )
| ( in @ ( kpair @ ( sK103_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SY3239 ) @ SV570 ) ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) @ SV426 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3693]) ).
thf(3767,plain,
! [SV570: $i,SV712: $i,SV426: $i,SV198: $i] :
( ( ( ! [SY3153: $i] :
( ~ ( in @ SY3153 @ SV198 )
| ! [SY3154: $i] :
( ~ ( in @ SY3154 @ SV426 )
| ~ ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV712 )
| ( in @ ( kpair @ SY3153 @ SY3154 ) @ SV570 ) ) ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV570 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3694]) ).
thf(3768,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( ~ ( in @ ( sK104_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SV198 )
| ! [SY3240: $i] :
( ~ ( in @ SY3240 @ SV426 )
| ~ ( in @ ( kpair @ ( sK104_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SY3240 ) @ SV712 )
| ( in @ ( kpair @ ( sK104_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SY3240 ) @ SV570 ) ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV712 )
= $false )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3695]) ).
thf(3769,plain,
! [SV212: $i,SV785: $i,SV436: $i > $o] :
( ( ( SV436 @ SV785 )
= $false )
| ( ( in @ SV785 @ SV212 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( in @ ( sK36_SY3121 @ SV436 @ SV212 ) @ SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3697]) ).
thf(3770,plain,
! [SV436: $i > $o,SV212: $i,SV799: $i] :
( ( ( in @ SV799 @ SV212 )
= $false )
| ( ( ~ ( SV436 @ SV799 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( SV436 @ ( sK15_SY2806 @ SV436 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3698]) ).
thf(3771,plain,
! [SV436: $i > $o,SV212: $i,SV813: $i] :
( ( ( ~ ( in @ SV813 @ SV212 ) )
= $true )
| ( ( ~ ( SV436 @ SV813 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( SV436 @ ( sK36_SY3121 @ SV436 @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3699]) ).
thf(3772,plain,
! [SV436: $i > $o,SV212: $i,SV800: $i] :
( ( ( in @ SV800 @ SV212 )
= $false )
| ( ( ~ ( SV436 @ SV800 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( ( sK15_SY2806 @ SV436 @ SV212 )
= ( sK36_SY3121 @ SV436 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3700]) ).
thf(3773,plain,
! [SV247: $i,SV600: $i,SV728: $i,SV803: $i,SV469: $i,SV818: $i] :
( ( ( ~ ( in @ SV818 @ SV469 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV803 @ SV818 ) @ SV728 )
| ( in @ ( kpair @ SV803 @ SV818 ) @ SV600 ) )
= $true )
| ( ( in @ SV803 @ SV247 )
= $false )
| ( ( in @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) @ SV247 )
= $true )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3701]) ).
thf(3774,plain,
! [SV247: $i,SV600: $i,SV728: $i,SV786: $i,SV469: $i,SV814: $i] :
( ( ( in @ SV814 @ SV469 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV786 @ SV814 ) @ SV728 )
| ( in @ ( kpair @ SV786 @ SV814 ) @ SV600 ) )
= $true )
| ( ( in @ SV786 @ SV247 )
= $false )
| ( ( ( ap @ SV247 @ SV469 @ SV600 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) )
= ( ap @ SV247 @ SV469 @ SV728 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) ) )
= $false )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3702]) ).
thf(3775,plain,
! [SV471: $i,SV249: $i > $i > $o,SV773: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK105_SY3202 @ SV773 @ SV249 @ SV471 ) @ SV471 )
| ~ ( SV249 @ ( sK105_SY3202 @ SV773 @ SV249 @ SV471 ) @ SV773 ) ) )
= $false )
| ( ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
= $false )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3703]) ).
thf(3776,plain,
! [SV773: $i,SV249: $i > $i > $o,SV471: $i,SV823: $i] :
( ( ( ~ ~ ( ~ ( in @ SV823 @ SV471 )
| ~ ( SV249 @ SV823 @ SV773 ) ) )
= $true )
| ( ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
= $true )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3704]) ).
thf(3777,plain,
! [SV471: $i,SV249: $i > $i > $o,SV757: $i] :
( ( ( ~ ! [SY3241: $i] :
~ ( ~ ( ~ ( in @ SY3241 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY3241 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY3241 ) )
| ( in @ SY3241 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) ) ) ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3705]) ).
thf(3778,plain,
! [SV471: $i,SV249: $i > $i > $o,SV757: $i] :
( ( ( ! [SY3234: $i] :
~ ( ~ ( ~ ( in @ SY3234 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY3234 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY3234 ) )
| ( in @ SY3234 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) ) ) ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3706]) ).
thf(3779,plain,
! [SV670: $i,SV819: $i,SV256: $i > $o] :
( ( ( ~ ( ~ ( SV256 @ SV819 )
| ( SV819
= ( sK94_SY2511 @ SV670 @ SV256 ) ) )
| ~ ( ( SV819
!= ( sK94_SY2511 @ SV670 @ SV256 ) )
| ( SV256 @ SV819 ) ) )
= $false )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV256 @ ( sK74_SY3127 @ SV670 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3707]) ).
thf(3780,plain,
! [SV670: $i,SV815: $i,SV256: $i > $o] :
( ( ( ~ ( ~ ( SV256 @ SV815 )
| ( SV815
= ( sK86_SY2511 @ SV670 @ SV256 ) ) ) )
= $false )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV670
= ( sK74_SY3127 @ SV670 @ SV256 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3708]) ).
thf(3781,plain,
! [SV256: $i > $o,SV670: $i,SV815: $i] :
( ( ( ~ ( ( SV815
!= ( sK86_SY2511 @ SV670 @ SV256 ) )
| ( SV256 @ SV815 ) ) )
= $false )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV670
= ( sK74_SY3127 @ SV670 @ SV256 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3708]) ).
thf(3782,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( SV35 @ ( sK87_SY1902 @ SV621 @ SV35 ) )
= $true )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV35 @ ( sK60_SY3073 @ SV621 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3709]) ).
thf(3783,plain,
! [SV621: $i,SV35: $i > $o] :
( ( ( ! [SY3221: $i] :
( ~ ( SV35 @ SY3221 )
| ( ( sK87_SY1902 @ SV621 @ SV35 )
= SY3221 ) ) )
= $true )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV35 @ ( sK60_SY3073 @ SV621 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3710]) ).
thf(3784,plain,
! [SV621: $i,SV824: $i,SV35: $i > $o] :
( ( ( ~ ( SV35 @ SV824 )
| ( ( sK78_SY1902 @ SV621 @ SV35 )
= SV824 ) )
= $true )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV621
= ( sK60_SY3073 @ SV621 @ SV35 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3712]) ).
thf(3785,plain,
! [SV286: $i,SV623: $i > $o,SV40: $i,SV676: $i > $o] :
( ( ( ~ ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
| ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) ) )
= $false )
| ( ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) )
= $true )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3713]) ).
thf(3786,plain,
! [SV286: $i,SV623: $i > $o,SV40: $i,SV676: $i > $o] :
( ( ( ~ ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) ) )
= $false )
| ( ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
= $false )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3714]) ).
thf(3787,plain,
! [SV40: $i,SV286: $i,SV676: $i > $o,SV623: $i > $o] :
( ( ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) )
= $false )
| ( ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
= $false )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3714]) ).
thf(3788,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ( SV44 @ ( sK99_SY1929 @ SV624 @ SV44 ) )
| ~ ! [SY3232: $i] :
( ~ ( SV44 @ SY3232 )
| ( ( sK99_SY1929 @ SV624 @ SV44 )
= SY3232 ) ) )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3715]) ).
thf(3789,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ( SV44 @ ( sK95_SY1929 @ SV624 @ SV44 ) ) )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3716]) ).
thf(3790,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ! [SY3229: $i] :
( ~ ( SV44 @ SY3229 )
| ( ( sK95_SY1929 @ SV624 @ SV44 )
= SY3229 ) ) )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3716]) ).
thf(3791,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ( SV44 @ ( sK96_SY1929 @ SV624 @ SV44 ) ) )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3717]) ).
thf(3792,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ! [SY3230: $i] :
( ~ ( SV44 @ SY3230 )
| ( ( sK96_SY1929 @ SV624 @ SV44 )
= SY3230 ) ) )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3717]) ).
thf(3793,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( SV44 @ ( sK88_SY1929 @ SV624 @ SV44 ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3718]) ).
thf(3794,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ! [SY3222: $i] :
( ~ ( SV44 @ SY3222 )
| ( ( sK88_SY1929 @ SV624 @ SV44 )
= SY3222 ) ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3719]) ).
thf(3795,plain,
! [SV82: $i,SV630: $i,SV804: $i] :
( ( ( in @ SV804 @ ( sK38_SY2017 @ SV630 @ SV82 ) )
= $false )
| ( ( ~ ( in @ SV804 @ SV82 ) )
= $true )
| ( ( in @ SV630 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3720]) ).
thf(3796,plain,
! [SV632: $i,SV787: $i,SV805: $i,SV91: $i > $o] :
( ( ( SV91 @ SV805 )
= $false )
| ( ( SV787 = SV805 )
= $true )
| ( ( SV91 @ SV787 )
= $false )
| ( ( SV91 @ SV632 )
= $false )
| ( ( SV91 @ ( sK62_SY3087 @ SV632 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3721]) ).
thf(3797,plain,
! [SV635: $i,SV791: $i,SV807: $i,SV106: $i > $o] :
( ( ( SV106 @ SV807 )
= $false )
| ( ( SV791 = SV807 )
= $true )
| ( ( SV106 @ SV791 )
= $false )
| ( ( SV106 @ SV635 )
= $false )
| ( ( SV106 @ ( sK65_SY3092 @ SV635 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3723]) ).
thf(3798,plain,
! [SV147: $i,SV793: $i,SV816: $i] :
( ( ( in @ SV816 @ SV793 )
= $false )
| ( ( in @ SV816 @ SV147 )
= $true )
| ( ( in @ SV793 @ ( sK3_SY2186 @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3725]) ).
thf(3799,plain,
! [SV808: $i,SV147: $i,SV794: $i] :
( ( ( ~ ( in @ SV794 @ SV147 ) )
= $true )
| ( ( ~ ( in @ SV808 @ SV147 ) )
= $true )
| ( ( ~ ! [SY3223: $i] :
( ~ ( in @ SY3223 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SV794 @ SY3223 )
| ( in @ SV808 @ SY3223 ) )
| ~ ( ~ ( in @ SV808 @ SY3223 )
| ( in @ SV794 @ SY3223 ) ) ) )
| ( SV794 = SV808 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3726]) ).
thf(3800,plain,
! [SV147: $i,SV779: $i,SV768: $i] :
( ( ( ! [SY3204: $i] :
( ~ ( in @ SY3204 @ SV768 )
| ( in @ SY3204 @ SV779 ) ) )
= $true )
| ( ( ! [SY3205: $i] :
( ~ ( in @ SY3205 @ SV779 )
| ( in @ SY3205 @ SV768 ) ) )
= $true )
| ( ( in @ SV768 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( in @ SV779 @ ( sK3_SY2186 @ SV147 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3727]) ).
thf(3801,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( ~ ( in @ SV825 @ SV747 ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( ~ ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3728]) ).
thf(3802,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( in @ SV820 @ SV747 )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( ~ ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3729]) ).
thf(3803,plain,
! [SV653: $i,SV826: $i,SV160: $i > $o] :
( ( ( ~ ( SV160 @ SV826 )
| ( ( sK81_SY2233 @ SV653 @ SV160 )
= SV826 ) )
= $true )
| ( ( SV160 @ ( sK49_SY2231 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3731]) ).
thf(3804,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( SV160 @ ( sK90_SY2233 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ ( sK58_SY3190 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3732]) ).
thf(3805,plain,
! [SV653: $i,SV160: $i > $o] :
( ( ( ! [SY3224: $i] :
( ~ ( SV160 @ SY3224 )
| ( ( sK90_SY2233 @ SV653 @ SV160 )
= SY3224 ) ) )
= $true )
| ( ( SV160 @ ( sK58_SY3190 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3733]) ).
thf(3806,plain,
! [SV653: $i,SV827: $i,SV160: $i > $o] :
( ( ( ~ ( SV160 @ SV827 )
| ( ( sK82_SY2233 @ SV653 @ SV160 )
= SV827 ) )
= $true )
| ( ( ( sK49_SY2231 @ SV653 @ SV160 )
= ( sK58_SY3190 @ SV653 @ SV160 ) )
= $false )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3735]) ).
thf(3807,plain,
! [SV181: $i,SV795: $i,SV409: $i > $o] :
( ( ( SV409 @ SV795 )
= $false )
| ( ( in @ SV795 @ SV181 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( SV409 @ ( sK12_SY2740 @ SV409 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3737]) ).
thf(3808,plain,
! [SV409: $i > $o,SV181: $i,SV809: $i] :
( ( ( in @ SV809 @ SV181 )
= $false )
| ( ( ~ ( SV409 @ SV809 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( SV409 @ ( sK34_SY3112 @ SV409 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3738]) ).
thf(3809,plain,
! [SV181: $i,SV796: $i,SV409: $i > $o] :
( ( ( SV409 @ SV796 )
= $false )
| ( ( in @ SV796 @ SV181 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( ( sK12_SY2740 @ SV409 @ SV181 )
= ( sK34_SY3112 @ SV409 @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3739]) ).
thf(3810,plain,
! [SV780: $i,SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ( SV183 @ ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) ) )
= $false )
| ( ( SV183 @ SV780 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3740]) ).
thf(3811,plain,
! [SV183: $i > $o,SV411: $i > $o,SV780: $i] :
( ( ( SV780
= ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $false )
| ( ( SV183 @ SV780 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3740]) ).
thf(3812,plain,
! [SV411: $i > $o,SV828: $i,SV183: $i > $o] :
( ( ( ~ ~ ( ~ ( SV183 @ SV828 )
| ~ ! [SY3244: $i] :
( ~ ( SV183 @ SY3244 )
| ( SV828 = SY3244 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3741]) ).
thf(3813,plain,
! [SV411: $i > $o,SV821: $i,SV183: $i > $o] :
( ( ( ~ ( ~ ( SV183 @ SV821 )
| ~ ! [SY3237: $i] :
( ~ ( SV183 @ SY3237 )
| ( SV821 = SY3237 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3742]) ).
thf(3814,plain,
! [SV411: $i > $o,SV822: $i,SV183: $i > $o] :
( ( ( ~ ( ~ ( SV183 @ SV822 )
| ~ ! [SY3238: $i] :
( ~ ( SV183 @ SY3238 )
| ( SV822 = SY3238 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3743]) ).
thf(3815,plain,
! [SV411: $i > $o,SV817: $i,SV183: $i > $o] :
( ( ( ~ ( SV183 @ SV817 )
| ~ ! [SY3233: $i] :
( ~ ( SV183 @ SY3233 )
| ( SV817 = SY3233 ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3744]) ).
thf(3816,plain,
! [SV186: $i,SV659: $i,SV414: $i] :
( ( ( in @ ( sK97_SY3115 @ SV414 @ SV659 @ SV186 ) @ SV659 )
= $true )
| ( ( SV414 = SV659 )
= $true )
| ( ( in @ ( sK59_SY3114 @ SV659 @ SV414 @ SV186 ) @ SV414 )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV414 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3747]) ).
thf(3817,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( SV188 @ ( sK93_SY2316 @ SV660 @ SV188 ) )
= $true )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV188 @ ( sK69_SY3116 @ SV660 @ SV188 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3750]) ).
thf(3818,plain,
! [SV660: $i,SV188: $i > $o] :
( ( ( ! [SY3225: $i] :
( ~ ( SV188 @ SY3225 )
| ( ( sK93_SY2316 @ SV660 @ SV188 )
= SY3225 ) ) )
= $true )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV188 @ ( sK69_SY3116 @ SV660 @ SV188 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3751]) ).
thf(3819,plain,
! [SV660: $i,SV829: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV829 )
| ( ( sK83_SY2316 @ SV660 @ SV188 )
= SV829 ) )
= $true )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV660
= ( sK69_SY3116 @ SV660 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3753]) ).
thf(3820,plain,
! [SV422: $i > $o,SV810: $i,SV193: $i > $o] :
( ( ( SV193 @ SV810 )
= $false )
| ( ( ~ ! [SY3226: $i] :
( ~ ( SV193 @ SY3226 )
| ( SV810 = SY3226 ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3754]) ).
thf(3821,plain,
! [SV193: $i > $o,SV811: $i,SV422: $i > $o] :
( ( ( SV422 @ SV811 )
= $false )
| ( ( ~ ! [SY3227: $i] :
( ~ ( SV422 @ SY3227 )
| ( SV811 = SY3227 ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3755]) ).
thf(3822,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3756]) ).
thf(3823,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3757]) ).
thf(3824,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) ) )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3758]) ).
thf(3825,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) ) )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3759]) ).
thf(3826,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) ) )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3760]) ).
thf(3827,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) ) )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3761]) ).
thf(3828,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3762]) ).
thf(3829,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3763]) ).
thf(3830,plain,
! [SV426: $i,SV570: $i,SV712: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK102_SY3231 @ SV198 @ SV712 @ SV570 @ SV426 ) @ SV426 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SV198 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3765]) ).
thf(3831,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK98_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK102_SY3231 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV712 )
| ( in @ ( kpair @ ( sK98_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK102_SY3231 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV570 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SV198 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3765]) ).
thf(3832,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( ~ ( in @ ( sK103_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SV198 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) @ SV426 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3766]) ).
thf(3833,plain,
! [SV198: $i,SV712: $i,SV570: $i,SV426: $i] :
( ( ( ! [SY3239: $i] :
( ~ ( in @ SY3239 @ SV426 )
| ~ ( in @ ( kpair @ ( sK103_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SY3239 ) @ SV712 )
| ( in @ ( kpair @ ( sK103_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SY3239 ) @ SV570 ) ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) @ SV426 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3766]) ).
thf(3834,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( ~ ( in @ ( sK107_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SV198 )
| ! [SY3245: $i] :
( ~ ( in @ SY3245 @ SV426 )
| ~ ( in @ ( kpair @ ( sK107_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SY3245 ) @ SV712 )
| ( in @ ( kpair @ ( sK107_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SY3245 ) @ SV570 ) ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV570 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3767]) ).
thf(3835,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( ~ ( in @ ( sK104_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SV198 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV712 )
= $false )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3768]) ).
thf(3836,plain,
! [SV198: $i,SV712: $i,SV570: $i,SV426: $i] :
( ( ( ! [SY3240: $i] :
( ~ ( in @ SY3240 @ SV426 )
| ~ ( in @ ( kpair @ ( sK104_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SY3240 ) @ SV712 )
| ( in @ ( kpair @ ( sK104_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SY3240 ) @ SV570 ) ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV712 )
= $false )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3768]) ).
thf(3837,plain,
! [SV212: $i,SV799: $i,SV436: $i > $o] :
( ( ( SV436 @ SV799 )
= $false )
| ( ( in @ SV799 @ SV212 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( SV436 @ ( sK15_SY2806 @ SV436 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3770]) ).
thf(3838,plain,
! [SV436: $i > $o,SV212: $i,SV813: $i] :
( ( ( in @ SV813 @ SV212 )
= $false )
| ( ( ~ ( SV436 @ SV813 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( SV436 @ ( sK36_SY3121 @ SV436 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3771]) ).
thf(3839,plain,
! [SV212: $i,SV800: $i,SV436: $i > $o] :
( ( ( SV436 @ SV800 )
= $false )
| ( ( in @ SV800 @ SV212 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( ( sK15_SY2806 @ SV436 @ SV212 )
= ( sK36_SY3121 @ SV436 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3772]) ).
thf(3840,plain,
! [SV247: $i,SV600: $i,SV728: $i,SV803: $i,SV469: $i,SV818: $i] :
( ( ( in @ SV818 @ SV469 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV803 @ SV818 ) @ SV728 )
| ( in @ ( kpair @ SV803 @ SV818 ) @ SV600 ) )
= $true )
| ( ( in @ SV803 @ SV247 )
= $false )
| ( ( in @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) @ SV247 )
= $true )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3773]) ).
thf(3841,plain,
! [SV247: $i,SV469: $i,SV600: $i,SV728: $i,SV814: $i,SV786: $i] :
( ( ( ~ ( in @ ( kpair @ SV786 @ SV814 ) @ SV728 ) )
= $true )
| ( ( in @ ( kpair @ SV786 @ SV814 ) @ SV600 )
= $true )
| ( ( in @ SV814 @ SV469 )
= $false )
| ( ( in @ SV786 @ SV247 )
= $false )
| ( ( ( ap @ SV247 @ SV469 @ SV600 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) )
= ( ap @ SV247 @ SV469 @ SV728 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) ) )
= $false )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3774]) ).
thf(3842,plain,
! [SV471: $i,SV249: $i > $i > $o,SV773: $i] :
( ( ( ~ ( ~ ( in @ ( sK105_SY3202 @ SV773 @ SV249 @ SV471 ) @ SV471 )
| ~ ( SV249 @ ( sK105_SY3202 @ SV773 @ SV249 @ SV471 ) @ SV773 ) ) )
= $true )
| ( ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
= $false )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3775]) ).
thf(3843,plain,
! [SV773: $i,SV249: $i > $i > $o,SV471: $i,SV823: $i] :
( ( ( ~ ( ~ ( in @ SV823 @ SV471 )
| ~ ( SV249 @ SV823 @ SV773 ) ) )
= $false )
| ( ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
= $true )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3776]) ).
thf(3844,plain,
! [SV471: $i,SV249: $i > $i > $o,SV757: $i] :
( ( ( ! [SY3241: $i] :
~ ( ~ ( ~ ( in @ SY3241 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
| ~ ! [SY2876: $i] :
~ ~ ( ~ ( in @ SY2876 @ SV471 )
| ~ ( SV249 @ SY2876 @ SY3241 ) ) )
| ~ ( ~ ~ ! [SY2877: $i] :
~ ~ ( ~ ( in @ SY2877 @ SV471 )
| ~ ( SV249 @ SY2877 @ SY3241 ) )
| ( in @ SY3241 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) ) ) ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3777]) ).
thf(3845,plain,
! [SV471: $i,SV249: $i > $i > $o,SV757: $i,SV830: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
| ~ ! [SY3246: $i] :
~ ~ ( ~ ( in @ SY3246 @ SV471 )
| ~ ( SV249 @ SY3246 @ SV830 ) ) )
| ~ ( ~ ~ ! [SY3247: $i] :
~ ~ ( ~ ( in @ SY3247 @ SV471 )
| ~ ( SV249 @ SY3247 @ SV830 ) )
| ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) ) ) ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3778]) ).
thf(3846,plain,
! [SV670: $i,SV819: $i,SV256: $i > $o] :
( ( ( ~ ( ~ ( SV256 @ SV819 )
| ( SV819
= ( sK94_SY2511 @ SV670 @ SV256 ) ) ) )
= $false )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV256 @ ( sK74_SY3127 @ SV670 @ SV256 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3779]) ).
thf(3847,plain,
! [SV256: $i > $o,SV670: $i,SV819: $i] :
( ( ( ~ ( ( SV819
!= ( sK94_SY2511 @ SV670 @ SV256 ) )
| ( SV256 @ SV819 ) ) )
= $false )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV256 @ ( sK74_SY3127 @ SV670 @ SV256 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3779]) ).
thf(3848,plain,
! [SV670: $i,SV815: $i,SV256: $i > $o] :
( ( ( ~ ( SV256 @ SV815 )
| ( SV815
= ( sK86_SY2511 @ SV670 @ SV256 ) ) )
= $true )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV670
= ( sK74_SY3127 @ SV670 @ SV256 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3780]) ).
thf(3849,plain,
! [SV256: $i > $o,SV670: $i,SV815: $i] :
( ( ( ( SV815
!= ( sK86_SY2511 @ SV670 @ SV256 ) )
| ( SV256 @ SV815 ) )
= $true )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV670
= ( sK74_SY3127 @ SV670 @ SV256 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3781]) ).
thf(3850,plain,
! [SV621: $i,SV831: $i,SV35: $i > $o] :
( ( ( ~ ( SV35 @ SV831 )
| ( ( sK87_SY1902 @ SV621 @ SV35 )
= SV831 ) )
= $true )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV35 @ ( sK60_SY3073 @ SV621 @ SV35 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3783]) ).
thf(3851,plain,
! [SV621: $i,SV824: $i,SV35: $i > $o] :
( ( ( ~ ( SV35 @ SV824 ) )
= $true )
| ( ( ( sK78_SY1902 @ SV621 @ SV35 )
= SV824 )
= $true )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV621
= ( sK60_SY3073 @ SV621 @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3784]) ).
thf(3852,plain,
! [SV286: $i,SV623: $i > $o,SV40: $i,SV676: $i > $o] :
( ( ( ~ ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) ) )
= $false )
| ( ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) )
= $true )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3785]) ).
thf(3853,plain,
! [SV40: $i,SV286: $i,SV676: $i > $o,SV623: $i > $o] :
( ( ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) )
= $false )
| ( ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) )
= $true )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3785]) ).
thf(3854,plain,
! [SV286: $i,SV623: $i > $o,SV40: $i,SV676: $i > $o] :
( ( ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
= $true )
| ( ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
= $false )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3786]) ).
thf(3855,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ( SV44 @ ( sK99_SY1929 @ SV624 @ SV44 ) ) )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3788]) ).
thf(3856,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ~ ! [SY3232: $i] :
( ~ ( SV44 @ SY3232 )
| ( ( sK99_SY1929 @ SV624 @ SV44 )
= SY3232 ) ) )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3788]) ).
thf(3857,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( SV44 @ ( sK95_SY1929 @ SV624 @ SV44 ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3789]) ).
thf(3858,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ! [SY3229: $i] :
( ~ ( SV44 @ SY3229 )
| ( ( sK95_SY1929 @ SV624 @ SV44 )
= SY3229 ) ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3790]) ).
thf(3859,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( SV44 @ ( sK96_SY1929 @ SV624 @ SV44 ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3791]) ).
thf(3860,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ! [SY3230: $i] :
( ~ ( SV44 @ SY3230 )
| ( ( sK96_SY1929 @ SV624 @ SV44 )
= SY3230 ) ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3792]) ).
thf(3861,plain,
! [SV624: $i,SV832: $i,SV44: $i > $o] :
( ( ( ~ ( SV44 @ SV832 )
| ( ( sK88_SY1929 @ SV624 @ SV44 )
= SV832 ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3794]) ).
thf(3862,plain,
! [SV630: $i,SV82: $i,SV804: $i] :
( ( ( in @ SV804 @ SV82 )
= $false )
| ( ( in @ SV804 @ ( sK38_SY2017 @ SV630 @ SV82 ) )
= $false )
| ( ( in @ SV630 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3795]) ).
thf(3863,plain,
! [SV808: $i,SV147: $i,SV794: $i] :
( ( ( in @ SV794 @ SV147 )
= $false )
| ( ( ~ ( in @ SV808 @ SV147 ) )
= $true )
| ( ( ~ ! [SY3223: $i] :
( ~ ( in @ SY3223 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SV794 @ SY3223 )
| ( in @ SV808 @ SY3223 ) )
| ~ ( ~ ( in @ SV808 @ SY3223 )
| ( in @ SV794 @ SY3223 ) ) ) )
| ( SV794 = SV808 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3799]) ).
thf(3864,plain,
! [SV147: $i,SV779: $i,SV768: $i,SV833: $i] :
( ( ( ~ ( in @ SV833 @ SV768 )
| ( in @ SV833 @ SV779 ) )
= $true )
| ( ( ! [SY3205: $i] :
( ~ ( in @ SY3205 @ SV779 )
| ( in @ SY3205 @ SV768 ) ) )
= $true )
| ( ( in @ SV768 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( in @ SV779 @ ( sK3_SY2186 @ SV147 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3800]) ).
thf(3865,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( in @ SV825 @ SV747 )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( ~ ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3801]) ).
thf(3866,plain,
! [SV820: $i,SV747: $i,SV147: $i] :
( ( ( ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3802]) ).
thf(3867,plain,
! [SV653: $i,SV826: $i,SV160: $i > $o] :
( ( ( ~ ( SV160 @ SV826 ) )
= $true )
| ( ( ( sK81_SY2233 @ SV653 @ SV160 )
= SV826 )
= $true )
| ( ( SV160 @ ( sK49_SY2231 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3803]) ).
thf(3868,plain,
! [SV653: $i,SV834: $i,SV160: $i > $o] :
( ( ( ~ ( SV160 @ SV834 )
| ( ( sK90_SY2233 @ SV653 @ SV160 )
= SV834 ) )
= $true )
| ( ( SV160 @ ( sK58_SY3190 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3805]) ).
thf(3869,plain,
! [SV653: $i,SV827: $i,SV160: $i > $o] :
( ( ( ~ ( SV160 @ SV827 ) )
= $true )
| ( ( ( sK82_SY2233 @ SV653 @ SV160 )
= SV827 )
= $true )
| ( ( ( sK49_SY2231 @ SV653 @ SV160 )
= ( sK58_SY3190 @ SV653 @ SV160 ) )
= $false )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3806]) ).
thf(3870,plain,
! [SV181: $i,SV809: $i,SV409: $i > $o] :
( ( ( SV409 @ SV809 )
= $false )
| ( ( in @ SV809 @ SV181 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV181
@ ^ [SY2743: $i] : ( SV409 @ SY2743 ) ) )
= $true )
| ( ( SV409 @ ( sK34_SY3112 @ SV409 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3808]) ).
thf(3871,plain,
! [SV780: $i,SV411: $i > $o,SV183: $i > $o] :
( ( ( SV183 @ ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3810]) ).
thf(3872,plain,
! [SV780: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV780
= ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $false )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3811]) ).
thf(3873,plain,
! [SV411: $i > $o,SV828: $i,SV183: $i > $o] :
( ( ( ~ ( ~ ( SV183 @ SV828 )
| ~ ! [SY3244: $i] :
( ~ ( SV183 @ SY3244 )
| ( SV828 = SY3244 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3812]) ).
thf(3874,plain,
! [SV411: $i > $o,SV821: $i,SV183: $i > $o] :
( ( ( ~ ( SV183 @ SV821 )
| ~ ! [SY3237: $i] :
( ~ ( SV183 @ SY3237 )
| ( SV821 = SY3237 ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3813]) ).
thf(3875,plain,
! [SV411: $i > $o,SV822: $i,SV183: $i > $o] :
( ( ( ~ ( SV183 @ SV822 )
| ~ ! [SY3238: $i] :
( ~ ( SV183 @ SY3238 )
| ( SV822 = SY3238 ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3814]) ).
thf(3876,plain,
! [SV411: $i > $o,SV817: $i,SV183: $i > $o] :
( ( ( ~ ( SV183 @ SV817 ) )
= $true )
| ( ( ~ ! [SY3233: $i] :
( ~ ( SV183 @ SY3233 )
| ( SV817 = SY3233 ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3815]) ).
thf(3877,plain,
! [SV660: $i,SV835: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV835 )
| ( ( sK93_SY2316 @ SV660 @ SV188 )
= SV835 ) )
= $true )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV188 @ ( sK69_SY3116 @ SV660 @ SV188 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3818]) ).
thf(3878,plain,
! [SV660: $i,SV829: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV829 ) )
= $true )
| ( ( ( sK83_SY2316 @ SV660 @ SV188 )
= SV829 )
= $true )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV660
= ( sK69_SY3116 @ SV660 @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3819]) ).
thf(3879,plain,
! [SV422: $i > $o,SV810: $i,SV193: $i > $o] :
( ( ( ! [SY3226: $i] :
( ~ ( SV193 @ SY3226 )
| ( SV810 = SY3226 ) ) )
= $false )
| ( ( SV193 @ SV810 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3820]) ).
thf(3880,plain,
! [SV193: $i > $o,SV811: $i,SV422: $i > $o] :
( ( ( ! [SY3227: $i] :
( ~ ( SV422 @ SY3227 )
| ( SV811 = SY3227 ) ) )
= $false )
| ( ( SV422 @ SV811 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3821]) ).
thf(3881,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) ) )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3822]) ).
thf(3882,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) ) )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3823]) ).
thf(3883,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3824]) ).
thf(3884,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3825]) ).
thf(3885,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3826]) ).
thf(3886,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3827]) ).
thf(3887,plain,
! [SV422: $i > $o,SV836: $i,SV193: $i > $o] :
( ( ( ~ ~ ( ~ ( SV193 @ SV836 )
| ~ ! [SY3248: $i] :
( ~ ( SV193 @ SY3248 )
| ( SV836 = SY3248 ) ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3828]) ).
thf(3888,plain,
! [SV193: $i > $o,SV837: $i,SV422: $i > $o] :
( ( ( ~ ~ ( ~ ( SV422 @ SV837 )
| ~ ! [SY3249: $i] :
( ~ ( SV422 @ SY3249 )
| ( SV837 = SY3249 ) ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3829]) ).
thf(3889,plain,
! [SV426: $i,SV570: $i,SV712: $i,SV198: $i] :
( ( ( in @ ( sK102_SY3231 @ SV198 @ SV712 @ SV570 @ SV426 ) @ SV426 )
= $true )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SV198 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3830]) ).
thf(3890,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK98_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK102_SY3231 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV712 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SV198 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3831]) ).
thf(3891,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( in @ ( kpair @ ( sK98_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK102_SY3231 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV570 )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SV198 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3831]) ).
thf(3892,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( in @ ( sK103_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SV198 )
= $true )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) @ SV426 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3832]) ).
thf(3893,plain,
! [SV426: $i,SV570: $i,SV712: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK108_SY3239 @ SV198 @ SV712 @ SV570 @ SV426 ) @ SV426 )
| ~ ( in @ ( kpair @ ( sK103_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK108_SY3239 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV712 )
| ( in @ ( kpair @ ( sK103_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK108_SY3239 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV570 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) @ SV426 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3833]) ).
thf(3894,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( ~ ( in @ ( sK107_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SV198 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV570 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3834]) ).
thf(3895,plain,
! [SV198: $i,SV712: $i,SV570: $i,SV426: $i] :
( ( ( ! [SY3245: $i] :
( ~ ( in @ SY3245 @ SV426 )
| ~ ( in @ ( kpair @ ( sK107_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SY3245 ) @ SV712 )
| ( in @ ( kpair @ ( sK107_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SY3245 ) @ SV570 ) ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV570 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3834]) ).
thf(3896,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( in @ ( sK104_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SV198 )
= $true )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV712 )
= $false )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3835]) ).
thf(3897,plain,
! [SV426: $i,SV570: $i,SV712: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK109_SY3240 @ SV198 @ SV712 @ SV570 @ SV426 ) @ SV426 )
| ~ ( in @ ( kpair @ ( sK104_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK109_SY3240 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV712 )
| ( in @ ( kpair @ ( sK104_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK109_SY3240 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV570 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV712 )
= $false )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3836]) ).
thf(3898,plain,
! [SV212: $i,SV813: $i,SV436: $i > $o] :
( ( ( SV436 @ SV813 )
= $false )
| ( ( in @ SV813 @ SV212 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV212
@ ^ [SY2809: $i] : ( SV436 @ SY2809 ) ) )
= $true )
| ( ( SV436 @ ( sK36_SY3121 @ SV436 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3838]) ).
thf(3899,plain,
! [SV247: $i,SV469: $i,SV600: $i,SV728: $i,SV818: $i,SV803: $i] :
( ( ( ~ ( in @ ( kpair @ SV803 @ SV818 ) @ SV728 ) )
= $true )
| ( ( in @ ( kpair @ SV803 @ SV818 ) @ SV600 )
= $true )
| ( ( in @ SV818 @ SV469 )
= $false )
| ( ( in @ SV803 @ SV247 )
= $false )
| ( ( in @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) @ SV247 )
= $true )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3840]) ).
thf(3900,plain,
! [SV247: $i,SV469: $i,SV600: $i,SV728: $i,SV814: $i,SV786: $i] :
( ( ( in @ ( kpair @ SV786 @ SV814 ) @ SV728 )
= $false )
| ( ( in @ ( kpair @ SV786 @ SV814 ) @ SV600 )
= $true )
| ( ( in @ SV814 @ SV469 )
= $false )
| ( ( in @ SV786 @ SV247 )
= $false )
| ( ( ( ap @ SV247 @ SV469 @ SV600 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) )
= ( ap @ SV247 @ SV469 @ SV728 @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) ) )
= $false )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3841]) ).
thf(3901,plain,
! [SV471: $i,SV249: $i > $i > $o,SV773: $i] :
( ( ( ~ ( in @ ( sK105_SY3202 @ SV773 @ SV249 @ SV471 ) @ SV471 )
| ~ ( SV249 @ ( sK105_SY3202 @ SV773 @ SV249 @ SV471 ) @ SV773 ) )
= $false )
| ( ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
= $false )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3842]) ).
thf(3902,plain,
! [SV773: $i,SV249: $i > $i > $o,SV471: $i,SV823: $i] :
( ( ( ~ ( in @ SV823 @ SV471 )
| ~ ( SV249 @ SV823 @ SV773 ) )
= $true )
| ( ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
= $true )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3843]) ).
thf(3903,plain,
! [SV471: $i,SV249: $i > $i > $o,SV757: $i,SV838: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
| ~ ! [SY3250: $i] :
~ ~ ( ~ ( in @ SY3250 @ SV471 )
| ~ ( SV249 @ SY3250 @ SV838 ) ) )
| ~ ( ~ ~ ! [SY3251: $i] :
~ ~ ( ~ ( in @ SY3251 @ SV471 )
| ~ ( SV249 @ SY3251 @ SV838 ) )
| ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) ) ) ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3844]) ).
thf(3904,plain,
! [SV471: $i,SV249: $i > $i > $o,SV757: $i,SV830: $i] :
( ( ( ~ ( ~ ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
| ~ ! [SY3246: $i] :
~ ~ ( ~ ( in @ SY3246 @ SV471 )
| ~ ( SV249 @ SY3246 @ SV830 ) ) )
| ~ ( ~ ~ ! [SY3247: $i] :
~ ~ ( ~ ( in @ SY3247 @ SV471 )
| ~ ( SV249 @ SY3247 @ SV830 ) )
| ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) ) ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3845]) ).
thf(3905,plain,
! [SV670: $i,SV819: $i,SV256: $i > $o] :
( ( ( ~ ( SV256 @ SV819 )
| ( SV819
= ( sK94_SY2511 @ SV670 @ SV256 ) ) )
= $true )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV256 @ ( sK74_SY3127 @ SV670 @ SV256 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3846]) ).
thf(3906,plain,
! [SV256: $i > $o,SV670: $i,SV819: $i] :
( ( ( ( SV819
!= ( sK94_SY2511 @ SV670 @ SV256 ) )
| ( SV256 @ SV819 ) )
= $true )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV256 @ ( sK74_SY3127 @ SV670 @ SV256 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3847]) ).
thf(3907,plain,
! [SV670: $i,SV815: $i,SV256: $i > $o] :
( ( ( ~ ( SV256 @ SV815 ) )
= $true )
| ( ( SV815
= ( sK86_SY2511 @ SV670 @ SV256 ) )
= $true )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV670
= ( sK74_SY3127 @ SV670 @ SV256 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3848]) ).
thf(3908,plain,
! [SV256: $i > $o,SV670: $i,SV815: $i] :
( ( ( SV815
!= ( sK86_SY2511 @ SV670 @ SV256 ) )
= $true )
| ( ( SV256 @ SV815 )
= $true )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV670
= ( sK74_SY3127 @ SV670 @ SV256 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3849]) ).
thf(3909,plain,
! [SV621: $i,SV831: $i,SV35: $i > $o] :
( ( ( ~ ( SV35 @ SV831 ) )
= $true )
| ( ( ( sK87_SY1902 @ SV621 @ SV35 )
= SV831 )
= $true )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV35 @ ( sK60_SY3073 @ SV621 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3850]) ).
thf(3910,plain,
! [SV621: $i,SV824: $i,SV35: $i > $o] :
( ( ( SV35 @ SV824 )
= $false )
| ( ( ( sK78_SY1902 @ SV621 @ SV35 )
= SV824 )
= $true )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV621
= ( sK60_SY3073 @ SV621 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3851]) ).
thf(3911,plain,
! [SV286: $i,SV623: $i > $o,SV40: $i,SV676: $i > $o] :
( ( ( SV676 @ ( sK61_SY3188 @ SV40 @ SV623 @ SV676 @ SV286 ) )
= $true )
| ( ( SV623 @ ( sK45_SY3132 @ SV676 @ SV623 @ SV286 @ SV40 ) )
= $true )
| ( ( ( dsetconstr @ SV40
@ ^ [SY3077: $i] : ( SV623 @ SY3077 ) )
= ( dsetconstr @ SV286
@ ^ [SY3135: $i] : ( SV676 @ SY3135 ) ) )
= $true )
| ( ( SV40 = SV286 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3852]) ).
thf(3912,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( SV44 @ ( sK99_SY1929 @ SV624 @ SV44 ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3855]) ).
thf(3913,plain,
! [SV624: $i,SV44: $i > $o] :
( ( ( ! [SY3232: $i] :
( ~ ( SV44 @ SY3232 )
| ( ( sK99_SY1929 @ SV624 @ SV44 )
= SY3232 ) ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3856]) ).
thf(3914,plain,
! [SV624: $i,SV839: $i,SV44: $i > $o] :
( ( ( ~ ( SV44 @ SV839 )
| ( ( sK95_SY1929 @ SV624 @ SV44 )
= SV839 ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3858]) ).
thf(3915,plain,
! [SV624: $i,SV840: $i,SV44: $i > $o] :
( ( ( ~ ( SV44 @ SV840 )
| ( ( sK96_SY1929 @ SV624 @ SV44 )
= SV840 ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3860]) ).
thf(3916,plain,
! [SV624: $i,SV832: $i,SV44: $i > $o] :
( ( ( ~ ( SV44 @ SV832 ) )
= $true )
| ( ( ( sK88_SY1929 @ SV624 @ SV44 )
= SV832 )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3861]) ).
thf(3917,plain,
! [SV794: $i,SV147: $i,SV808: $i] :
( ( ( in @ SV808 @ SV147 )
= $false )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( ~ ! [SY3223: $i] :
( ~ ( in @ SY3223 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SV794 @ SY3223 )
| ( in @ SV808 @ SY3223 ) )
| ~ ( ~ ( in @ SV808 @ SY3223 )
| ( in @ SV794 @ SY3223 ) ) ) )
| ( SV794 = SV808 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3863]) ).
thf(3918,plain,
! [SV147: $i,SV779: $i,SV768: $i,SV833: $i] :
( ( ( ~ ( in @ SV833 @ SV768 ) )
= $true )
| ( ( in @ SV833 @ SV779 )
= $true )
| ( ( ! [SY3205: $i] :
( ~ ( in @ SY3205 @ SV779 )
| ( in @ SY3205 @ SV768 ) ) )
= $true )
| ( ( in @ SV768 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( in @ SV779 @ ( sK3_SY2186 @ SV147 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3864]) ).
thf(3919,plain,
! [SV825: $i,SV747: $i,SV147: $i] :
( ( ( ! [SY3178: $i] :
~ ~ ! [SY3179: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3178 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3179 @ SV747 ) )
| ~ ~ ~ ! [SY3180: $i] :
~ ~ ( ~ ( in @ SY3180 @ SY3178 )
| ~ ( in @ SY3180 @ SV747 ) ) )
| ~ ! [SY2968: $i] :
( ~ ( in @ SY2968 @ ( sK3_SY2186 @ SV147 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2968 )
| ( in @ SX6 @ SY3178 ) )
| ( in @ SY3179 @ SY2968 ) ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3865]) ).
thf(3920,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( ~ ~ ! [SY3252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3252 @ SV747 ) )
| ~ ~ ~ ! [SY3253: $i] :
~ ~ ( ~ ( in @ SY3253 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
| ~ ( in @ SY3253 @ SV747 ) ) )
| ~ ! [SY3254: $i] :
( ~ ( in @ SY3254 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3255: $i] :
( ~ ( in @ SY3255 @ SY3254 )
| ( in @ SY3255 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) ) )
| ( in @ SY3252 @ SY3254 ) ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3866]) ).
thf(3921,plain,
! [SV653: $i,SV826: $i,SV160: $i > $o] :
( ( ( SV160 @ SV826 )
= $false )
| ( ( ( sK81_SY2233 @ SV653 @ SV160 )
= SV826 )
= $true )
| ( ( SV160 @ ( sK49_SY2231 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3867]) ).
thf(3922,plain,
! [SV653: $i,SV834: $i,SV160: $i > $o] :
( ( ( ~ ( SV160 @ SV834 ) )
= $true )
| ( ( ( sK90_SY2233 @ SV653 @ SV160 )
= SV834 )
= $true )
| ( ( SV160 @ ( sK58_SY3190 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3868]) ).
thf(3923,plain,
! [SV653: $i,SV827: $i,SV160: $i > $o] :
( ( ( SV160 @ SV827 )
= $false )
| ( ( ( sK82_SY2233 @ SV653 @ SV160 )
= SV827 )
= $true )
| ( ( ( sK49_SY2231 @ SV653 @ SV160 )
= ( sK58_SY3190 @ SV653 @ SV160 ) )
= $false )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3869]) ).
thf(3924,plain,
! [SV780: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV183 @ ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3871]) ).
thf(3925,plain,
! [SV780: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV780
= ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $false )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3872]) ).
thf(3926,plain,
! [SV411: $i > $o,SV828: $i,SV183: $i > $o] :
( ( ( ~ ( SV183 @ SV828 )
| ~ ! [SY3244: $i] :
( ~ ( SV183 @ SY3244 )
| ( SV828 = SY3244 ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3873]) ).
thf(3927,plain,
! [SV411: $i > $o,SV821: $i,SV183: $i > $o] :
( ( ( ~ ( SV183 @ SV821 ) )
= $true )
| ( ( ~ ! [SY3237: $i] :
( ~ ( SV183 @ SY3237 )
| ( SV821 = SY3237 ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3874]) ).
thf(3928,plain,
! [SV411: $i > $o,SV822: $i,SV183: $i > $o] :
( ( ( ~ ( SV183 @ SV822 ) )
= $true )
| ( ( ~ ! [SY3238: $i] :
( ~ ( SV183 @ SY3238 )
| ( SV822 = SY3238 ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3875]) ).
thf(3929,plain,
! [SV411: $i > $o,SV817: $i,SV183: $i > $o] :
( ( ( SV183 @ SV817 )
= $false )
| ( ( ~ ! [SY3233: $i] :
( ~ ( SV183 @ SY3233 )
| ( SV817 = SY3233 ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3876]) ).
thf(3930,plain,
! [SV660: $i,SV835: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV835 ) )
= $true )
| ( ( ( sK93_SY2316 @ SV660 @ SV188 )
= SV835 )
= $true )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV188 @ ( sK69_SY3116 @ SV660 @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3877]) ).
thf(3931,plain,
! [SV660: $i,SV829: $i,SV188: $i > $o] :
( ( ( SV188 @ SV829 )
= $false )
| ( ( ( sK83_SY2316 @ SV660 @ SV188 )
= SV829 )
= $true )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV660
= ( sK69_SY3116 @ SV660 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3878]) ).
thf(3932,plain,
! [SV810: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
| ( SV810
= ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) ) )
= $false )
| ( ( SV193 @ SV810 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3879]) ).
thf(3933,plain,
! [SV811: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
| ( SV811
= ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) ) )
= $false )
| ( ( SV422 @ SV811 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3880]) ).
thf(3934,plain,
! [SV422: $i > $o,SV193: $i > $o] :
( ( ( ! [SY2331: $i] :
~ ~ ( ~ ( SV193 @ SY2331 )
| ~ ! [SY2332: $i] :
( ~ ( SV193 @ SY2332 )
| ( SY2331 = SY2332 ) ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3881]) ).
thf(3935,plain,
! [SV193: $i > $o,SV422: $i > $o] :
( ( ( ! [SY2772: $i] :
~ ~ ( ~ ( SV422 @ SY2772 )
| ~ ! [SY2773: $i] :
( ~ ( SV422 @ SY2773 )
| ( SY2772 = SY2773 ) ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3882]) ).
thf(3936,plain,
! [SV422: $i > $o,SV841: $i,SV193: $i > $o] :
( ( ( ~ ~ ( ~ ( SV193 @ SV841 )
| ~ ! [SY3256: $i] :
( ~ ( SV193 @ SY3256 )
| ( SV841 = SY3256 ) ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3883]) ).
thf(3937,plain,
! [SV193: $i > $o,SV842: $i,SV422: $i > $o] :
( ( ( ~ ~ ( ~ ( SV422 @ SV842 )
| ~ ! [SY3257: $i] :
( ~ ( SV422 @ SY3257 )
| ( SV842 = SY3257 ) ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3884]) ).
thf(3938,plain,
! [SV422: $i > $o,SV843: $i,SV193: $i > $o] :
( ( ( ~ ~ ( ~ ( SV193 @ SV843 )
| ~ ! [SY3258: $i] :
( ~ ( SV193 @ SY3258 )
| ( SV843 = SY3258 ) ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3885]) ).
thf(3939,plain,
! [SV193: $i > $o,SV844: $i,SV422: $i > $o] :
( ( ( ~ ~ ( ~ ( SV422 @ SV844 )
| ~ ! [SY3259: $i] :
( ~ ( SV422 @ SY3259 )
| ( SV844 = SY3259 ) ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3886]) ).
thf(3940,plain,
! [SV422: $i > $o,SV836: $i,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ SV836 )
| ~ ! [SY3248: $i] :
( ~ ( SV193 @ SY3248 )
| ( SV836 = SY3248 ) ) ) )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3887]) ).
thf(3941,plain,
! [SV193: $i > $o,SV837: $i,SV422: $i > $o] :
( ( ( ~ ( ~ ( SV422 @ SV837 )
| ~ ! [SY3249: $i] :
( ~ ( SV422 @ SY3249 )
| ( SV837 = SY3249 ) ) ) )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3888]) ).
thf(3942,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( in @ ( kpair @ ( sK98_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK102_SY3231 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV712 )
= $true )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ SV198 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3890]) ).
thf(3943,plain,
! [SV426: $i,SV570: $i,SV712: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK108_SY3239 @ SV198 @ SV712 @ SV570 @ SV426 ) @ SV426 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) @ SV426 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3893]) ).
thf(3944,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK103_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK108_SY3239 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV712 )
| ( in @ ( kpair @ ( sK103_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK108_SY3239 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV570 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) @ SV426 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3893]) ).
thf(3945,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( in @ ( sK107_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ SV198 )
= $true )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV570 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3894]) ).
thf(3946,plain,
! [SV426: $i,SV570: $i,SV712: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK113_SY3245 @ SV198 @ SV712 @ SV570 @ SV426 ) @ SV426 )
| ~ ( in @ ( kpair @ ( sK107_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK113_SY3245 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV712 )
| ( in @ ( kpair @ ( sK107_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK113_SY3245 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV570 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV570 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3895]) ).
thf(3947,plain,
! [SV426: $i,SV570: $i,SV712: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK109_SY3240 @ SV198 @ SV712 @ SV570 @ SV426 ) @ SV426 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV712 )
= $false )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3897]) ).
thf(3948,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK104_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK109_SY3240 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV712 )
| ( in @ ( kpair @ ( sK104_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK109_SY3240 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV570 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV712 )
= $false )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3897]) ).
thf(3949,plain,
! [SV247: $i,SV469: $i,SV600: $i,SV728: $i,SV818: $i,SV803: $i] :
( ( ( in @ ( kpair @ SV803 @ SV818 ) @ SV728 )
= $false )
| ( ( in @ ( kpair @ SV803 @ SV818 ) @ SV600 )
= $true )
| ( ( in @ SV818 @ SV469 )
= $false )
| ( ( in @ SV803 @ SV247 )
= $false )
| ( ( in @ ( sK73_SY3165 @ SV728 @ SV600 @ SV469 @ SV247 ) @ SV247 )
= $true )
| ( ( func @ SV247 @ SV469 @ SV728 )
= $false )
| ( ( func @ SV247 @ SV469 @ SV600 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3899]) ).
thf(3950,plain,
! [SV471: $i,SV249: $i > $i > $o,SV773: $i] :
( ( ( ~ ( in @ ( sK105_SY3202 @ SV773 @ SV249 @ SV471 ) @ SV471 ) )
= $false )
| ( ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
= $false )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3901]) ).
thf(3951,plain,
! [SV471: $i,SV773: $i,SV249: $i > $i > $o] :
( ( ( ~ ( SV249 @ ( sK105_SY3202 @ SV773 @ SV249 @ SV471 ) @ SV773 ) )
= $false )
| ( ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
= $false )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3901]) ).
thf(3952,plain,
! [SV773: $i,SV249: $i > $i > $o,SV471: $i,SV823: $i] :
( ( ( ~ ( in @ SV823 @ SV471 ) )
= $true )
| ( ( ~ ( SV249 @ SV823 @ SV773 ) )
= $true )
| ( ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
= $true )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3902]) ).
thf(3953,plain,
! [SV471: $i,SV249: $i > $i > $o,SV757: $i,SV838: $i] :
( ( ( ~ ( ~ ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
| ~ ! [SY3250: $i] :
~ ~ ( ~ ( in @ SY3250 @ SV471 )
| ~ ( SV249 @ SY3250 @ SV838 ) ) )
| ~ ( ~ ~ ! [SY3251: $i] :
~ ~ ( ~ ( in @ SY3251 @ SV471 )
| ~ ( SV249 @ SY3251 @ SV838 ) )
| ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) ) ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3903]) ).
thf(3954,plain,
! [SV471: $i,SV249: $i > $i > $o,SV757: $i,SV830: $i] :
( ( ( ~ ( ~ ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
| ~ ! [SY3246: $i] :
~ ~ ( ~ ( in @ SY3246 @ SV471 )
| ~ ( SV249 @ SY3246 @ SV830 ) ) ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3904]) ).
thf(3955,plain,
! [SV757: $i,SV830: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ~ ( ~ ~ ! [SY3247: $i] :
~ ~ ( ~ ( in @ SY3247 @ SV471 )
| ~ ( SV249 @ SY3247 @ SV830 ) )
| ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) ) ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3904]) ).
thf(3956,plain,
! [SV670: $i,SV819: $i,SV256: $i > $o] :
( ( ( ~ ( SV256 @ SV819 ) )
= $true )
| ( ( SV819
= ( sK94_SY2511 @ SV670 @ SV256 ) )
= $true )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV256 @ ( sK74_SY3127 @ SV670 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3905]) ).
thf(3957,plain,
! [SV256: $i > $o,SV670: $i,SV819: $i] :
( ( ( SV819
!= ( sK94_SY2511 @ SV670 @ SV256 ) )
= $true )
| ( ( SV256 @ SV819 )
= $true )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV256 @ ( sK74_SY3127 @ SV670 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3906]) ).
thf(3958,plain,
! [SV670: $i,SV815: $i,SV256: $i > $o] :
( ( ( SV256 @ SV815 )
= $false )
| ( ( SV815
= ( sK86_SY2511 @ SV670 @ SV256 ) )
= $true )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV670
= ( sK74_SY3127 @ SV670 @ SV256 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3907]) ).
thf(3959,plain,
! [SV256: $i > $o,SV670: $i,SV815: $i] :
( ( ( SV815
= ( sK86_SY2511 @ SV670 @ SV256 ) )
= $false )
| ( ( SV256 @ SV815 )
= $true )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV670
= ( sK74_SY3127 @ SV670 @ SV256 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3908]) ).
thf(3960,plain,
! [SV621: $i,SV831: $i,SV35: $i > $o] :
( ( ( SV35 @ SV831 )
= $false )
| ( ( ( sK87_SY1902 @ SV621 @ SV35 )
= SV831 )
= $true )
| ( ( SV35 @ SV621 )
= $false )
| ( ( SV35 @ ( sK60_SY3073 @ SV621 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3909]) ).
thf(3961,plain,
! [SV624: $i,SV845: $i,SV44: $i > $o] :
( ( ( ~ ( SV44 @ SV845 )
| ( ( sK99_SY1929 @ SV624 @ SV44 )
= SV845 ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3913]) ).
thf(3962,plain,
! [SV624: $i,SV839: $i,SV44: $i > $o] :
( ( ( ~ ( SV44 @ SV839 ) )
= $true )
| ( ( ( sK95_SY1929 @ SV624 @ SV44 )
= SV839 )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3914]) ).
thf(3963,plain,
! [SV624: $i,SV840: $i,SV44: $i > $o] :
( ( ( ~ ( SV44 @ SV840 ) )
= $true )
| ( ( ( sK96_SY1929 @ SV624 @ SV44 )
= SV840 )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3915]) ).
thf(3964,plain,
! [SV624: $i,SV832: $i,SV44: $i > $o] :
( ( ( SV44 @ SV832 )
= $false )
| ( ( ( sK88_SY1929 @ SV624 @ SV44 )
= SV832 )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3916]) ).
thf(3965,plain,
! [SV808: $i,SV794: $i,SV147: $i] :
( ( ( ~ ! [SY3223: $i] :
( ~ ( in @ SY3223 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SV794 @ SY3223 )
| ( in @ SV808 @ SY3223 ) )
| ~ ( ~ ( in @ SV808 @ SY3223 )
| ( in @ SV794 @ SY3223 ) ) ) ) )
= $true )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3917]) ).
thf(3966,plain,
! [SV147: $i,SV779: $i,SV768: $i,SV833: $i] :
( ( ( in @ SV833 @ SV768 )
= $false )
| ( ( in @ SV833 @ SV779 )
= $true )
| ( ( ! [SY3205: $i] :
( ~ ( in @ SY3205 @ SV779 )
| ( in @ SY3205 @ SV768 ) ) )
= $true )
| ( ( in @ SV768 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( in @ SV779 @ ( sK3_SY2186 @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3918]) ).
thf(3967,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( ~ ~ ! [SY3260: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3260 @ SV747 ) )
| ~ ~ ~ ! [SY3261: $i] :
~ ~ ( ~ ( in @ SY3261 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
| ~ ( in @ SY3261 @ SV747 ) ) )
| ~ ! [SY3262: $i] :
( ~ ( in @ SY3262 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3263: $i] :
( ~ ( in @ SY3263 @ SY3262 )
| ( in @ SY3263 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) ) )
| ( in @ SY3260 @ SY3262 ) ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3919]) ).
thf(3968,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( ~ ! [SY3252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3252 @ SV747 ) )
| ~ ~ ~ ! [SY3253: $i] :
~ ~ ( ~ ( in @ SY3253 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
| ~ ( in @ SY3253 @ SV747 ) ) )
| ~ ! [SY3254: $i] :
( ~ ( in @ SY3254 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3255: $i] :
( ~ ( in @ SY3255 @ SY3254 )
| ( in @ SY3255 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) ) )
| ( in @ SY3252 @ SY3254 ) ) ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3920]) ).
thf(3969,plain,
! [SV653: $i,SV834: $i,SV160: $i > $o] :
( ( ( SV160 @ SV834 )
= $false )
| ( ( ( sK90_SY2233 @ SV653 @ SV160 )
= SV834 )
= $true )
| ( ( SV160 @ ( sK58_SY3190 @ SV653 @ SV160 ) )
= $true )
| ( ( SV160 @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3922]) ).
thf(3970,plain,
! [SV780: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV183 @ ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3924]) ).
thf(3971,plain,
! [SV780: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV780
= ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $false )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3925]) ).
thf(3972,plain,
! [SV411: $i > $o,SV828: $i,SV183: $i > $o] :
( ( ( ~ ( SV183 @ SV828 ) )
= $true )
| ( ( ~ ! [SY3244: $i] :
( ~ ( SV183 @ SY3244 )
| ( SV828 = SY3244 ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3926]) ).
thf(3973,plain,
! [SV411: $i > $o,SV821: $i,SV183: $i > $o] :
( ( ( SV183 @ SV821 )
= $false )
| ( ( ~ ! [SY3237: $i] :
( ~ ( SV183 @ SY3237 )
| ( SV821 = SY3237 ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3927]) ).
thf(3974,plain,
! [SV411: $i > $o,SV822: $i,SV183: $i > $o] :
( ( ( SV183 @ SV822 )
= $false )
| ( ( ~ ! [SY3238: $i] :
( ~ ( SV183 @ SY3238 )
| ( SV822 = SY3238 ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3928]) ).
thf(3975,plain,
! [SV411: $i > $o,SV817: $i,SV183: $i > $o] :
( ( ( ! [SY3233: $i] :
( ~ ( SV183 @ SY3233 )
| ( SV817 = SY3233 ) ) )
= $false )
| ( ( SV183 @ SV817 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3929]) ).
thf(3976,plain,
! [SV660: $i,SV835: $i,SV188: $i > $o] :
( ( ( SV188 @ SV835 )
= $false )
| ( ( ( sK93_SY2316 @ SV660 @ SV188 )
= SV835 )
= $true )
| ( ( SV188 @ SV660 )
= $false )
| ( ( SV188 @ ( sK69_SY3116 @ SV660 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3930]) ).
thf(3977,plain,
! [SV810: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) ) )
= $false )
| ( ( SV193 @ SV810 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3932]) ).
thf(3978,plain,
! [SV193: $i > $o,SV422: $i > $o,SV810: $i] :
( ( ( SV810
= ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $false )
| ( ( SV193 @ SV810 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3932]) ).
thf(3979,plain,
! [SV811: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) ) )
= $false )
| ( ( SV422 @ SV811 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3933]) ).
thf(3980,plain,
! [SV422: $i > $o,SV193: $i > $o,SV811: $i] :
( ( ( SV811
= ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $false )
| ( ( SV422 @ SV811 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3933]) ).
thf(3981,plain,
! [SV422: $i > $o,SV846: $i,SV193: $i > $o] :
( ( ( ~ ~ ( ~ ( SV193 @ SV846 )
| ~ ! [SY3264: $i] :
( ~ ( SV193 @ SY3264 )
| ( SV846 = SY3264 ) ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3934]) ).
thf(3982,plain,
! [SV193: $i > $o,SV847: $i,SV422: $i > $o] :
( ( ( ~ ~ ( ~ ( SV422 @ SV847 )
| ~ ! [SY3265: $i] :
( ~ ( SV422 @ SY3265 )
| ( SV847 = SY3265 ) ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3935]) ).
thf(3983,plain,
! [SV422: $i > $o,SV841: $i,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ SV841 )
| ~ ! [SY3256: $i] :
( ~ ( SV193 @ SY3256 )
| ( SV841 = SY3256 ) ) ) )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3936]) ).
thf(3984,plain,
! [SV193: $i > $o,SV842: $i,SV422: $i > $o] :
( ( ( ~ ( ~ ( SV422 @ SV842 )
| ~ ! [SY3257: $i] :
( ~ ( SV422 @ SY3257 )
| ( SV842 = SY3257 ) ) ) )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3937]) ).
thf(3985,plain,
! [SV422: $i > $o,SV843: $i,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ SV843 )
| ~ ! [SY3258: $i] :
( ~ ( SV193 @ SY3258 )
| ( SV843 = SY3258 ) ) ) )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3938]) ).
thf(3986,plain,
! [SV193: $i > $o,SV844: $i,SV422: $i > $o] :
( ( ( ~ ( ~ ( SV422 @ SV844 )
| ~ ! [SY3259: $i] :
( ~ ( SV422 @ SY3259 )
| ( SV844 = SY3259 ) ) ) )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3939]) ).
thf(3987,plain,
! [SV422: $i > $o,SV836: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV836 )
| ~ ! [SY3248: $i] :
( ~ ( SV193 @ SY3248 )
| ( SV836 = SY3248 ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3940]) ).
thf(3988,plain,
! [SV193: $i > $o,SV837: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV837 )
| ~ ! [SY3249: $i] :
( ~ ( SV422 @ SY3249 )
| ( SV837 = SY3249 ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3941]) ).
thf(3989,plain,
! [SV426: $i,SV570: $i,SV712: $i,SV198: $i] :
( ( ( in @ ( sK108_SY3239 @ SV198 @ SV712 @ SV570 @ SV426 ) @ SV426 )
= $true )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) @ SV426 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3943]) ).
thf(3990,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK103_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK108_SY3239 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV712 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) @ SV426 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3944]) ).
thf(3991,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( in @ ( kpair @ ( sK103_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK108_SY3239 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV570 )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) @ SV426 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3944]) ).
thf(3992,plain,
! [SV426: $i,SV570: $i,SV712: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK113_SY3245 @ SV198 @ SV712 @ SV570 @ SV426 ) @ SV426 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV570 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3946]) ).
thf(3993,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK107_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK113_SY3245 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV712 )
| ( in @ ( kpair @ ( sK107_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK113_SY3245 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV570 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV570 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3946]) ).
thf(3994,plain,
! [SV426: $i,SV570: $i,SV712: $i,SV198: $i] :
( ( ( in @ ( sK109_SY3240 @ SV198 @ SV712 @ SV570 @ SV426 ) @ SV426 )
= $true )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV712 )
= $false )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3947]) ).
thf(3995,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK104_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK109_SY3240 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV712 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV712 )
= $false )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3948]) ).
thf(3996,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( in @ ( kpair @ ( sK104_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK109_SY3240 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV570 )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV712 )
= $false )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3948]) ).
thf(3997,plain,
! [SV471: $i,SV249: $i > $i > $o,SV773: $i] :
( ( ( in @ ( sK105_SY3202 @ SV773 @ SV249 @ SV471 ) @ SV471 )
= $true )
| ( ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
= $false )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3950]) ).
thf(3998,plain,
! [SV471: $i,SV773: $i,SV249: $i > $i > $o] :
( ( ( SV249 @ ( sK105_SY3202 @ SV773 @ SV249 @ SV471 ) @ SV773 )
= $true )
| ( ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
= $false )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3951]) ).
thf(3999,plain,
! [SV773: $i,SV249: $i > $i > $o,SV471: $i,SV823: $i] :
( ( ( in @ SV823 @ SV471 )
= $false )
| ( ( ~ ( SV249 @ SV823 @ SV773 ) )
= $true )
| ( ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
= $true )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3952]) ).
thf(4000,plain,
! [SV471: $i,SV249: $i > $i > $o,SV757: $i,SV838: $i] :
( ( ( ~ ( ~ ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
| ~ ! [SY3250: $i] :
~ ~ ( ~ ( in @ SY3250 @ SV471 )
| ~ ( SV249 @ SY3250 @ SV838 ) ) ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3953]) ).
thf(4001,plain,
! [SV757: $i,SV838: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ~ ( ~ ~ ! [SY3251: $i] :
~ ~ ( ~ ( in @ SY3251 @ SV471 )
| ~ ( SV249 @ SY3251 @ SV838 ) )
| ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) ) ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3953]) ).
thf(4002,plain,
! [SV471: $i,SV249: $i > $i > $o,SV757: $i,SV830: $i] :
( ( ( ~ ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
| ~ ! [SY3246: $i] :
~ ~ ( ~ ( in @ SY3246 @ SV471 )
| ~ ( SV249 @ SY3246 @ SV830 ) ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3954]) ).
thf(4003,plain,
! [SV757: $i,SV830: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ~ ~ ! [SY3247: $i] :
~ ~ ( ~ ( in @ SY3247 @ SV471 )
| ~ ( SV249 @ SY3247 @ SV830 ) )
| ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3955]) ).
thf(4004,plain,
! [SV670: $i,SV819: $i,SV256: $i > $o] :
( ( ( SV256 @ SV819 )
= $false )
| ( ( SV819
= ( sK94_SY2511 @ SV670 @ SV256 ) )
= $true )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV256 @ ( sK74_SY3127 @ SV670 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3956]) ).
thf(4005,plain,
! [SV256: $i > $o,SV670: $i,SV819: $i] :
( ( ( SV819
= ( sK94_SY2511 @ SV670 @ SV256 ) )
= $false )
| ( ( SV256 @ SV819 )
= $true )
| ( ( SV256 @ SV670 )
= $false )
| ( ( SV256 @ ( sK74_SY3127 @ SV670 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3957]) ).
thf(4006,plain,
! [SV624: $i,SV845: $i,SV44: $i > $o] :
( ( ( ~ ( SV44 @ SV845 ) )
= $true )
| ( ( ( sK99_SY1929 @ SV624 @ SV44 )
= SV845 )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3961]) ).
thf(4007,plain,
! [SV624: $i,SV839: $i,SV44: $i > $o] :
( ( ( SV44 @ SV839 )
= $false )
| ( ( ( sK95_SY1929 @ SV624 @ SV44 )
= SV839 )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3962]) ).
thf(4008,plain,
! [SV624: $i,SV840: $i,SV44: $i > $o] :
( ( ( SV44 @ SV840 )
= $false )
| ( ( ( sK96_SY1929 @ SV624 @ SV44 )
= SV840 )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $false )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3963]) ).
thf(4009,plain,
! [SV808: $i,SV794: $i,SV147: $i] :
( ( ( ! [SY3223: $i] :
( ~ ( in @ SY3223 @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SV794 @ SY3223 )
| ( in @ SV808 @ SY3223 ) )
| ~ ( ~ ( in @ SV808 @ SY3223 )
| ( in @ SV794 @ SY3223 ) ) ) ) )
= $false )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3965]) ).
thf(4010,plain,
! [SV147: $i,SV833: $i,SV768: $i,SV779: $i,SV848: $i] :
( ( ( ~ ( in @ SV848 @ SV779 )
| ( in @ SV848 @ SV768 ) )
= $true )
| ( ( in @ SV833 @ SV779 )
= $true )
| ( ( in @ SV833 @ SV768 )
= $false )
| ( ( in @ SV768 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( in @ SV779 @ ( sK3_SY2186 @ SV147 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3966]) ).
thf(4011,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( ~ ! [SY3260: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3260 @ SV747 ) )
| ~ ~ ~ ! [SY3261: $i] :
~ ~ ( ~ ( in @ SY3261 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
| ~ ( in @ SY3261 @ SV747 ) ) )
| ~ ! [SY3262: $i] :
( ~ ( in @ SY3262 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3263: $i] :
( ~ ( in @ SY3263 @ SY3262 )
| ( in @ SY3263 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) ) )
| ( in @ SY3260 @ SY3262 ) ) ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3967]) ).
thf(4012,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( ! [SY3252: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3252 @ SV747 ) )
| ~ ~ ~ ! [SY3253: $i] :
~ ~ ( ~ ( in @ SY3253 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
| ~ ( in @ SY3253 @ SV747 ) ) )
| ~ ! [SY3254: $i] :
( ~ ( in @ SY3254 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3255: $i] :
( ~ ( in @ SY3255 @ SY3254 )
| ( in @ SY3255 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) ) )
| ( in @ SY3252 @ SY3254 ) ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3968]) ).
thf(4013,plain,
! [SV780: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV183 @ ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3970]) ).
thf(4014,plain,
! [SV780: $i,SV183: $i > $o,SV849: $i,SV411: $i > $o] :
( ( ( ~ ~ ( ~ ( SV411 @ SV849 )
| ~ ! [SY3266: $i] :
( ~ ( SV411 @ SY3266 )
| ( SV849 = SY3266 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV780
= ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $false )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3971]) ).
thf(4015,plain,
! [SV411: $i > $o,SV828: $i,SV183: $i > $o] :
( ( ( SV183 @ SV828 )
= $false )
| ( ( ~ ! [SY3244: $i] :
( ~ ( SV183 @ SY3244 )
| ( SV828 = SY3244 ) ) )
= $true )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3972]) ).
thf(4016,plain,
! [SV411: $i > $o,SV821: $i,SV183: $i > $o] :
( ( ( ! [SY3237: $i] :
( ~ ( SV183 @ SY3237 )
| ( SV821 = SY3237 ) ) )
= $false )
| ( ( SV183 @ SV821 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3973]) ).
thf(4017,plain,
! [SV411: $i > $o,SV822: $i,SV183: $i > $o] :
( ( ( ! [SY3238: $i] :
( ~ ( SV183 @ SY3238 )
| ( SV822 = SY3238 ) ) )
= $false )
| ( ( SV183 @ SV822 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3974]) ).
thf(4018,plain,
! [SV817: $i,SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ( SV183 @ ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
| ( SV817
= ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) ) )
= $false )
| ( ( SV183 @ SV817 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3975]) ).
thf(4019,plain,
! [SV810: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( SV193 @ ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $true )
| ( ( SV193 @ SV810 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3977]) ).
thf(4020,plain,
! [SV810: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $false )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV810
= ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3978]) ).
thf(4021,plain,
! [SV811: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( SV422 @ ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $true )
| ( ( SV422 @ SV811 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3979]) ).
thf(4022,plain,
! [SV811: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $false )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV811
= ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3980]) ).
thf(4023,plain,
! [SV422: $i > $o,SV846: $i,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ SV846 )
| ~ ! [SY3264: $i] :
( ~ ( SV193 @ SY3264 )
| ( SV846 = SY3264 ) ) ) )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3981]) ).
thf(4024,plain,
! [SV193: $i > $o,SV847: $i,SV422: $i > $o] :
( ( ( ~ ( ~ ( SV422 @ SV847 )
| ~ ! [SY3265: $i] :
( ~ ( SV422 @ SY3265 )
| ( SV847 = SY3265 ) ) ) )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3982]) ).
thf(4025,plain,
! [SV422: $i > $o,SV841: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV841 )
| ~ ! [SY3256: $i] :
( ~ ( SV193 @ SY3256 )
| ( SV841 = SY3256 ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3983]) ).
thf(4026,plain,
! [SV193: $i > $o,SV842: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV842 )
| ~ ! [SY3257: $i] :
( ~ ( SV422 @ SY3257 )
| ( SV842 = SY3257 ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3984]) ).
thf(4027,plain,
! [SV422: $i > $o,SV843: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV843 )
| ~ ! [SY3258: $i] :
( ~ ( SV193 @ SY3258 )
| ( SV843 = SY3258 ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3985]) ).
thf(4028,plain,
! [SV193: $i > $o,SV844: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV844 )
| ~ ! [SY3259: $i] :
( ~ ( SV422 @ SY3259 )
| ( SV844 = SY3259 ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3986]) ).
thf(4029,plain,
! [SV422: $i > $o,SV836: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV836 ) )
= $true )
| ( ( ~ ! [SY3248: $i] :
( ~ ( SV193 @ SY3248 )
| ( SV836 = SY3248 ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3987]) ).
thf(4030,plain,
! [SV193: $i > $o,SV837: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV837 ) )
= $true )
| ( ( ~ ! [SY3249: $i] :
( ~ ( SV422 @ SY3249 )
| ( SV837 = SY3249 ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3988]) ).
thf(4031,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( in @ ( kpair @ ( sK103_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK108_SY3239 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV712 )
= $true )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) @ SV426 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3990]) ).
thf(4032,plain,
! [SV426: $i,SV570: $i,SV712: $i,SV198: $i] :
( ( ( in @ ( sK113_SY3245 @ SV198 @ SV712 @ SV570 @ SV426 ) @ SV426 )
= $true )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV570 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3992]) ).
thf(4033,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK107_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK113_SY3245 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV712 ) )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV570 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3993]) ).
thf(4034,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( in @ ( kpair @ ( sK107_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK113_SY3245 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV570 )
= $false )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV570 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3993]) ).
thf(4035,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( in @ ( kpair @ ( sK104_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK109_SY3240 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV712 )
= $true )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV712 )
= $false )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3995]) ).
thf(4036,plain,
! [SV471: $i,SV773: $i,SV823: $i,SV249: $i > $i > $o] :
( ( ( SV249 @ SV823 @ SV773 )
= $false )
| ( ( in @ SV823 @ SV471 )
= $false )
| ( ( in @ SV773 @ ( sK51_SY2874 @ SV249 @ SV471 ) )
= $true )
| ( ( in @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV471 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3999]) ).
thf(4037,plain,
! [SV471: $i,SV249: $i > $i > $o,SV757: $i,SV838: $i] :
( ( ( ~ ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
| ~ ! [SY3250: $i] :
~ ~ ( ~ ( in @ SY3250 @ SV471 )
| ~ ( SV249 @ SY3250 @ SV838 ) ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4000]) ).
thf(4038,plain,
! [SV757: $i,SV838: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ~ ~ ! [SY3251: $i] :
~ ~ ( ~ ( in @ SY3251 @ SV471 )
| ~ ( SV249 @ SY3251 @ SV838 ) )
| ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4001]) ).
thf(4039,plain,
! [SV471: $i,SV249: $i > $i > $o,SV757: $i,SV830: $i] :
( ( ( ~ ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) ) )
= $true )
| ( ( ~ ! [SY3246: $i] :
~ ~ ( ~ ( in @ SY3246 @ SV471 )
| ~ ( SV249 @ SY3246 @ SV830 ) ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4002]) ).
thf(4040,plain,
! [SV757: $i,SV830: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ~ ~ ! [SY3247: $i] :
~ ~ ( ~ ( in @ SY3247 @ SV471 )
| ~ ( SV249 @ SY3247 @ SV830 ) ) )
= $true )
| ( ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4003]) ).
thf(4041,plain,
! [SV624: $i,SV845: $i,SV44: $i > $o] :
( ( ( SV44 @ SV845 )
= $false )
| ( ( ( sK99_SY1929 @ SV624 @ SV44 )
= SV845 )
= $true )
| ( ( SV44 @ ( sK31_SY3079 @ SV624 @ SV44 ) )
= $true )
| ( ( ( sK31_SY3079 @ SV624 @ SV44 )
= SV624 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4006]) ).
thf(4042,plain,
! [SV147: $i,SV794: $i,SV808: $i] :
( ( ( ~ ( in @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( ~ ( ~ ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
| ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) ) )
| ~ ( ~ ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
| ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) ) ) ) )
= $false )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4009]) ).
thf(4043,plain,
! [SV147: $i,SV833: $i,SV768: $i,SV779: $i,SV848: $i] :
( ( ( ~ ( in @ SV848 @ SV779 ) )
= $true )
| ( ( in @ SV848 @ SV768 )
= $true )
| ( ( in @ SV833 @ SV779 )
= $true )
| ( ( in @ SV833 @ SV768 )
= $false )
| ( ( in @ SV768 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( in @ SV779 @ ( sK3_SY2186 @ SV147 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4010]) ).
thf(4044,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( ! [SY3260: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ SY3260 @ SV747 ) )
| ~ ~ ~ ! [SY3261: $i] :
~ ~ ( ~ ( in @ SY3261 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
| ~ ( in @ SY3261 @ SV747 ) ) )
| ~ ! [SY3262: $i] :
( ~ ( in @ SY3262 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3263: $i] :
( ~ ( in @ SY3263 @ SY3262 )
| ( in @ SY3263 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) ) )
| ( in @ SY3260 @ SY3262 ) ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4011]) ).
thf(4045,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SV747 ) )
| ~ ~ ~ ! [SY3253: $i] :
~ ~ ( ~ ( in @ SY3253 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
| ~ ( in @ SY3253 @ SV747 ) ) )
| ~ ! [SY3268: $i] :
( ~ ( in @ SY3268 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3255: $i] :
( ~ ( in @ SY3255 @ SY3268 )
| ( in @ SY3255 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) ) )
| ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SY3268 ) ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4012]) ).
thf(4046,plain,
! [SV780: $i,SV183: $i > $o,SV850: $i,SV411: $i > $o] :
( ( ( ~ ~ ( ~ ( SV411 @ SV850 )
| ~ ! [SY3270: $i] :
( ~ ( SV411 @ SY3270 )
| ( SV850 = SY3270 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV183 @ ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4013]) ).
thf(4047,plain,
! [SV780: $i,SV183: $i > $o,SV849: $i,SV411: $i > $o] :
( ( ( ~ ( ~ ( SV411 @ SV849 )
| ~ ! [SY3266: $i] :
( ~ ( SV411 @ SY3266 )
| ( SV849 = SY3266 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV780
= ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $false )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4014]) ).
thf(4048,plain,
! [SV411: $i > $o,SV828: $i,SV183: $i > $o] :
( ( ( ! [SY3244: $i] :
( ~ ( SV183 @ SY3244 )
| ( SV828 = SY3244 ) ) )
= $false )
| ( ( SV183 @ SV828 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4015]) ).
thf(4049,plain,
! [SV821: $i,SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ( SV183 @ ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
| ( SV821
= ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) ) )
= $false )
| ( ( SV183 @ SV821 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4016]) ).
thf(4050,plain,
! [SV822: $i,SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ( SV183 @ ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
| ( SV822
= ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) ) )
= $false )
| ( ( SV183 @ SV822 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4017]) ).
thf(4051,plain,
! [SV817: $i,SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ( SV183 @ ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) ) )
= $false )
| ( ( SV183 @ SV817 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4018]) ).
thf(4052,plain,
! [SV183: $i > $o,SV411: $i > $o,SV817: $i] :
( ( ( SV817
= ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $false )
| ( ( SV183 @ SV817 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4018]) ).
thf(4053,plain,
! [SV810: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $false )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV193 @ ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4019]) ).
thf(4054,plain,
! [SV193: $i > $o,SV810: $i,SV422: $i > $o] :
( ( ( ~ ~ ( ~ ( SV422 @ ( sK120_SY2770 @ SV810 @ SV193 @ SV422 ) )
| ~ ! [SY3271: $i] :
( ~ ( SV422 @ SY3271 )
| ( ( sK120_SY2770 @ SV810 @ SV193 @ SV422 )
= SY3271 ) ) ) )
= $false )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV810
= ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4020]) ).
thf(4055,plain,
! [SV811: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $false )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV422 @ ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4021]) ).
thf(4056,plain,
! [SV422: $i > $o,SV811: $i,SV193: $i > $o] :
( ( ( ~ ~ ( ~ ( SV193 @ ( sK121_SY2337 @ SV811 @ SV422 @ SV193 ) )
| ~ ! [SY3272: $i] :
( ~ ( SV193 @ SY3272 )
| ( ( sK121_SY2337 @ SV811 @ SV422 @ SV193 )
= SY3272 ) ) ) )
= $false )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV811
= ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4022]) ).
thf(4057,plain,
! [SV422: $i > $o,SV846: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV846 )
| ~ ! [SY3264: $i] :
( ~ ( SV193 @ SY3264 )
| ( SV846 = SY3264 ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4023]) ).
thf(4058,plain,
! [SV193: $i > $o,SV847: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV847 )
| ~ ! [SY3265: $i] :
( ~ ( SV422 @ SY3265 )
| ( SV847 = SY3265 ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4024]) ).
thf(4059,plain,
! [SV422: $i > $o,SV841: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV841 ) )
= $true )
| ( ( ~ ! [SY3256: $i] :
( ~ ( SV193 @ SY3256 )
| ( SV841 = SY3256 ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4025]) ).
thf(4060,plain,
! [SV193: $i > $o,SV842: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV842 ) )
= $true )
| ( ( ~ ! [SY3257: $i] :
( ~ ( SV422 @ SY3257 )
| ( SV842 = SY3257 ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4026]) ).
thf(4061,plain,
! [SV422: $i > $o,SV843: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV843 ) )
= $true )
| ( ( ~ ! [SY3258: $i] :
( ~ ( SV193 @ SY3258 )
| ( SV843 = SY3258 ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4027]) ).
thf(4062,plain,
! [SV193: $i > $o,SV844: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV844 ) )
= $true )
| ( ( ~ ! [SY3259: $i] :
( ~ ( SV422 @ SY3259 )
| ( SV844 = SY3259 ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4028]) ).
thf(4063,plain,
! [SV422: $i > $o,SV836: $i,SV193: $i > $o] :
( ( ( SV193 @ SV836 )
= $false )
| ( ( ~ ! [SY3248: $i] :
( ~ ( SV193 @ SY3248 )
| ( SV836 = SY3248 ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4029]) ).
thf(4064,plain,
! [SV193: $i > $o,SV837: $i,SV422: $i > $o] :
( ( ( SV422 @ SV837 )
= $false )
| ( ( ~ ! [SY3249: $i] :
( ~ ( SV422 @ SY3249 )
| ( SV837 = SY3249 ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4030]) ).
thf(4065,plain,
! [SV198: $i,SV426: $i,SV712: $i,SV570: $i] :
( ( ( in @ ( kpair @ ( sK107_SY3153 @ SV570 @ SV712 @ SV426 @ SV198 ) @ ( sK113_SY3245 @ SV198 @ SV712 @ SV570 @ SV426 ) ) @ SV712 )
= $true )
| ( ( SV570 = SV712 )
= $true )
| ( ( in @ ( kpair @ ( sK70_SY3151 @ SV712 @ SV570 @ SV426 @ SV198 ) @ ( sK77_SY3201 @ SV198 @ SV570 @ SV712 @ SV426 ) ) @ SV570 )
= $true )
| ( ( subset @ SV712 @ ( cartprod @ SV198 @ SV426 ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV198 @ SV426 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4033]) ).
thf(4066,plain,
! [SV471: $i,SV249: $i > $i > $o,SV757: $i,SV838: $i] :
( ( ( ~ ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) ) )
= $true )
| ( ( ~ ! [SY3250: $i] :
~ ~ ( ~ ( in @ SY3250 @ SV471 )
| ~ ( SV249 @ SY3250 @ SV838 ) ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4037]) ).
thf(4067,plain,
! [SV757: $i,SV838: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ~ ~ ! [SY3251: $i] :
~ ~ ( ~ ( in @ SY3251 @ SV471 )
| ~ ( SV249 @ SY3251 @ SV838 ) ) )
= $true )
| ( ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4038]) ).
thf(4068,plain,
! [SV471: $i,SV249: $i > $i > $o,SV757: $i,SV830: $i] :
( ( ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $false )
| ( ( ~ ! [SY3246: $i] :
~ ~ ( ~ ( in @ SY3246 @ SV471 )
| ~ ( SV249 @ SY3246 @ SV830 ) ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4039]) ).
thf(4069,plain,
! [SV757: $i,SV830: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ~ ! [SY3247: $i] :
~ ~ ( ~ ( in @ SY3247 @ SV471 )
| ~ ( SV249 @ SY3247 @ SV830 ) ) )
= $false )
| ( ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4040]) ).
thf(4070,plain,
! [SV147: $i,SV794: $i,SV808: $i] :
( ( ( ~ ( in @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) ) )
= $false )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4042]) ).
thf(4071,plain,
! [SV147: $i,SV808: $i,SV794: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
| ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) ) )
| ~ ( ~ ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
| ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) ) ) ) )
= $false )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4042]) ).
thf(4072,plain,
! [SV147: $i,SV833: $i,SV768: $i,SV779: $i,SV848: $i] :
( ( ( in @ SV848 @ SV779 )
= $false )
| ( ( in @ SV848 @ SV768 )
= $true )
| ( ( in @ SV833 @ SV779 )
= $true )
| ( ( in @ SV833 @ SV768 )
= $false )
| ( ( in @ SV768 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( in @ SV779 @ ( sK3_SY2186 @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4043]) ).
thf(4073,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SV747 ) )
| ~ ~ ~ ! [SY3261: $i] :
~ ~ ( ~ ( in @ SY3261 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
| ~ ( in @ SY3261 @ SV747 ) ) )
| ~ ! [SY3274: $i] :
( ~ ( in @ SY3274 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3263: $i] :
( ~ ( in @ SY3263 @ SY3274 )
| ( in @ SY3263 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) ) )
| ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SY3274 ) ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4044]) ).
thf(4074,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SV747 ) )
| ~ ~ ~ ! [SY3253: $i] :
~ ~ ( ~ ( in @ SY3253 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
| ~ ( in @ SY3253 @ SV747 ) ) )
| ~ ! [SY3268: $i] :
( ~ ( in @ SY3268 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3255: $i] :
( ~ ( in @ SY3255 @ SY3268 )
| ( in @ SY3255 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) ) )
| ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SY3268 ) ) ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4045]) ).
thf(4075,plain,
! [SV780: $i,SV183: $i > $o,SV850: $i,SV411: $i > $o] :
( ( ( ~ ( ~ ( SV411 @ SV850 )
| ~ ! [SY3270: $i] :
( ~ ( SV411 @ SY3270 )
| ( SV850 = SY3270 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV183 @ ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4046]) ).
thf(4076,plain,
! [SV780: $i,SV183: $i > $o,SV849: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV849 )
| ~ ! [SY3266: $i] :
( ~ ( SV411 @ SY3266 )
| ( SV849 = SY3266 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV780
= ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $false )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4047]) ).
thf(4077,plain,
! [SV828: $i,SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ( SV183 @ ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
| ( SV828
= ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) ) )
= $false )
| ( ( SV183 @ SV828 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4048]) ).
thf(4078,plain,
! [SV821: $i,SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ( SV183 @ ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) ) )
= $false )
| ( ( SV183 @ SV821 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4049]) ).
thf(4079,plain,
! [SV183: $i > $o,SV411: $i > $o,SV821: $i] :
( ( ( SV821
= ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $false )
| ( ( SV183 @ SV821 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4049]) ).
thf(4080,plain,
! [SV822: $i,SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ( SV183 @ ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) ) )
= $false )
| ( ( SV183 @ SV822 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4050]) ).
thf(4081,plain,
! [SV183: $i > $o,SV411: $i > $o,SV822: $i] :
( ( ( SV822
= ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $false )
| ( ( SV183 @ SV822 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4050]) ).
thf(4082,plain,
! [SV817: $i,SV411: $i > $o,SV183: $i > $o] :
( ( ( SV183 @ ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4051]) ).
thf(4083,plain,
! [SV817: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV817
= ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4052]) ).
thf(4084,plain,
! [SV193: $i > $o,SV810: $i,SV422: $i > $o] :
( ( ( ~ ~ ( ~ ( SV422 @ ( sK124_SY2770 @ SV810 @ SV193 @ SV422 ) )
| ~ ! [SY3276: $i] :
( ~ ( SV422 @ SY3276 )
| ( ( sK124_SY2770 @ SV810 @ SV193 @ SV422 )
= SY3276 ) ) ) )
= $false )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV193 @ ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4053]) ).
thf(4085,plain,
! [SV193: $i > $o,SV810: $i,SV422: $i > $o] :
( ( ( ~ ( ~ ( SV422 @ ( sK120_SY2770 @ SV810 @ SV193 @ SV422 ) )
| ~ ! [SY3271: $i] :
( ~ ( SV422 @ SY3271 )
| ( ( sK120_SY2770 @ SV810 @ SV193 @ SV422 )
= SY3271 ) ) ) )
= $true )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV810
= ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4054]) ).
thf(4086,plain,
! [SV422: $i > $o,SV811: $i,SV193: $i > $o] :
( ( ( ~ ~ ( ~ ( SV193 @ ( sK125_SY2337 @ SV811 @ SV422 @ SV193 ) )
| ~ ! [SY3277: $i] :
( ~ ( SV193 @ SY3277 )
| ( ( sK125_SY2337 @ SV811 @ SV422 @ SV193 )
= SY3277 ) ) ) )
= $false )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV422 @ ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4055]) ).
thf(4087,plain,
! [SV422: $i > $o,SV811: $i,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ ( sK121_SY2337 @ SV811 @ SV422 @ SV193 ) )
| ~ ! [SY3272: $i] :
( ~ ( SV193 @ SY3272 )
| ( ( sK121_SY2337 @ SV811 @ SV422 @ SV193 )
= SY3272 ) ) ) )
= $true )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV811
= ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4056]) ).
thf(4088,plain,
! [SV422: $i > $o,SV846: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV846 ) )
= $true )
| ( ( ~ ! [SY3264: $i] :
( ~ ( SV193 @ SY3264 )
| ( SV846 = SY3264 ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4057]) ).
thf(4089,plain,
! [SV193: $i > $o,SV847: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV847 ) )
= $true )
| ( ( ~ ! [SY3265: $i] :
( ~ ( SV422 @ SY3265 )
| ( SV847 = SY3265 ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4058]) ).
thf(4090,plain,
! [SV422: $i > $o,SV841: $i,SV193: $i > $o] :
( ( ( SV193 @ SV841 )
= $false )
| ( ( ~ ! [SY3256: $i] :
( ~ ( SV193 @ SY3256 )
| ( SV841 = SY3256 ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4059]) ).
thf(4091,plain,
! [SV193: $i > $o,SV842: $i,SV422: $i > $o] :
( ( ( SV422 @ SV842 )
= $false )
| ( ( ~ ! [SY3257: $i] :
( ~ ( SV422 @ SY3257 )
| ( SV842 = SY3257 ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4060]) ).
thf(4092,plain,
! [SV422: $i > $o,SV843: $i,SV193: $i > $o] :
( ( ( SV193 @ SV843 )
= $false )
| ( ( ~ ! [SY3258: $i] :
( ~ ( SV193 @ SY3258 )
| ( SV843 = SY3258 ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4061]) ).
thf(4093,plain,
! [SV193: $i > $o,SV844: $i,SV422: $i > $o] :
( ( ( SV422 @ SV844 )
= $false )
| ( ( ~ ! [SY3259: $i] :
( ~ ( SV422 @ SY3259 )
| ( SV844 = SY3259 ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4062]) ).
thf(4094,plain,
! [SV422: $i > $o,SV836: $i,SV193: $i > $o] :
( ( ( ! [SY3248: $i] :
( ~ ( SV193 @ SY3248 )
| ( SV836 = SY3248 ) ) )
= $false )
| ( ( SV193 @ SV836 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4063]) ).
thf(4095,plain,
! [SV193: $i > $o,SV837: $i,SV422: $i > $o] :
( ( ( ! [SY3249: $i] :
( ~ ( SV422 @ SY3249 )
| ( SV837 = SY3249 ) ) )
= $false )
| ( ( SV422 @ SV837 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4064]) ).
thf(4096,plain,
! [SV471: $i,SV249: $i > $i > $o,SV757: $i,SV838: $i] :
( ( ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $false )
| ( ( ~ ! [SY3250: $i] :
~ ~ ( ~ ( in @ SY3250 @ SV471 )
| ~ ( SV249 @ SY3250 @ SV838 ) ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4066]) ).
thf(4097,plain,
! [SV757: $i,SV838: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ~ ! [SY3251: $i] :
~ ~ ( ~ ( in @ SY3251 @ SV471 )
| ~ ( SV249 @ SY3251 @ SV838 ) ) )
= $false )
| ( ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4067]) ).
thf(4098,plain,
! [SV757: $i,SV830: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ! [SY3246: $i] :
~ ~ ( ~ ( in @ SY3246 @ SV471 )
| ~ ( SV249 @ SY3246 @ SV830 ) ) )
= $false )
| ( ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4068]) ).
thf(4099,plain,
! [SV757: $i,SV830: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ! [SY3247: $i] :
~ ~ ( ~ ( in @ SY3247 @ SV471 )
| ~ ( SV249 @ SY3247 @ SV830 ) ) )
= $true )
| ( ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4069]) ).
thf(4100,plain,
! [SV147: $i,SV794: $i,SV808: $i] :
( ( ( in @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
= $true )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4070]) ).
thf(4101,plain,
! [SV147: $i,SV808: $i,SV794: $i] :
( ( ( ~ ( ~ ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
| ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) ) )
| ~ ( ~ ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
| ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) ) ) )
= $true )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4071]) ).
thf(4102,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SV747 ) )
| ~ ~ ~ ! [SY3261: $i] :
~ ~ ( ~ ( in @ SY3261 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
| ~ ( in @ SY3261 @ SV747 ) ) )
| ~ ! [SY3274: $i] :
( ~ ( in @ SY3274 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3263: $i] :
( ~ ( in @ SY3263 @ SY3274 )
| ( in @ SY3263 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) ) )
| ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SY3274 ) ) ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4073]) ).
thf(4103,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SV747 ) )
| ~ ~ ~ ! [SY3253: $i] :
~ ~ ( ~ ( in @ SY3253 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
| ~ ( in @ SY3253 @ SV747 ) ) )
| ~ ! [SY3268: $i] :
( ~ ( in @ SY3268 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3255: $i] :
( ~ ( in @ SY3255 @ SY3268 )
| ( in @ SY3255 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) ) )
| ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SY3268 ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4074]) ).
thf(4104,plain,
! [SV780: $i,SV183: $i > $o,SV850: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV850 )
| ~ ! [SY3270: $i] :
( ~ ( SV411 @ SY3270 )
| ( SV850 = SY3270 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV183 @ ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4075]) ).
thf(4105,plain,
! [SV780: $i,SV183: $i > $o,SV849: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV849 ) )
= $true )
| ( ( ~ ! [SY3266: $i] :
( ~ ( SV411 @ SY3266 )
| ( SV849 = SY3266 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV780
= ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $false )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4076]) ).
thf(4106,plain,
! [SV828: $i,SV411: $i > $o,SV183: $i > $o] :
( ( ( ~ ( SV183 @ ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) ) )
= $false )
| ( ( SV183 @ SV828 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4077]) ).
thf(4107,plain,
! [SV183: $i > $o,SV411: $i > $o,SV828: $i] :
( ( ( SV828
= ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $false )
| ( ( SV183 @ SV828 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4077]) ).
thf(4108,plain,
! [SV821: $i,SV411: $i > $o,SV183: $i > $o] :
( ( ( SV183 @ ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4078]) ).
thf(4109,plain,
! [SV821: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV821
= ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4079]) ).
thf(4110,plain,
! [SV822: $i,SV411: $i > $o,SV183: $i > $o] :
( ( ( SV183 @ ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4080]) ).
thf(4111,plain,
! [SV822: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV822
= ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4081]) ).
thf(4112,plain,
! [SV817: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV183 @ ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4082]) ).
thf(4113,plain,
! [SV817: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV817
= ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4083]) ).
thf(4114,plain,
! [SV193: $i > $o,SV810: $i,SV422: $i > $o] :
( ( ( ~ ( ~ ( SV422 @ ( sK124_SY2770 @ SV810 @ SV193 @ SV422 ) )
| ~ ! [SY3276: $i] :
( ~ ( SV422 @ SY3276 )
| ( ( sK124_SY2770 @ SV810 @ SV193 @ SV422 )
= SY3276 ) ) ) )
= $true )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV193 @ ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4084]) ).
thf(4115,plain,
! [SV193: $i > $o,SV810: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK120_SY2770 @ SV810 @ SV193 @ SV422 ) )
| ~ ! [SY3271: $i] :
( ~ ( SV422 @ SY3271 )
| ( ( sK120_SY2770 @ SV810 @ SV193 @ SV422 )
= SY3271 ) ) )
= $false )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV810
= ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4085]) ).
thf(4116,plain,
! [SV422: $i > $o,SV811: $i,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ ( sK125_SY2337 @ SV811 @ SV422 @ SV193 ) )
| ~ ! [SY3277: $i] :
( ~ ( SV193 @ SY3277 )
| ( ( sK125_SY2337 @ SV811 @ SV422 @ SV193 )
= SY3277 ) ) ) )
= $true )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV422 @ ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4086]) ).
thf(4117,plain,
! [SV422: $i > $o,SV811: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK121_SY2337 @ SV811 @ SV422 @ SV193 ) )
| ~ ! [SY3272: $i] :
( ~ ( SV193 @ SY3272 )
| ( ( sK121_SY2337 @ SV811 @ SV422 @ SV193 )
= SY3272 ) ) )
= $false )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV811
= ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4087]) ).
thf(4118,plain,
! [SV422: $i > $o,SV846: $i,SV193: $i > $o] :
( ( ( SV193 @ SV846 )
= $false )
| ( ( ~ ! [SY3264: $i] :
( ~ ( SV193 @ SY3264 )
| ( SV846 = SY3264 ) ) )
= $true )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4088]) ).
thf(4119,plain,
! [SV193: $i > $o,SV847: $i,SV422: $i > $o] :
( ( ( SV422 @ SV847 )
= $false )
| ( ( ~ ! [SY3265: $i] :
( ~ ( SV422 @ SY3265 )
| ( SV847 = SY3265 ) ) )
= $true )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4089]) ).
thf(4120,plain,
! [SV422: $i > $o,SV841: $i,SV193: $i > $o] :
( ( ( ! [SY3256: $i] :
( ~ ( SV193 @ SY3256 )
| ( SV841 = SY3256 ) ) )
= $false )
| ( ( SV193 @ SV841 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4090]) ).
thf(4121,plain,
! [SV193: $i > $o,SV842: $i,SV422: $i > $o] :
( ( ( ! [SY3257: $i] :
( ~ ( SV422 @ SY3257 )
| ( SV842 = SY3257 ) ) )
= $false )
| ( ( SV422 @ SV842 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4091]) ).
thf(4122,plain,
! [SV422: $i > $o,SV843: $i,SV193: $i > $o] :
( ( ( ! [SY3258: $i] :
( ~ ( SV193 @ SY3258 )
| ( SV843 = SY3258 ) ) )
= $false )
| ( ( SV193 @ SV843 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4092]) ).
thf(4123,plain,
! [SV193: $i > $o,SV844: $i,SV422: $i > $o] :
( ( ( ! [SY3259: $i] :
( ~ ( SV422 @ SY3259 )
| ( SV844 = SY3259 ) ) )
= $false )
| ( ( SV422 @ SV844 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4093]) ).
thf(4124,plain,
! [SV836: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
| ( SV836
= ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) ) )
= $false )
| ( ( SV193 @ SV836 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4094]) ).
thf(4125,plain,
! [SV837: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
| ( SV837
= ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) ) )
= $false )
| ( ( SV422 @ SV837 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4095]) ).
thf(4126,plain,
! [SV757: $i,SV838: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ! [SY3250: $i] :
~ ~ ( ~ ( in @ SY3250 @ SV471 )
| ~ ( SV249 @ SY3250 @ SV838 ) ) )
= $false )
| ( ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4096]) ).
thf(4127,plain,
! [SV757: $i,SV838: $i,SV249: $i > $i > $o,SV471: $i] :
( ( ( ! [SY3251: $i] :
~ ~ ( ~ ( in @ SY3251 @ SV471 )
| ~ ( SV249 @ SY3251 @ SV838 ) ) )
= $true )
| ( ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4097]) ).
thf(4128,plain,
! [SV471: $i,SV249: $i > $i > $o,SV830: $i,SV757: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK128_SY3246 @ SV757 @ SV830 @ SV249 @ SV471 ) @ SV471 )
| ~ ( SV249 @ ( sK128_SY3246 @ SV757 @ SV830 @ SV249 @ SV471 ) @ SV830 ) ) )
= $false )
| ( ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4098]) ).
thf(4129,plain,
! [SV757: $i,SV830: $i,SV249: $i > $i > $o,SV471: $i,SV851: $i] :
( ( ( ~ ~ ( ~ ( in @ SV851 @ SV471 )
| ~ ( SV249 @ SV851 @ SV830 ) ) )
= $true )
| ( ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4099]) ).
thf(4130,plain,
! [SV147: $i,SV808: $i,SV794: $i] :
( ( ( ~ ( ~ ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
| ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
| ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) ) ) )
= $true )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4101]) ).
thf(4131,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SV747 ) )
| ~ ~ ~ ! [SY3261: $i] :
~ ~ ( ~ ( in @ SY3261 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
| ~ ( in @ SY3261 @ SV747 ) ) )
| ~ ! [SY3274: $i] :
( ~ ( in @ SY3274 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3263: $i] :
( ~ ( in @ SY3263 @ SY3274 )
| ( in @ SY3263 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) ) )
| ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SY3274 ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4102]) ).
thf(4132,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SV747 ) )
| ~ ~ ~ ! [SY3253: $i] :
~ ~ ( ~ ( in @ SY3253 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
| ~ ( in @ SY3253 @ SV747 ) ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4103]) ).
thf(4133,plain,
! [SV747: $i,SV820: $i,SV147: $i] :
( ( ( ~ ! [SY3268: $i] :
( ~ ( in @ SY3268 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3255: $i] :
( ~ ( in @ SY3255 @ SY3268 )
| ( in @ SY3255 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) ) )
| ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SY3268 ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4103]) ).
thf(4134,plain,
! [SV780: $i,SV183: $i > $o,SV850: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV850 ) )
= $true )
| ( ( ~ ! [SY3270: $i] :
( ~ ( SV411 @ SY3270 )
| ( SV850 = SY3270 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV183 @ ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4104]) ).
thf(4135,plain,
! [SV780: $i,SV183: $i > $o,SV849: $i,SV411: $i > $o] :
( ( ( SV411 @ SV849 )
= $false )
| ( ( ~ ! [SY3266: $i] :
( ~ ( SV411 @ SY3266 )
| ( SV849 = SY3266 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV780
= ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $false )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4105]) ).
thf(4136,plain,
! [SV828: $i,SV411: $i > $o,SV183: $i > $o] :
( ( ( SV183 @ ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) )
| ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4106]) ).
thf(4137,plain,
! [SV828: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV828
= ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4107]) ).
thf(4138,plain,
! [SV821: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV183 @ ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4108]) ).
thf(4139,plain,
! [SV821: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV821
= ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4109]) ).
thf(4140,plain,
! [SV822: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV183 @ ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4110]) ).
thf(4141,plain,
! [SV822: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV822
= ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4111]) ).
thf(4142,plain,
! [SV817: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV183 @ ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4112]) ).
thf(4143,plain,
! [SV817: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV817
= ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4113]) ).
thf(4144,plain,
! [SV193: $i > $o,SV810: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK124_SY2770 @ SV810 @ SV193 @ SV422 ) )
| ~ ! [SY3276: $i] :
( ~ ( SV422 @ SY3276 )
| ( ( sK124_SY2770 @ SV810 @ SV193 @ SV422 )
= SY3276 ) ) )
= $false )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV193 @ ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4114]) ).
thf(4145,plain,
! [SV193: $i > $o,SV810: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK120_SY2770 @ SV810 @ SV193 @ SV422 ) ) )
= $false )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV810
= ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4115]) ).
thf(4146,plain,
! [SV193: $i > $o,SV810: $i,SV422: $i > $o] :
( ( ( ~ ! [SY3271: $i] :
( ~ ( SV422 @ SY3271 )
| ( ( sK120_SY2770 @ SV810 @ SV193 @ SV422 )
= SY3271 ) ) )
= $false )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV810
= ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4115]) ).
thf(4147,plain,
! [SV422: $i > $o,SV811: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK125_SY2337 @ SV811 @ SV422 @ SV193 ) )
| ~ ! [SY3277: $i] :
( ~ ( SV193 @ SY3277 )
| ( ( sK125_SY2337 @ SV811 @ SV422 @ SV193 )
= SY3277 ) ) )
= $false )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV422 @ ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4116]) ).
thf(4148,plain,
! [SV422: $i > $o,SV811: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK121_SY2337 @ SV811 @ SV422 @ SV193 ) ) )
= $false )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV811
= ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4117]) ).
thf(4149,plain,
! [SV422: $i > $o,SV811: $i,SV193: $i > $o] :
( ( ( ~ ! [SY3272: $i] :
( ~ ( SV193 @ SY3272 )
| ( ( sK121_SY2337 @ SV811 @ SV422 @ SV193 )
= SY3272 ) ) )
= $false )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV811
= ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4117]) ).
thf(4150,plain,
! [SV422: $i > $o,SV846: $i,SV193: $i > $o] :
( ( ( ! [SY3264: $i] :
( ~ ( SV193 @ SY3264 )
| ( SV846 = SY3264 ) ) )
= $false )
| ( ( SV193 @ SV846 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4118]) ).
thf(4151,plain,
! [SV193: $i > $o,SV847: $i,SV422: $i > $o] :
( ( ( ! [SY3265: $i] :
( ~ ( SV422 @ SY3265 )
| ( SV847 = SY3265 ) ) )
= $false )
| ( ( SV422 @ SV847 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4119]) ).
thf(4152,plain,
! [SV841: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
| ( SV841
= ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) ) )
= $false )
| ( ( SV193 @ SV841 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4120]) ).
thf(4153,plain,
! [SV842: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
| ( SV842
= ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) ) )
= $false )
| ( ( SV422 @ SV842 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4121]) ).
thf(4154,plain,
! [SV843: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
| ( SV843
= ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) ) )
= $false )
| ( ( SV193 @ SV843 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4122]) ).
thf(4155,plain,
! [SV844: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
| ( SV844
= ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) ) )
= $false )
| ( ( SV422 @ SV844 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4123]) ).
thf(4156,plain,
! [SV836: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) ) )
= $false )
| ( ( SV193 @ SV836 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4124]) ).
thf(4157,plain,
! [SV193: $i > $o,SV422: $i > $o,SV836: $i] :
( ( ( SV836
= ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $false )
| ( ( SV193 @ SV836 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4124]) ).
thf(4158,plain,
! [SV837: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) ) )
= $false )
| ( ( SV422 @ SV837 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4125]) ).
thf(4159,plain,
! [SV422: $i > $o,SV193: $i > $o,SV837: $i] :
( ( ( SV837
= ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $false )
| ( ( SV422 @ SV837 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4125]) ).
thf(4160,plain,
! [SV471: $i,SV249: $i > $i > $o,SV838: $i,SV757: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK133_SY3250 @ SV757 @ SV838 @ SV249 @ SV471 ) @ SV471 )
| ~ ( SV249 @ ( sK133_SY3250 @ SV757 @ SV838 @ SV249 @ SV471 ) @ SV838 ) ) )
= $false )
| ( ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4126]) ).
thf(4161,plain,
! [SV757: $i,SV838: $i,SV249: $i > $i > $o,SV471: $i,SV852: $i] :
( ( ( ~ ~ ( ~ ( in @ SV852 @ SV471 )
| ~ ( SV249 @ SV852 @ SV838 ) ) )
= $true )
| ( ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4127]) ).
thf(4162,plain,
! [SV471: $i,SV249: $i > $i > $o,SV830: $i,SV757: $i] :
( ( ( ~ ( ~ ( in @ ( sK128_SY3246 @ SV757 @ SV830 @ SV249 @ SV471 ) @ SV471 )
| ~ ( SV249 @ ( sK128_SY3246 @ SV757 @ SV830 @ SV249 @ SV471 ) @ SV830 ) ) )
= $true )
| ( ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4128]) ).
thf(4163,plain,
! [SV757: $i,SV830: $i,SV249: $i > $i > $o,SV471: $i,SV851: $i] :
( ( ( ~ ( ~ ( in @ SV851 @ SV471 )
| ~ ( SV249 @ SV851 @ SV830 ) ) )
= $false )
| ( ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4129]) ).
thf(4164,plain,
! [SV147: $i,SV808: $i,SV794: $i] :
( ( ( ~ ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
| ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
| ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) ) ) )
= $true )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4130]) ).
thf(4165,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SV747 ) )
| ~ ~ ~ ! [SY3261: $i] :
~ ~ ( ~ ( in @ SY3261 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
| ~ ( in @ SY3261 @ SV747 ) ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4131]) ).
thf(4166,plain,
! [SV747: $i,SV825: $i,SV147: $i] :
( ( ( ~ ! [SY3274: $i] :
( ~ ( in @ SY3274 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3263: $i] :
( ~ ( in @ SY3263 @ SY3274 )
| ( in @ SY3263 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) ) )
| ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SY3274 ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4131]) ).
thf(4167,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SV747 ) )
| ~ ~ ~ ! [SY3253: $i] :
~ ~ ( ~ ( in @ SY3253 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
| ~ ( in @ SY3253 @ SV747 ) ) ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4132]) ).
thf(4168,plain,
! [SV747: $i,SV820: $i,SV147: $i] :
( ( ( ! [SY3268: $i] :
( ~ ( in @ SY3268 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3255: $i] :
( ~ ( in @ SY3255 @ SY3268 )
| ( in @ SY3255 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) ) )
| ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SY3268 ) ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4133]) ).
thf(4169,plain,
! [SV780: $i,SV183: $i > $o,SV850: $i,SV411: $i > $o] :
( ( ( SV411 @ SV850 )
= $false )
| ( ( ~ ! [SY3270: $i] :
( ~ ( SV411 @ SY3270 )
| ( SV850 = SY3270 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV183 @ ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4134]) ).
thf(4170,plain,
! [SV780: $i,SV183: $i > $o,SV849: $i,SV411: $i > $o] :
( ( ( ! [SY3266: $i] :
( ~ ( SV411 @ SY3266 )
| ( SV849 = SY3266 ) ) )
= $false )
| ( ( SV411 @ SV849 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV780
= ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $false )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4135]) ).
thf(4171,plain,
! [SV828: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV183 @ ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4136]) ).
thf(4172,plain,
! [SV828: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV828
= ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4137]) ).
thf(4173,plain,
! [SV821: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV183 @ ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4138]) ).
thf(4174,plain,
! [SV821: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV821
= ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4139]) ).
thf(4175,plain,
! [SV822: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV183 @ ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4140]) ).
thf(4176,plain,
! [SV822: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV822
= ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4141]) ).
thf(4177,plain,
! [SV817: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV183 @ ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4142]) ).
thf(4178,plain,
! [SV817: $i,SV183: $i > $o,SV853: $i,SV411: $i > $o] :
( ( ( ~ ~ ( ~ ( SV411 @ SV853 )
| ~ ! [SY3278: $i] :
( ~ ( SV411 @ SY3278 )
| ( SV853 = SY3278 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV817
= ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4143]) ).
thf(4179,plain,
! [SV193: $i > $o,SV810: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK124_SY2770 @ SV810 @ SV193 @ SV422 ) ) )
= $false )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV193 @ ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4144]) ).
thf(4180,plain,
! [SV193: $i > $o,SV810: $i,SV422: $i > $o] :
( ( ( ~ ! [SY3276: $i] :
( ~ ( SV422 @ SY3276 )
| ( ( sK124_SY2770 @ SV810 @ SV193 @ SV422 )
= SY3276 ) ) )
= $false )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV193 @ ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4144]) ).
thf(4181,plain,
! [SV193: $i > $o,SV810: $i,SV422: $i > $o] :
( ( ( SV422 @ ( sK120_SY2770 @ SV810 @ SV193 @ SV422 ) )
= $true )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV810
= ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4145]) ).
thf(4182,plain,
! [SV193: $i > $o,SV810: $i,SV422: $i > $o] :
( ( ( ! [SY3271: $i] :
( ~ ( SV422 @ SY3271 )
| ( ( sK120_SY2770 @ SV810 @ SV193 @ SV422 )
= SY3271 ) ) )
= $true )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV810
= ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4146]) ).
thf(4183,plain,
! [SV422: $i > $o,SV811: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK125_SY2337 @ SV811 @ SV422 @ SV193 ) ) )
= $false )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV422 @ ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4147]) ).
thf(4184,plain,
! [SV422: $i > $o,SV811: $i,SV193: $i > $o] :
( ( ( ~ ! [SY3277: $i] :
( ~ ( SV193 @ SY3277 )
| ( ( sK125_SY2337 @ SV811 @ SV422 @ SV193 )
= SY3277 ) ) )
= $false )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV422 @ ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4147]) ).
thf(4185,plain,
! [SV422: $i > $o,SV811: $i,SV193: $i > $o] :
( ( ( SV193 @ ( sK121_SY2337 @ SV811 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV811
= ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4148]) ).
thf(4186,plain,
! [SV422: $i > $o,SV811: $i,SV193: $i > $o] :
( ( ( ! [SY3272: $i] :
( ~ ( SV193 @ SY3272 )
| ( ( sK121_SY2337 @ SV811 @ SV422 @ SV193 )
= SY3272 ) ) )
= $true )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV811
= ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4149]) ).
thf(4187,plain,
! [SV846: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
| ( SV846
= ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) ) )
= $false )
| ( ( SV193 @ SV846 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4150]) ).
thf(4188,plain,
! [SV847: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
| ( SV847
= ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) ) )
= $false )
| ( ( SV422 @ SV847 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4151]) ).
thf(4189,plain,
! [SV841: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) ) )
= $false )
| ( ( SV193 @ SV841 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4152]) ).
thf(4190,plain,
! [SV193: $i > $o,SV422: $i > $o,SV841: $i] :
( ( ( SV841
= ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $false )
| ( ( SV193 @ SV841 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4152]) ).
thf(4191,plain,
! [SV842: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) ) )
= $false )
| ( ( SV422 @ SV842 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4153]) ).
thf(4192,plain,
! [SV422: $i > $o,SV193: $i > $o,SV842: $i] :
( ( ( SV842
= ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $false )
| ( ( SV422 @ SV842 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4153]) ).
thf(4193,plain,
! [SV843: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) ) )
= $false )
| ( ( SV193 @ SV843 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4154]) ).
thf(4194,plain,
! [SV193: $i > $o,SV422: $i > $o,SV843: $i] :
( ( ( SV843
= ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $false )
| ( ( SV193 @ SV843 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4154]) ).
thf(4195,plain,
! [SV844: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) ) )
= $false )
| ( ( SV422 @ SV844 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4155]) ).
thf(4196,plain,
! [SV422: $i > $o,SV193: $i > $o,SV844: $i] :
( ( ( SV844
= ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $false )
| ( ( SV422 @ SV844 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4155]) ).
thf(4197,plain,
! [SV836: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( SV193 @ ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $true )
| ( ( SV193 @ SV836 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4156]) ).
thf(4198,plain,
! [SV836: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $false )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV836
= ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4157]) ).
thf(4199,plain,
! [SV837: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( SV422 @ ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $true )
| ( ( SV422 @ SV837 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4158]) ).
thf(4200,plain,
! [SV837: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $false )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV837
= ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4159]) ).
thf(4201,plain,
! [SV471: $i,SV249: $i > $i > $o,SV838: $i,SV757: $i] :
( ( ( ~ ( ~ ( in @ ( sK133_SY3250 @ SV757 @ SV838 @ SV249 @ SV471 ) @ SV471 )
| ~ ( SV249 @ ( sK133_SY3250 @ SV757 @ SV838 @ SV249 @ SV471 ) @ SV838 ) ) )
= $true )
| ( ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4160]) ).
thf(4202,plain,
! [SV757: $i,SV838: $i,SV249: $i > $i > $o,SV471: $i,SV852: $i] :
( ( ( ~ ( ~ ( in @ SV852 @ SV471 )
| ~ ( SV249 @ SV852 @ SV838 ) ) )
= $false )
| ( ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4161]) ).
thf(4203,plain,
! [SV471: $i,SV249: $i > $i > $o,SV830: $i,SV757: $i] :
( ( ( ~ ( in @ ( sK128_SY3246 @ SV757 @ SV830 @ SV249 @ SV471 ) @ SV471 )
| ~ ( SV249 @ ( sK128_SY3246 @ SV757 @ SV830 @ SV249 @ SV471 ) @ SV830 ) )
= $false )
| ( ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4162]) ).
thf(4204,plain,
! [SV757: $i,SV830: $i,SV249: $i > $i > $o,SV471: $i,SV851: $i] :
( ( ( ~ ( in @ SV851 @ SV471 )
| ~ ( SV249 @ SV851 @ SV830 ) )
= $true )
| ( ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4163]) ).
thf(4205,plain,
! [SV147: $i,SV808: $i,SV794: $i] :
( ( ( ~ ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
| ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) ) ) )
= $true )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4164]) ).
thf(4206,plain,
! [SV147: $i,SV794: $i,SV808: $i] :
( ( ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
| ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) ) ) )
= $true )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4164]) ).
thf(4207,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SV747 ) )
| ~ ~ ~ ! [SY3261: $i] :
~ ~ ( ~ ( in @ SY3261 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
| ~ ( in @ SY3261 @ SV747 ) ) ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4165]) ).
thf(4208,plain,
! [SV747: $i,SV825: $i,SV147: $i] :
( ( ( ! [SY3274: $i] :
( ~ ( in @ SY3274 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3263: $i] :
( ~ ( in @ SY3263 @ SY3274 )
| ( in @ SY3263 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) ) )
| ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SY3274 ) ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4166]) ).
thf(4209,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SV747 ) )
| ~ ~ ~ ! [SY3253: $i] :
~ ~ ( ~ ( in @ SY3253 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
| ~ ( in @ SY3253 @ SV747 ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4167]) ).
thf(4210,plain,
! [SV747: $i,SV820: $i,SV147: $i,SV854: $i] :
( ( ( ~ ( in @ SV854 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3279: $i] :
( ~ ( in @ SY3279 @ SV854 )
| ( in @ SY3279 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) ) )
| ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SV854 ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4168]) ).
thf(4211,plain,
! [SV780: $i,SV183: $i > $o,SV850: $i,SV411: $i > $o] :
( ( ( ! [SY3270: $i] :
( ~ ( SV411 @ SY3270 )
| ( SV850 = SY3270 ) ) )
= $false )
| ( ( SV411 @ SV850 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV183 @ ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4169]) ).
thf(4212,plain,
! [SV849: $i,SV183: $i > $o,SV780: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK136_SY3266 @ SV780 @ SV183 @ SV849 @ SV411 ) )
| ( SV849
= ( sK136_SY3266 @ SV780 @ SV183 @ SV849 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV849 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV780
= ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $false )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4170]) ).
thf(4213,plain,
! [SV828: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ~ ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV183 @ ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4171]) ).
thf(4214,plain,
! [SV828: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV828
= ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4172]) ).
thf(4215,plain,
! [SV821: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV183 @ ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4173]) ).
thf(4216,plain,
! [SV821: $i,SV183: $i > $o,SV855: $i,SV411: $i > $o] :
( ( ( ~ ~ ( ~ ( SV411 @ SV855 )
| ~ ! [SY3280: $i] :
( ~ ( SV411 @ SY3280 )
| ( SV855 = SY3280 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV821
= ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4174]) ).
thf(4217,plain,
! [SV822: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV183 @ ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4175]) ).
thf(4218,plain,
! [SV822: $i,SV183: $i > $o,SV856: $i,SV411: $i > $o] :
( ( ( ~ ~ ( ~ ( SV411 @ SV856 )
| ~ ! [SY3281: $i] :
( ~ ( SV411 @ SY3281 )
| ( SV856 = SY3281 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV822
= ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4176]) ).
thf(4219,plain,
! [SV817: $i,SV183: $i > $o,SV857: $i,SV411: $i > $o] :
( ( ( ~ ~ ( ~ ( SV411 @ SV857 )
| ~ ! [SY3282: $i] :
( ~ ( SV411 @ SY3282 )
| ( SV857 = SY3282 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV183 @ ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4177]) ).
thf(4220,plain,
! [SV817: $i,SV183: $i > $o,SV853: $i,SV411: $i > $o] :
( ( ( ~ ( ~ ( SV411 @ SV853 )
| ~ ! [SY3278: $i] :
( ~ ( SV411 @ SY3278 )
| ( SV853 = SY3278 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV817
= ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4178]) ).
thf(4221,plain,
! [SV193: $i > $o,SV810: $i,SV422: $i > $o] :
( ( ( SV422 @ ( sK124_SY2770 @ SV810 @ SV193 @ SV422 ) )
= $true )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV193 @ ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4179]) ).
thf(4222,plain,
! [SV193: $i > $o,SV810: $i,SV422: $i > $o] :
( ( ( ! [SY3276: $i] :
( ~ ( SV422 @ SY3276 )
| ( ( sK124_SY2770 @ SV810 @ SV193 @ SV422 )
= SY3276 ) ) )
= $true )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV193 @ ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4180]) ).
thf(4223,plain,
! [SV193: $i > $o,SV810: $i,SV858: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV858 )
| ( ( sK120_SY2770 @ SV810 @ SV193 @ SV422 )
= SV858 ) )
= $true )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV810
= ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4182]) ).
thf(4224,plain,
! [SV422: $i > $o,SV811: $i,SV193: $i > $o] :
( ( ( SV193 @ ( sK125_SY2337 @ SV811 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV422 @ ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4183]) ).
thf(4225,plain,
! [SV422: $i > $o,SV811: $i,SV193: $i > $o] :
( ( ( ! [SY3277: $i] :
( ~ ( SV193 @ SY3277 )
| ( ( sK125_SY2337 @ SV811 @ SV422 @ SV193 )
= SY3277 ) ) )
= $true )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV422 @ ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4184]) ).
thf(4226,plain,
! [SV422: $i > $o,SV811: $i,SV859: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV859 )
| ( ( sK121_SY2337 @ SV811 @ SV422 @ SV193 )
= SV859 ) )
= $true )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV811
= ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4186]) ).
thf(4227,plain,
! [SV846: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) ) )
= $false )
| ( ( SV193 @ SV846 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4187]) ).
thf(4228,plain,
! [SV193: $i > $o,SV422: $i > $o,SV846: $i] :
( ( ( SV846
= ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $false )
| ( ( SV193 @ SV846 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4187]) ).
thf(4229,plain,
! [SV847: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) ) )
= $false )
| ( ( SV422 @ SV847 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4188]) ).
thf(4230,plain,
! [SV422: $i > $o,SV193: $i > $o,SV847: $i] :
( ( ( SV847
= ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $false )
| ( ( SV422 @ SV847 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4188]) ).
thf(4231,plain,
! [SV841: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( SV193 @ ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $true )
| ( ( SV193 @ SV841 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4189]) ).
thf(4232,plain,
! [SV841: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $false )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV841
= ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4190]) ).
thf(4233,plain,
! [SV842: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( SV422 @ ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $true )
| ( ( SV422 @ SV842 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4191]) ).
thf(4234,plain,
! [SV842: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $false )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV842
= ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4192]) ).
thf(4235,plain,
! [SV843: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( SV193 @ ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $true )
| ( ( SV193 @ SV843 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4193]) ).
thf(4236,plain,
! [SV843: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $false )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV843
= ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4194]) ).
thf(4237,plain,
! [SV844: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( SV422 @ ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $true )
| ( ( SV422 @ SV844 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4195]) ).
thf(4238,plain,
! [SV844: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $false )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV844
= ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4196]) ).
thf(4239,plain,
! [SV836: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $false )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV193 @ ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4197]) ).
thf(4240,plain,
! [SV193: $i > $o,SV836: $i,SV422: $i > $o] :
( ( ( ~ ~ ( ~ ( SV422 @ ( sK137_SY2770 @ SV836 @ SV193 @ SV422 ) )
| ~ ! [SY3283: $i] :
( ~ ( SV422 @ SY3283 )
| ( ( sK137_SY2770 @ SV836 @ SV193 @ SV422 )
= SY3283 ) ) ) )
= $false )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV836
= ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4198]) ).
thf(4241,plain,
! [SV837: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $false )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV422 @ ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4199]) ).
thf(4242,plain,
! [SV422: $i > $o,SV837: $i,SV193: $i > $o] :
( ( ( ~ ~ ( ~ ( SV193 @ ( sK138_SY2337 @ SV837 @ SV422 @ SV193 ) )
| ~ ! [SY3284: $i] :
( ~ ( SV193 @ SY3284 )
| ( ( sK138_SY2337 @ SV837 @ SV422 @ SV193 )
= SY3284 ) ) ) )
= $false )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV837
= ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4200]) ).
thf(4243,plain,
! [SV471: $i,SV249: $i > $i > $o,SV838: $i,SV757: $i] :
( ( ( ~ ( in @ ( sK133_SY3250 @ SV757 @ SV838 @ SV249 @ SV471 ) @ SV471 )
| ~ ( SV249 @ ( sK133_SY3250 @ SV757 @ SV838 @ SV249 @ SV471 ) @ SV838 ) )
= $false )
| ( ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4201]) ).
thf(4244,plain,
! [SV757: $i,SV838: $i,SV249: $i > $i > $o,SV471: $i,SV852: $i] :
( ( ( ~ ( in @ SV852 @ SV471 )
| ~ ( SV249 @ SV852 @ SV838 ) )
= $true )
| ( ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4202]) ).
thf(4245,plain,
! [SV471: $i,SV249: $i > $i > $o,SV830: $i,SV757: $i] :
( ( ( ~ ( in @ ( sK128_SY3246 @ SV757 @ SV830 @ SV249 @ SV471 ) @ SV471 ) )
= $false )
| ( ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4203]) ).
thf(4246,plain,
! [SV471: $i,SV830: $i,SV757: $i,SV249: $i > $i > $o] :
( ( ( ~ ( SV249 @ ( sK128_SY3246 @ SV757 @ SV830 @ SV249 @ SV471 ) @ SV830 ) )
= $false )
| ( ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4203]) ).
thf(4247,plain,
! [SV757: $i,SV830: $i,SV249: $i > $i > $o,SV471: $i,SV851: $i] :
( ( ( ~ ( in @ SV851 @ SV471 ) )
= $true )
| ( ( ~ ( SV249 @ SV851 @ SV830 ) )
= $true )
| ( ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4204]) ).
thf(4248,plain,
! [SV147: $i,SV808: $i,SV794: $i] :
( ( ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
| ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) ) ) )
= $true )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4205]) ).
thf(4249,plain,
! [SV147: $i,SV794: $i,SV808: $i] :
( ( ( ~ ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
| ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) ) )
= $false )
| ( ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
= $false )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4206]) ).
thf(4250,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SV747 ) )
| ~ ~ ~ ! [SY3261: $i] :
~ ~ ( ~ ( in @ SY3261 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
| ~ ( in @ SY3261 @ SV747 ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4207]) ).
thf(4251,plain,
! [SV747: $i,SV825: $i,SV147: $i,SV860: $i] :
( ( ( ~ ( in @ SV860 @ ( sK3_SY2186 @ SV147 ) )
| ! [SY3285: $i] :
( ~ ( in @ SY3285 @ SV860 )
| ( in @ SY3285 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) ) )
| ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SV860 ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4208]) ).
thf(4252,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SV747 ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4209]) ).
thf(4253,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( ~ ~ ~ ! [SY3253: $i] :
~ ~ ( ~ ( in @ SY3253 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
| ~ ( in @ SY3253 @ SV747 ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4209]) ).
thf(4254,plain,
! [SV747: $i,SV820: $i,SV147: $i,SV854: $i] :
( ( ( ~ ( in @ SV854 @ ( sK3_SY2186 @ SV147 ) ) )
= $true )
| ( ( ! [SY3279: $i] :
( ~ ( in @ SY3279 @ SV854 )
| ( in @ SY3279 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) ) )
| ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SV854 ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4210]) ).
thf(4255,plain,
! [SV850: $i,SV183: $i > $o,SV780: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK139_SY3270 @ SV780 @ SV183 @ SV850 @ SV411 ) )
| ( SV850
= ( sK139_SY3270 @ SV780 @ SV183 @ SV850 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV850 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV183 @ ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4211]) ).
thf(4256,plain,
! [SV849: $i,SV183: $i > $o,SV780: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK136_SY3266 @ SV780 @ SV183 @ SV849 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV849 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV780
= ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $false )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4212]) ).
thf(4257,plain,
! [SV411: $i > $o,SV183: $i > $o,SV780: $i,SV849: $i] :
( ( ( SV849
= ( sK136_SY3266 @ SV780 @ SV183 @ SV849 @ SV411 ) )
= $false )
| ( ( SV411 @ SV849 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV780
= ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $false )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4212]) ).
thf(4258,plain,
! [SV828: $i,SV183: $i > $o,SV411: $i > $o] :
( ( ( ! [SY2748: $i] :
~ ~ ( ~ ( SV411 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( SV411 @ SY2749 )
| ( SY2748 = SY2749 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV183 @ ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4213]) ).
thf(4259,plain,
! [SV828: $i,SV183: $i > $o,SV861: $i,SV411: $i > $o] :
( ( ( ~ ~ ( ~ ( SV411 @ SV861 )
| ~ ! [SY3286: $i] :
( ~ ( SV411 @ SY3286 )
| ( SV861 = SY3286 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV828
= ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4214]) ).
thf(4260,plain,
! [SV821: $i,SV183: $i > $o,SV862: $i,SV411: $i > $o] :
( ( ( ~ ~ ( ~ ( SV411 @ SV862 )
| ~ ! [SY3287: $i] :
( ~ ( SV411 @ SY3287 )
| ( SV862 = SY3287 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV183 @ ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4215]) ).
thf(4261,plain,
! [SV821: $i,SV183: $i > $o,SV855: $i,SV411: $i > $o] :
( ( ( ~ ( ~ ( SV411 @ SV855 )
| ~ ! [SY3280: $i] :
( ~ ( SV411 @ SY3280 )
| ( SV855 = SY3280 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV821
= ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4216]) ).
thf(4262,plain,
! [SV822: $i,SV183: $i > $o,SV863: $i,SV411: $i > $o] :
( ( ( ~ ~ ( ~ ( SV411 @ SV863 )
| ~ ! [SY3288: $i] :
( ~ ( SV411 @ SY3288 )
| ( SV863 = SY3288 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV183 @ ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4217]) ).
thf(4263,plain,
! [SV822: $i,SV183: $i > $o,SV856: $i,SV411: $i > $o] :
( ( ( ~ ( ~ ( SV411 @ SV856 )
| ~ ! [SY3281: $i] :
( ~ ( SV411 @ SY3281 )
| ( SV856 = SY3281 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV822
= ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4218]) ).
thf(4264,plain,
! [SV817: $i,SV183: $i > $o,SV857: $i,SV411: $i > $o] :
( ( ( ~ ( ~ ( SV411 @ SV857 )
| ~ ! [SY3282: $i] :
( ~ ( SV411 @ SY3282 )
| ( SV857 = SY3282 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV183 @ ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4219]) ).
thf(4265,plain,
! [SV817: $i,SV183: $i > $o,SV853: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV853 )
| ~ ! [SY3278: $i] :
( ~ ( SV411 @ SY3278 )
| ( SV853 = SY3278 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV817
= ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4220]) ).
thf(4266,plain,
! [SV193: $i > $o,SV810: $i,SV864: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV864 )
| ( ( sK124_SY2770 @ SV810 @ SV193 @ SV422 )
= SV864 ) )
= $true )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV193 @ ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4222]) ).
thf(4267,plain,
! [SV193: $i > $o,SV810: $i,SV858: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV858 ) )
= $true )
| ( ( ( sK120_SY2770 @ SV810 @ SV193 @ SV422 )
= SV858 )
= $true )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV810
= ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4223]) ).
thf(4268,plain,
! [SV422: $i > $o,SV811: $i,SV865: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV865 )
| ( ( sK125_SY2337 @ SV811 @ SV422 @ SV193 )
= SV865 ) )
= $true )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV422 @ ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4225]) ).
thf(4269,plain,
! [SV422: $i > $o,SV811: $i,SV859: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV859 ) )
= $true )
| ( ( ( sK121_SY2337 @ SV811 @ SV422 @ SV193 )
= SV859 )
= $true )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV811
= ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4226]) ).
thf(4270,plain,
! [SV846: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( SV193 @ ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $true )
| ( ( SV193 @ SV846 )
= $false )
| ( ( ~ ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4227]) ).
thf(4271,plain,
! [SV846: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $false )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV846
= ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4228]) ).
thf(4272,plain,
! [SV847: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( SV422 @ ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $true )
| ( ( SV422 @ SV847 )
= $false )
| ( ( ~ ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4229]) ).
thf(4273,plain,
! [SV847: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $false )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV847
= ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4230]) ).
thf(4274,plain,
! [SV841: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $false )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV193 @ ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4231]) ).
thf(4275,plain,
! [SV193: $i > $o,SV841: $i,SV422: $i > $o] :
( ( ( ~ ~ ( ~ ( SV422 @ ( sK140_SY2770 @ SV841 @ SV193 @ SV422 ) )
| ~ ! [SY3289: $i] :
( ~ ( SV422 @ SY3289 )
| ( ( sK140_SY2770 @ SV841 @ SV193 @ SV422 )
= SY3289 ) ) ) )
= $false )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV841
= ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4232]) ).
thf(4276,plain,
! [SV842: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $false )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV422 @ ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4233]) ).
thf(4277,plain,
! [SV422: $i > $o,SV842: $i,SV193: $i > $o] :
( ( ( ~ ~ ( ~ ( SV193 @ ( sK141_SY2337 @ SV842 @ SV422 @ SV193 ) )
| ~ ! [SY3290: $i] :
( ~ ( SV193 @ SY3290 )
| ( ( sK141_SY2337 @ SV842 @ SV422 @ SV193 )
= SY3290 ) ) ) )
= $false )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV842
= ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4234]) ).
thf(4278,plain,
! [SV843: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $false )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV193 @ ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4235]) ).
thf(4279,plain,
! [SV193: $i > $o,SV843: $i,SV422: $i > $o] :
( ( ( ~ ~ ( ~ ( SV422 @ ( sK142_SY2770 @ SV843 @ SV193 @ SV422 ) )
| ~ ! [SY3291: $i] :
( ~ ( SV422 @ SY3291 )
| ( ( sK142_SY2770 @ SV843 @ SV193 @ SV422 )
= SY3291 ) ) ) )
= $false )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV843
= ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4236]) ).
thf(4280,plain,
! [SV844: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $false )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV422 @ ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4237]) ).
thf(4281,plain,
! [SV422: $i > $o,SV844: $i,SV193: $i > $o] :
( ( ( ~ ~ ( ~ ( SV193 @ ( sK143_SY2337 @ SV844 @ SV422 @ SV193 ) )
| ~ ! [SY3292: $i] :
( ~ ( SV193 @ SY3292 )
| ( ( sK143_SY2337 @ SV844 @ SV422 @ SV193 )
= SY3292 ) ) ) )
= $false )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV844
= ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4238]) ).
thf(4282,plain,
! [SV193: $i > $o,SV836: $i,SV422: $i > $o] :
( ( ( ~ ~ ( ~ ( SV422 @ ( sK144_SY2770 @ SV836 @ SV193 @ SV422 ) )
| ~ ! [SY3293: $i] :
( ~ ( SV422 @ SY3293 )
| ( ( sK144_SY2770 @ SV836 @ SV193 @ SV422 )
= SY3293 ) ) ) )
= $false )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV193 @ ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4239]) ).
thf(4283,plain,
! [SV193: $i > $o,SV836: $i,SV422: $i > $o] :
( ( ( ~ ( ~ ( SV422 @ ( sK137_SY2770 @ SV836 @ SV193 @ SV422 ) )
| ~ ! [SY3283: $i] :
( ~ ( SV422 @ SY3283 )
| ( ( sK137_SY2770 @ SV836 @ SV193 @ SV422 )
= SY3283 ) ) ) )
= $true )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV836
= ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4240]) ).
thf(4284,plain,
! [SV422: $i > $o,SV837: $i,SV193: $i > $o] :
( ( ( ~ ~ ( ~ ( SV193 @ ( sK145_SY2337 @ SV837 @ SV422 @ SV193 ) )
| ~ ! [SY3294: $i] :
( ~ ( SV193 @ SY3294 )
| ( ( sK145_SY2337 @ SV837 @ SV422 @ SV193 )
= SY3294 ) ) ) )
= $false )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV422 @ ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4241]) ).
thf(4285,plain,
! [SV422: $i > $o,SV837: $i,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ ( sK138_SY2337 @ SV837 @ SV422 @ SV193 ) )
| ~ ! [SY3284: $i] :
( ~ ( SV193 @ SY3284 )
| ( ( sK138_SY2337 @ SV837 @ SV422 @ SV193 )
= SY3284 ) ) ) )
= $true )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV837
= ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4242]) ).
thf(4286,plain,
! [SV471: $i,SV249: $i > $i > $o,SV838: $i,SV757: $i] :
( ( ( ~ ( in @ ( sK133_SY3250 @ SV757 @ SV838 @ SV249 @ SV471 ) @ SV471 ) )
= $false )
| ( ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4243]) ).
thf(4287,plain,
! [SV471: $i,SV838: $i,SV757: $i,SV249: $i > $i > $o] :
( ( ( ~ ( SV249 @ ( sK133_SY3250 @ SV757 @ SV838 @ SV249 @ SV471 ) @ SV838 ) )
= $false )
| ( ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4243]) ).
thf(4288,plain,
! [SV757: $i,SV838: $i,SV249: $i > $i > $o,SV471: $i,SV852: $i] :
( ( ( ~ ( in @ SV852 @ SV471 ) )
= $true )
| ( ( ~ ( SV249 @ SV852 @ SV838 ) )
= $true )
| ( ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4244]) ).
thf(4289,plain,
! [SV471: $i,SV249: $i > $i > $o,SV830: $i,SV757: $i] :
( ( ( in @ ( sK128_SY3246 @ SV757 @ SV830 @ SV249 @ SV471 ) @ SV471 )
= $true )
| ( ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4245]) ).
thf(4290,plain,
! [SV471: $i,SV830: $i,SV757: $i,SV249: $i > $i > $o] :
( ( ( SV249 @ ( sK128_SY3246 @ SV757 @ SV830 @ SV249 @ SV471 ) @ SV830 )
= $true )
| ( ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4246]) ).
thf(4291,plain,
! [SV757: $i,SV830: $i,SV249: $i > $i > $o,SV471: $i,SV851: $i] :
( ( ( in @ SV851 @ SV471 )
= $false )
| ( ( ~ ( SV249 @ SV851 @ SV830 ) )
= $true )
| ( ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4247]) ).
thf(4292,plain,
! [SV147: $i,SV794: $i,SV808: $i] :
( ( ( ~ ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
| ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) ) )
= $false )
| ( ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
= $true )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4248]) ).
thf(4293,plain,
! [SV147: $i,SV794: $i,SV808: $i] :
( ( ( ~ ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) ) )
= $false )
| ( ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
= $false )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4249]) ).
thf(4294,plain,
! [SV147: $i,SV808: $i,SV794: $i] :
( ( ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
= $false )
| ( ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
= $false )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4249]) ).
thf(4295,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SV747 ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4250]) ).
thf(4296,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( ~ ~ ~ ! [SY3261: $i] :
~ ~ ( ~ ( in @ SY3261 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
| ~ ( in @ SY3261 @ SV747 ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4250]) ).
thf(4297,plain,
! [SV747: $i,SV825: $i,SV147: $i,SV860: $i] :
( ( ( ~ ( in @ SV860 @ ( sK3_SY2186 @ SV147 ) ) )
= $true )
| ( ( ! [SY3285: $i] :
( ~ ( in @ SY3285 @ SV860 )
| ( in @ SY3285 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) ) )
| ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SV860 ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4251]) ).
thf(4298,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( ~ ( ~ ( in @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SV747 ) ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4252]) ).
thf(4299,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( ~ ~ ! [SY3253: $i] :
~ ~ ( ~ ( in @ SY3253 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
| ~ ( in @ SY3253 @ SV747 ) ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4253]) ).
thf(4300,plain,
! [SV747: $i,SV820: $i,SV147: $i,SV854: $i] :
( ( ( in @ SV854 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( ! [SY3279: $i] :
( ~ ( in @ SY3279 @ SV854 )
| ( in @ SY3279 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) ) )
| ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SV854 ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4254]) ).
thf(4301,plain,
! [SV850: $i,SV183: $i > $o,SV780: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK139_SY3270 @ SV780 @ SV183 @ SV850 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV850 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV183 @ ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4255]) ).
thf(4302,plain,
! [SV411: $i > $o,SV183: $i > $o,SV780: $i,SV850: $i] :
( ( ( SV850
= ( sK139_SY3270 @ SV780 @ SV183 @ SV850 @ SV411 ) )
= $false )
| ( ( SV411 @ SV850 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV183 @ ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4255]) ).
thf(4303,plain,
! [SV849: $i,SV183: $i > $o,SV780: $i,SV411: $i > $o] :
( ( ( SV411 @ ( sK136_SY3266 @ SV780 @ SV183 @ SV849 @ SV411 ) )
= $true )
| ( ( SV411 @ SV849 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV780
= ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $false )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4256]) ).
thf(4304,plain,
! [SV828: $i,SV183: $i > $o,SV866: $i,SV411: $i > $o] :
( ( ( ~ ~ ( ~ ( SV411 @ SV866 )
| ~ ! [SY3295: $i] :
( ~ ( SV411 @ SY3295 )
| ( SV866 = SY3295 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV183 @ ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4258]) ).
thf(4305,plain,
! [SV828: $i,SV183: $i > $o,SV861: $i,SV411: $i > $o] :
( ( ( ~ ( ~ ( SV411 @ SV861 )
| ~ ! [SY3286: $i] :
( ~ ( SV411 @ SY3286 )
| ( SV861 = SY3286 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV828
= ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4259]) ).
thf(4306,plain,
! [SV821: $i,SV183: $i > $o,SV862: $i,SV411: $i > $o] :
( ( ( ~ ( ~ ( SV411 @ SV862 )
| ~ ! [SY3287: $i] :
( ~ ( SV411 @ SY3287 )
| ( SV862 = SY3287 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV183 @ ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4260]) ).
thf(4307,plain,
! [SV821: $i,SV183: $i > $o,SV855: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV855 )
| ~ ! [SY3280: $i] :
( ~ ( SV411 @ SY3280 )
| ( SV855 = SY3280 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV821
= ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4261]) ).
thf(4308,plain,
! [SV822: $i,SV183: $i > $o,SV863: $i,SV411: $i > $o] :
( ( ( ~ ( ~ ( SV411 @ SV863 )
| ~ ! [SY3288: $i] :
( ~ ( SV411 @ SY3288 )
| ( SV863 = SY3288 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV183 @ ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4262]) ).
thf(4309,plain,
! [SV822: $i,SV183: $i > $o,SV856: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV856 )
| ~ ! [SY3281: $i] :
( ~ ( SV411 @ SY3281 )
| ( SV856 = SY3281 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV822
= ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4263]) ).
thf(4310,plain,
! [SV817: $i,SV183: $i > $o,SV857: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV857 )
| ~ ! [SY3282: $i] :
( ~ ( SV411 @ SY3282 )
| ( SV857 = SY3282 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV183 @ ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4264]) ).
thf(4311,plain,
! [SV817: $i,SV183: $i > $o,SV853: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV853 ) )
= $true )
| ( ( ~ ! [SY3278: $i] :
( ~ ( SV411 @ SY3278 )
| ( SV853 = SY3278 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV817
= ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4265]) ).
thf(4312,plain,
! [SV193: $i > $o,SV810: $i,SV864: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV864 ) )
= $true )
| ( ( ( sK124_SY2770 @ SV810 @ SV193 @ SV422 )
= SV864 )
= $true )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV193 @ ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4266]) ).
thf(4313,plain,
! [SV193: $i > $o,SV810: $i,SV858: $i,SV422: $i > $o] :
( ( ( SV422 @ SV858 )
= $false )
| ( ( ( sK120_SY2770 @ SV810 @ SV193 @ SV422 )
= SV858 )
= $true )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV810
= ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4267]) ).
thf(4314,plain,
! [SV422: $i > $o,SV811: $i,SV865: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV865 ) )
= $true )
| ( ( ( sK125_SY2337 @ SV811 @ SV422 @ SV193 )
= SV865 )
= $true )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV422 @ ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4268]) ).
thf(4315,plain,
! [SV422: $i > $o,SV811: $i,SV859: $i,SV193: $i > $o] :
( ( ( SV193 @ SV859 )
= $false )
| ( ( ( sK121_SY2337 @ SV811 @ SV422 @ SV193 )
= SV859 )
= $true )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV811
= ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $false )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4269]) ).
thf(4316,plain,
! [SV846: $i,SV193: $i > $o,SV422: $i > $o] :
( ( ( ! [SY2770: $i] :
~ ~ ( ~ ( SV422 @ SY2770 )
| ~ ! [SY2771: $i] :
( ~ ( SV422 @ SY2771 )
| ( SY2770 = SY2771 ) ) ) )
= $false )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV193 @ ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4270]) ).
thf(4317,plain,
! [SV193: $i > $o,SV846: $i,SV422: $i > $o] :
( ( ( ~ ~ ( ~ ( SV422 @ ( sK146_SY2770 @ SV846 @ SV193 @ SV422 ) )
| ~ ! [SY3296: $i] :
( ~ ( SV422 @ SY3296 )
| ( ( sK146_SY2770 @ SV846 @ SV193 @ SV422 )
= SY3296 ) ) ) )
= $false )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV846
= ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4271]) ).
thf(4318,plain,
! [SV847: $i,SV422: $i > $o,SV193: $i > $o] :
( ( ( ! [SY2337: $i] :
~ ~ ( ~ ( SV193 @ SY2337 )
| ~ ! [SY2338: $i] :
( ~ ( SV193 @ SY2338 )
| ( SY2337 = SY2338 ) ) ) )
= $false )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV422 @ ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4272]) ).
thf(4319,plain,
! [SV422: $i > $o,SV847: $i,SV193: $i > $o] :
( ( ( ~ ~ ( ~ ( SV193 @ ( sK147_SY2337 @ SV847 @ SV422 @ SV193 ) )
| ~ ! [SY3297: $i] :
( ~ ( SV193 @ SY3297 )
| ( ( sK147_SY2337 @ SV847 @ SV422 @ SV193 )
= SY3297 ) ) ) )
= $false )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV847
= ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4273]) ).
thf(4320,plain,
! [SV193: $i > $o,SV841: $i,SV422: $i > $o] :
( ( ( ~ ~ ( ~ ( SV422 @ ( sK148_SY2770 @ SV841 @ SV193 @ SV422 ) )
| ~ ! [SY3298: $i] :
( ~ ( SV422 @ SY3298 )
| ( ( sK148_SY2770 @ SV841 @ SV193 @ SV422 )
= SY3298 ) ) ) )
= $false )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV193 @ ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4274]) ).
thf(4321,plain,
! [SV193: $i > $o,SV841: $i,SV422: $i > $o] :
( ( ( ~ ( ~ ( SV422 @ ( sK140_SY2770 @ SV841 @ SV193 @ SV422 ) )
| ~ ! [SY3289: $i] :
( ~ ( SV422 @ SY3289 )
| ( ( sK140_SY2770 @ SV841 @ SV193 @ SV422 )
= SY3289 ) ) ) )
= $true )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV841
= ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4275]) ).
thf(4322,plain,
! [SV422: $i > $o,SV842: $i,SV193: $i > $o] :
( ( ( ~ ~ ( ~ ( SV193 @ ( sK149_SY2337 @ SV842 @ SV422 @ SV193 ) )
| ~ ! [SY3299: $i] :
( ~ ( SV193 @ SY3299 )
| ( ( sK149_SY2337 @ SV842 @ SV422 @ SV193 )
= SY3299 ) ) ) )
= $false )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV422 @ ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4276]) ).
thf(4323,plain,
! [SV422: $i > $o,SV842: $i,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ ( sK141_SY2337 @ SV842 @ SV422 @ SV193 ) )
| ~ ! [SY3290: $i] :
( ~ ( SV193 @ SY3290 )
| ( ( sK141_SY2337 @ SV842 @ SV422 @ SV193 )
= SY3290 ) ) ) )
= $true )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV842
= ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4277]) ).
thf(4324,plain,
! [SV193: $i > $o,SV843: $i,SV422: $i > $o] :
( ( ( ~ ~ ( ~ ( SV422 @ ( sK150_SY2770 @ SV843 @ SV193 @ SV422 ) )
| ~ ! [SY3300: $i] :
( ~ ( SV422 @ SY3300 )
| ( ( sK150_SY2770 @ SV843 @ SV193 @ SV422 )
= SY3300 ) ) ) )
= $false )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV193 @ ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4278]) ).
thf(4325,plain,
! [SV193: $i > $o,SV843: $i,SV422: $i > $o] :
( ( ( ~ ( ~ ( SV422 @ ( sK142_SY2770 @ SV843 @ SV193 @ SV422 ) )
| ~ ! [SY3291: $i] :
( ~ ( SV422 @ SY3291 )
| ( ( sK142_SY2770 @ SV843 @ SV193 @ SV422 )
= SY3291 ) ) ) )
= $true )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV843
= ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4279]) ).
thf(4326,plain,
! [SV422: $i > $o,SV844: $i,SV193: $i > $o] :
( ( ( ~ ~ ( ~ ( SV193 @ ( sK151_SY2337 @ SV844 @ SV422 @ SV193 ) )
| ~ ! [SY3301: $i] :
( ~ ( SV193 @ SY3301 )
| ( ( sK151_SY2337 @ SV844 @ SV422 @ SV193 )
= SY3301 ) ) ) )
= $false )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV422 @ ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4280]) ).
thf(4327,plain,
! [SV422: $i > $o,SV844: $i,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ ( sK143_SY2337 @ SV844 @ SV422 @ SV193 ) )
| ~ ! [SY3292: $i] :
( ~ ( SV193 @ SY3292 )
| ( ( sK143_SY2337 @ SV844 @ SV422 @ SV193 )
= SY3292 ) ) ) )
= $true )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV844
= ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4281]) ).
thf(4328,plain,
! [SV193: $i > $o,SV836: $i,SV422: $i > $o] :
( ( ( ~ ( ~ ( SV422 @ ( sK144_SY2770 @ SV836 @ SV193 @ SV422 ) )
| ~ ! [SY3293: $i] :
( ~ ( SV422 @ SY3293 )
| ( ( sK144_SY2770 @ SV836 @ SV193 @ SV422 )
= SY3293 ) ) ) )
= $true )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV193 @ ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4282]) ).
thf(4329,plain,
! [SV193: $i > $o,SV836: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK137_SY2770 @ SV836 @ SV193 @ SV422 ) )
| ~ ! [SY3283: $i] :
( ~ ( SV422 @ SY3283 )
| ( ( sK137_SY2770 @ SV836 @ SV193 @ SV422 )
= SY3283 ) ) )
= $false )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV836
= ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4283]) ).
thf(4330,plain,
! [SV422: $i > $o,SV837: $i,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ ( sK145_SY2337 @ SV837 @ SV422 @ SV193 ) )
| ~ ! [SY3294: $i] :
( ~ ( SV193 @ SY3294 )
| ( ( sK145_SY2337 @ SV837 @ SV422 @ SV193 )
= SY3294 ) ) ) )
= $true )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV422 @ ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4284]) ).
thf(4331,plain,
! [SV422: $i > $o,SV837: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK138_SY2337 @ SV837 @ SV422 @ SV193 ) )
| ~ ! [SY3284: $i] :
( ~ ( SV193 @ SY3284 )
| ( ( sK138_SY2337 @ SV837 @ SV422 @ SV193 )
= SY3284 ) ) )
= $false )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV837
= ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4285]) ).
thf(4332,plain,
! [SV471: $i,SV249: $i > $i > $o,SV838: $i,SV757: $i] :
( ( ( in @ ( sK133_SY3250 @ SV757 @ SV838 @ SV249 @ SV471 ) @ SV471 )
= $true )
| ( ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4286]) ).
thf(4333,plain,
! [SV471: $i,SV838: $i,SV757: $i,SV249: $i > $i > $o] :
( ( ( SV249 @ ( sK133_SY3250 @ SV757 @ SV838 @ SV249 @ SV471 ) @ SV838 )
= $true )
| ( ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4287]) ).
thf(4334,plain,
! [SV757: $i,SV838: $i,SV249: $i > $i > $o,SV471: $i,SV852: $i] :
( ( ( in @ SV852 @ SV471 )
= $false )
| ( ( ~ ( SV249 @ SV852 @ SV838 ) )
= $true )
| ( ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4288]) ).
thf(4335,plain,
! [SV757: $i,SV471: $i,SV830: $i,SV851: $i,SV249: $i > $i > $o] :
( ( ( SV249 @ SV851 @ SV830 )
= $false )
| ( ( in @ SV851 @ SV471 )
= $false )
| ( ( in @ SV830 @ ( sK100_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV757
= ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4291]) ).
thf(4336,plain,
! [SV147: $i,SV794: $i,SV808: $i] :
( ( ( ~ ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) ) )
= $false )
| ( ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
= $true )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4292]) ).
thf(4337,plain,
! [SV147: $i,SV808: $i,SV794: $i] :
( ( ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
= $false )
| ( ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
= $true )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4292]) ).
thf(4338,plain,
! [SV147: $i,SV794: $i,SV808: $i] :
( ( ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
= $true )
| ( ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
= $false )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4293]) ).
thf(4339,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( ~ ( ~ ( in @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SV747 ) ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4295]) ).
thf(4340,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( ~ ~ ! [SY3261: $i] :
~ ~ ( ~ ( in @ SY3261 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
| ~ ( in @ SY3261 @ SV747 ) ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4296]) ).
thf(4341,plain,
! [SV747: $i,SV825: $i,SV147: $i,SV860: $i] :
( ( ( in @ SV860 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( ! [SY3285: $i] :
( ~ ( in @ SY3285 @ SV860 )
| ( in @ SY3285 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) ) )
| ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SV860 ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4297]) ).
thf(4342,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( ~ ( in @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SV747 ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4298]) ).
thf(4343,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( ~ ! [SY3253: $i] :
~ ~ ( ~ ( in @ SY3253 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
| ~ ( in @ SY3253 @ SV747 ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4299]) ).
thf(4344,plain,
! [SV147: $i,SV747: $i,SV820: $i,SV854: $i] :
( ( ( ! [SY3279: $i] :
( ~ ( in @ SY3279 @ SV854 )
| ( in @ SY3279 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) ) ) )
= $true )
| ( ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SV854 )
= $true )
| ( ( in @ SV854 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4300]) ).
thf(4345,plain,
! [SV850: $i,SV183: $i > $o,SV780: $i,SV411: $i > $o] :
( ( ( SV411 @ ( sK139_SY3270 @ SV780 @ SV183 @ SV850 @ SV411 ) )
= $true )
| ( ( SV411 @ SV850 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV780 )
= $false )
| ( ( SV183 @ ( sK101_SY3206 @ SV411 @ SV780 @ SV183 ) )
= $true )
| ( ( ( sK13_SY2744 @ SV411 @ SV183 )
= ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4301]) ).
thf(4346,plain,
! [SV828: $i,SV183: $i > $o,SV866: $i,SV411: $i > $o] :
( ( ( ~ ( ~ ( SV411 @ SV866 )
| ~ ! [SY3295: $i] :
( ~ ( SV411 @ SY3295 )
| ( SV866 = SY3295 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV183 @ ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4304]) ).
thf(4347,plain,
! [SV828: $i,SV183: $i > $o,SV861: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV861 )
| ~ ! [SY3286: $i] :
( ~ ( SV411 @ SY3286 )
| ( SV861 = SY3286 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV828
= ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4305]) ).
thf(4348,plain,
! [SV821: $i,SV183: $i > $o,SV862: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV862 )
| ~ ! [SY3287: $i] :
( ~ ( SV411 @ SY3287 )
| ( SV862 = SY3287 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV183 @ ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4306]) ).
thf(4349,plain,
! [SV821: $i,SV183: $i > $o,SV855: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV855 ) )
= $true )
| ( ( ~ ! [SY3280: $i] :
( ~ ( SV411 @ SY3280 )
| ( SV855 = SY3280 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV821
= ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4307]) ).
thf(4350,plain,
! [SV822: $i,SV183: $i > $o,SV863: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV863 )
| ~ ! [SY3288: $i] :
( ~ ( SV411 @ SY3288 )
| ( SV863 = SY3288 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV183 @ ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4308]) ).
thf(4351,plain,
! [SV822: $i,SV183: $i > $o,SV856: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV856 ) )
= $true )
| ( ( ~ ! [SY3281: $i] :
( ~ ( SV411 @ SY3281 )
| ( SV856 = SY3281 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV822
= ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4309]) ).
thf(4352,plain,
! [SV817: $i,SV183: $i > $o,SV857: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV857 ) )
= $true )
| ( ( ~ ! [SY3282: $i] :
( ~ ( SV411 @ SY3282 )
| ( SV857 = SY3282 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV183 @ ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4310]) ).
thf(4353,plain,
! [SV817: $i,SV183: $i > $o,SV853: $i,SV411: $i > $o] :
( ( ( SV411 @ SV853 )
= $false )
| ( ( ~ ! [SY3278: $i] :
( ~ ( SV411 @ SY3278 )
| ( SV853 = SY3278 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV817
= ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4311]) ).
thf(4354,plain,
! [SV193: $i > $o,SV810: $i,SV864: $i,SV422: $i > $o] :
( ( ( SV422 @ SV864 )
= $false )
| ( ( ( sK124_SY2770 @ SV810 @ SV193 @ SV422 )
= SV864 )
= $true )
| ( ( SV193 @ SV810 )
= $false )
| ( ( SV193 @ ( sK111_SY3226 @ SV422 @ SV810 @ SV193 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4312]) ).
thf(4355,plain,
! [SV422: $i > $o,SV811: $i,SV865: $i,SV193: $i > $o] :
( ( ( SV193 @ SV865 )
= $false )
| ( ( ( sK125_SY2337 @ SV811 @ SV422 @ SV193 )
= SV865 )
= $true )
| ( ( SV422 @ SV811 )
= $false )
| ( ( SV422 @ ( sK112_SY3227 @ SV193 @ SV811 @ SV422 ) )
= $true )
| ( ( ( sK14_SY2766 @ SV422 @ SV193 )
= ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4314]) ).
thf(4356,plain,
! [SV193: $i > $o,SV846: $i,SV422: $i > $o] :
( ( ( ~ ~ ( ~ ( SV422 @ ( sK152_SY2770 @ SV846 @ SV193 @ SV422 ) )
| ~ ! [SY3302: $i] :
( ~ ( SV422 @ SY3302 )
| ( ( sK152_SY2770 @ SV846 @ SV193 @ SV422 )
= SY3302 ) ) ) )
= $false )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV193 @ ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4316]) ).
thf(4357,plain,
! [SV193: $i > $o,SV846: $i,SV422: $i > $o] :
( ( ( ~ ( ~ ( SV422 @ ( sK146_SY2770 @ SV846 @ SV193 @ SV422 ) )
| ~ ! [SY3296: $i] :
( ~ ( SV422 @ SY3296 )
| ( ( sK146_SY2770 @ SV846 @ SV193 @ SV422 )
= SY3296 ) ) ) )
= $true )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV846
= ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4317]) ).
thf(4358,plain,
! [SV422: $i > $o,SV847: $i,SV193: $i > $o] :
( ( ( ~ ~ ( ~ ( SV193 @ ( sK153_SY2337 @ SV847 @ SV422 @ SV193 ) )
| ~ ! [SY3303: $i] :
( ~ ( SV193 @ SY3303 )
| ( ( sK153_SY2337 @ SV847 @ SV422 @ SV193 )
= SY3303 ) ) ) )
= $false )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV422 @ ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4318]) ).
thf(4359,plain,
! [SV422: $i > $o,SV847: $i,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ ( sK147_SY2337 @ SV847 @ SV422 @ SV193 ) )
| ~ ! [SY3297: $i] :
( ~ ( SV193 @ SY3297 )
| ( ( sK147_SY2337 @ SV847 @ SV422 @ SV193 )
= SY3297 ) ) ) )
= $true )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV847
= ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4319]) ).
thf(4360,plain,
! [SV193: $i > $o,SV841: $i,SV422: $i > $o] :
( ( ( ~ ( ~ ( SV422 @ ( sK148_SY2770 @ SV841 @ SV193 @ SV422 ) )
| ~ ! [SY3298: $i] :
( ~ ( SV422 @ SY3298 )
| ( ( sK148_SY2770 @ SV841 @ SV193 @ SV422 )
= SY3298 ) ) ) )
= $true )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV193 @ ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4320]) ).
thf(4361,plain,
! [SV193: $i > $o,SV841: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK140_SY2770 @ SV841 @ SV193 @ SV422 ) )
| ~ ! [SY3289: $i] :
( ~ ( SV422 @ SY3289 )
| ( ( sK140_SY2770 @ SV841 @ SV193 @ SV422 )
= SY3289 ) ) )
= $false )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV841
= ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4321]) ).
thf(4362,plain,
! [SV422: $i > $o,SV842: $i,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ ( sK149_SY2337 @ SV842 @ SV422 @ SV193 ) )
| ~ ! [SY3299: $i] :
( ~ ( SV193 @ SY3299 )
| ( ( sK149_SY2337 @ SV842 @ SV422 @ SV193 )
= SY3299 ) ) ) )
= $true )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV422 @ ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4322]) ).
thf(4363,plain,
! [SV422: $i > $o,SV842: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK141_SY2337 @ SV842 @ SV422 @ SV193 ) )
| ~ ! [SY3290: $i] :
( ~ ( SV193 @ SY3290 )
| ( ( sK141_SY2337 @ SV842 @ SV422 @ SV193 )
= SY3290 ) ) )
= $false )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV842
= ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4323]) ).
thf(4364,plain,
! [SV193: $i > $o,SV843: $i,SV422: $i > $o] :
( ( ( ~ ( ~ ( SV422 @ ( sK150_SY2770 @ SV843 @ SV193 @ SV422 ) )
| ~ ! [SY3300: $i] :
( ~ ( SV422 @ SY3300 )
| ( ( sK150_SY2770 @ SV843 @ SV193 @ SV422 )
= SY3300 ) ) ) )
= $true )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV193 @ ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4324]) ).
thf(4365,plain,
! [SV193: $i > $o,SV843: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK142_SY2770 @ SV843 @ SV193 @ SV422 ) )
| ~ ! [SY3291: $i] :
( ~ ( SV422 @ SY3291 )
| ( ( sK142_SY2770 @ SV843 @ SV193 @ SV422 )
= SY3291 ) ) )
= $false )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV843
= ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4325]) ).
thf(4366,plain,
! [SV422: $i > $o,SV844: $i,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ ( sK151_SY2337 @ SV844 @ SV422 @ SV193 ) )
| ~ ! [SY3301: $i] :
( ~ ( SV193 @ SY3301 )
| ( ( sK151_SY2337 @ SV844 @ SV422 @ SV193 )
= SY3301 ) ) ) )
= $true )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV422 @ ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4326]) ).
thf(4367,plain,
! [SV422: $i > $o,SV844: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK143_SY2337 @ SV844 @ SV422 @ SV193 ) )
| ~ ! [SY3292: $i] :
( ~ ( SV193 @ SY3292 )
| ( ( sK143_SY2337 @ SV844 @ SV422 @ SV193 )
= SY3292 ) ) )
= $false )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV844
= ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4327]) ).
thf(4368,plain,
! [SV193: $i > $o,SV836: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK144_SY2770 @ SV836 @ SV193 @ SV422 ) )
| ~ ! [SY3293: $i] :
( ~ ( SV422 @ SY3293 )
| ( ( sK144_SY2770 @ SV836 @ SV193 @ SV422 )
= SY3293 ) ) )
= $false )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV193 @ ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4328]) ).
thf(4369,plain,
! [SV193: $i > $o,SV836: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK137_SY2770 @ SV836 @ SV193 @ SV422 ) ) )
= $false )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV836
= ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4329]) ).
thf(4370,plain,
! [SV193: $i > $o,SV836: $i,SV422: $i > $o] :
( ( ( ~ ! [SY3283: $i] :
( ~ ( SV422 @ SY3283 )
| ( ( sK137_SY2770 @ SV836 @ SV193 @ SV422 )
= SY3283 ) ) )
= $false )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV836
= ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4329]) ).
thf(4371,plain,
! [SV422: $i > $o,SV837: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK145_SY2337 @ SV837 @ SV422 @ SV193 ) )
| ~ ! [SY3294: $i] :
( ~ ( SV193 @ SY3294 )
| ( ( sK145_SY2337 @ SV837 @ SV422 @ SV193 )
= SY3294 ) ) )
= $false )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV422 @ ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4330]) ).
thf(4372,plain,
! [SV422: $i > $o,SV837: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK138_SY2337 @ SV837 @ SV422 @ SV193 ) ) )
= $false )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV837
= ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4331]) ).
thf(4373,plain,
! [SV422: $i > $o,SV837: $i,SV193: $i > $o] :
( ( ( ~ ! [SY3284: $i] :
( ~ ( SV193 @ SY3284 )
| ( ( sK138_SY2337 @ SV837 @ SV422 @ SV193 )
= SY3284 ) ) )
= $false )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV837
= ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4331]) ).
thf(4374,plain,
! [SV757: $i,SV471: $i,SV838: $i,SV852: $i,SV249: $i > $i > $o] :
( ( ( SV249 @ SV852 @ SV838 )
= $false )
| ( ( in @ SV852 @ SV471 )
= $false )
| ( ( in @ SV838 @ ( sK106_SY2874 @ SV757 @ SV249 @ SV471 ) )
= $true )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ SV757 )
= $false )
| ( ( SV249 @ ( sK17_SY2871 @ SV249 @ SV471 ) @ ( sK85_SY3187 @ SV757 @ SV471 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4334]) ).
thf(4375,plain,
! [SV147: $i,SV794: $i,SV808: $i] :
( ( ( in @ SV808 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
= $true )
| ( ( in @ SV794 @ ( sK116_SY3223 @ SV808 @ SV794 @ SV147 ) )
= $true )
| ( ( SV794 = SV808 )
= $true )
| ( ( in @ SV794 @ SV147 )
= $false )
| ( ( in @ SV808 @ SV147 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4336]) ).
thf(4376,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( ~ ( in @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
| ~ ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SV747 ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4339]) ).
thf(4377,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( ~ ! [SY3261: $i] :
~ ~ ( ~ ( in @ SY3261 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
| ~ ( in @ SY3261 @ SV747 ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4340]) ).
thf(4378,plain,
! [SV147: $i,SV747: $i,SV825: $i,SV860: $i] :
( ( ( ! [SY3285: $i] :
( ~ ( in @ SY3285 @ SV860 )
| ( in @ SY3285 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) ) ) )
= $true )
| ( ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SV860 )
= $true )
| ( ( in @ SV860 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4341]) ).
thf(4379,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( ~ ( in @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4342]) ).
thf(4380,plain,
! [SV820: $i,SV747: $i,SV147: $i] :
( ( ( ~ ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SV747 ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4342]) ).
thf(4381,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( ! [SY3253: $i] :
~ ~ ( ~ ( in @ SY3253 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
| ~ ( in @ SY3253 @ SV747 ) ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4343]) ).
thf(4382,plain,
! [SV147: $i,SV747: $i,SV820: $i,SV854: $i,SV867: $i] :
( ( ( ~ ( in @ SV867 @ SV854 )
| ( in @ SV867 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) ) )
= $true )
| ( ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SV854 )
= $true )
| ( ( in @ SV854 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4344]) ).
thf(4383,plain,
! [SV828: $i,SV183: $i > $o,SV866: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV866 )
| ~ ! [SY3295: $i] :
( ~ ( SV411 @ SY3295 )
| ( SV866 = SY3295 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV183 @ ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4346]) ).
thf(4384,plain,
! [SV828: $i,SV183: $i > $o,SV861: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV861 ) )
= $true )
| ( ( ~ ! [SY3286: $i] :
( ~ ( SV411 @ SY3286 )
| ( SV861 = SY3286 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV828
= ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4347]) ).
thf(4385,plain,
! [SV821: $i,SV183: $i > $o,SV862: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV862 ) )
= $true )
| ( ( ~ ! [SY3287: $i] :
( ~ ( SV411 @ SY3287 )
| ( SV862 = SY3287 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV183 @ ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4348]) ).
thf(4386,plain,
! [SV821: $i,SV183: $i > $o,SV855: $i,SV411: $i > $o] :
( ( ( SV411 @ SV855 )
= $false )
| ( ( ~ ! [SY3280: $i] :
( ~ ( SV411 @ SY3280 )
| ( SV855 = SY3280 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV821
= ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4349]) ).
thf(4387,plain,
! [SV822: $i,SV183: $i > $o,SV863: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV863 ) )
= $true )
| ( ( ~ ! [SY3288: $i] :
( ~ ( SV411 @ SY3288 )
| ( SV863 = SY3288 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV183 @ ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4350]) ).
thf(4388,plain,
! [SV822: $i,SV183: $i > $o,SV856: $i,SV411: $i > $o] :
( ( ( SV411 @ SV856 )
= $false )
| ( ( ~ ! [SY3281: $i] :
( ~ ( SV411 @ SY3281 )
| ( SV856 = SY3281 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV822
= ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4351]) ).
thf(4389,plain,
! [SV817: $i,SV183: $i > $o,SV857: $i,SV411: $i > $o] :
( ( ( SV411 @ SV857 )
= $false )
| ( ( ~ ! [SY3282: $i] :
( ~ ( SV411 @ SY3282 )
| ( SV857 = SY3282 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV183 @ ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4352]) ).
thf(4390,plain,
! [SV817: $i,SV183: $i > $o,SV853: $i,SV411: $i > $o] :
( ( ( ! [SY3278: $i] :
( ~ ( SV411 @ SY3278 )
| ( SV853 = SY3278 ) ) )
= $false )
| ( ( SV411 @ SV853 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV817
= ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4353]) ).
thf(4391,plain,
! [SV193: $i > $o,SV846: $i,SV422: $i > $o] :
( ( ( ~ ( ~ ( SV422 @ ( sK152_SY2770 @ SV846 @ SV193 @ SV422 ) )
| ~ ! [SY3302: $i] :
( ~ ( SV422 @ SY3302 )
| ( ( sK152_SY2770 @ SV846 @ SV193 @ SV422 )
= SY3302 ) ) ) )
= $true )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV193 @ ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4356]) ).
thf(4392,plain,
! [SV193: $i > $o,SV846: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK146_SY2770 @ SV846 @ SV193 @ SV422 ) )
| ~ ! [SY3296: $i] :
( ~ ( SV422 @ SY3296 )
| ( ( sK146_SY2770 @ SV846 @ SV193 @ SV422 )
= SY3296 ) ) )
= $false )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV846
= ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4357]) ).
thf(4393,plain,
! [SV422: $i > $o,SV847: $i,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ ( sK153_SY2337 @ SV847 @ SV422 @ SV193 ) )
| ~ ! [SY3303: $i] :
( ~ ( SV193 @ SY3303 )
| ( ( sK153_SY2337 @ SV847 @ SV422 @ SV193 )
= SY3303 ) ) ) )
= $true )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV422 @ ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4358]) ).
thf(4394,plain,
! [SV422: $i > $o,SV847: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK147_SY2337 @ SV847 @ SV422 @ SV193 ) )
| ~ ! [SY3297: $i] :
( ~ ( SV193 @ SY3297 )
| ( ( sK147_SY2337 @ SV847 @ SV422 @ SV193 )
= SY3297 ) ) )
= $false )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV847
= ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4359]) ).
thf(4395,plain,
! [SV193: $i > $o,SV841: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK148_SY2770 @ SV841 @ SV193 @ SV422 ) )
| ~ ! [SY3298: $i] :
( ~ ( SV422 @ SY3298 )
| ( ( sK148_SY2770 @ SV841 @ SV193 @ SV422 )
= SY3298 ) ) )
= $false )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV193 @ ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4360]) ).
thf(4396,plain,
! [SV193: $i > $o,SV841: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK140_SY2770 @ SV841 @ SV193 @ SV422 ) ) )
= $false )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV841
= ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4361]) ).
thf(4397,plain,
! [SV193: $i > $o,SV841: $i,SV422: $i > $o] :
( ( ( ~ ! [SY3289: $i] :
( ~ ( SV422 @ SY3289 )
| ( ( sK140_SY2770 @ SV841 @ SV193 @ SV422 )
= SY3289 ) ) )
= $false )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV841
= ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4361]) ).
thf(4398,plain,
! [SV422: $i > $o,SV842: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK149_SY2337 @ SV842 @ SV422 @ SV193 ) )
| ~ ! [SY3299: $i] :
( ~ ( SV193 @ SY3299 )
| ( ( sK149_SY2337 @ SV842 @ SV422 @ SV193 )
= SY3299 ) ) )
= $false )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV422 @ ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4362]) ).
thf(4399,plain,
! [SV422: $i > $o,SV842: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK141_SY2337 @ SV842 @ SV422 @ SV193 ) ) )
= $false )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV842
= ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4363]) ).
thf(4400,plain,
! [SV422: $i > $o,SV842: $i,SV193: $i > $o] :
( ( ( ~ ! [SY3290: $i] :
( ~ ( SV193 @ SY3290 )
| ( ( sK141_SY2337 @ SV842 @ SV422 @ SV193 )
= SY3290 ) ) )
= $false )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV842
= ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4363]) ).
thf(4401,plain,
! [SV193: $i > $o,SV843: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK150_SY2770 @ SV843 @ SV193 @ SV422 ) )
| ~ ! [SY3300: $i] :
( ~ ( SV422 @ SY3300 )
| ( ( sK150_SY2770 @ SV843 @ SV193 @ SV422 )
= SY3300 ) ) )
= $false )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV193 @ ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4364]) ).
thf(4402,plain,
! [SV193: $i > $o,SV843: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK142_SY2770 @ SV843 @ SV193 @ SV422 ) ) )
= $false )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV843
= ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4365]) ).
thf(4403,plain,
! [SV193: $i > $o,SV843: $i,SV422: $i > $o] :
( ( ( ~ ! [SY3291: $i] :
( ~ ( SV422 @ SY3291 )
| ( ( sK142_SY2770 @ SV843 @ SV193 @ SV422 )
= SY3291 ) ) )
= $false )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV843
= ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4365]) ).
thf(4404,plain,
! [SV422: $i > $o,SV844: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK151_SY2337 @ SV844 @ SV422 @ SV193 ) )
| ~ ! [SY3301: $i] :
( ~ ( SV193 @ SY3301 )
| ( ( sK151_SY2337 @ SV844 @ SV422 @ SV193 )
= SY3301 ) ) )
= $false )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV422 @ ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4366]) ).
thf(4405,plain,
! [SV422: $i > $o,SV844: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK143_SY2337 @ SV844 @ SV422 @ SV193 ) ) )
= $false )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV844
= ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4367]) ).
thf(4406,plain,
! [SV422: $i > $o,SV844: $i,SV193: $i > $o] :
( ( ( ~ ! [SY3292: $i] :
( ~ ( SV193 @ SY3292 )
| ( ( sK143_SY2337 @ SV844 @ SV422 @ SV193 )
= SY3292 ) ) )
= $false )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV844
= ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4367]) ).
thf(4407,plain,
! [SV193: $i > $o,SV836: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK144_SY2770 @ SV836 @ SV193 @ SV422 ) ) )
= $false )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV193 @ ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4368]) ).
thf(4408,plain,
! [SV193: $i > $o,SV836: $i,SV422: $i > $o] :
( ( ( ~ ! [SY3293: $i] :
( ~ ( SV422 @ SY3293 )
| ( ( sK144_SY2770 @ SV836 @ SV193 @ SV422 )
= SY3293 ) ) )
= $false )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV193 @ ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4368]) ).
thf(4409,plain,
! [SV193: $i > $o,SV836: $i,SV422: $i > $o] :
( ( ( SV422 @ ( sK137_SY2770 @ SV836 @ SV193 @ SV422 ) )
= $true )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV836
= ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4369]) ).
thf(4410,plain,
! [SV193: $i > $o,SV836: $i,SV422: $i > $o] :
( ( ( ! [SY3283: $i] :
( ~ ( SV422 @ SY3283 )
| ( ( sK137_SY2770 @ SV836 @ SV193 @ SV422 )
= SY3283 ) ) )
= $true )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV836
= ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4370]) ).
thf(4411,plain,
! [SV422: $i > $o,SV837: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK145_SY2337 @ SV837 @ SV422 @ SV193 ) ) )
= $false )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV422 @ ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4371]) ).
thf(4412,plain,
! [SV422: $i > $o,SV837: $i,SV193: $i > $o] :
( ( ( ~ ! [SY3294: $i] :
( ~ ( SV193 @ SY3294 )
| ( ( sK145_SY2337 @ SV837 @ SV422 @ SV193 )
= SY3294 ) ) )
= $false )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV422 @ ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4371]) ).
thf(4413,plain,
! [SV422: $i > $o,SV837: $i,SV193: $i > $o] :
( ( ( SV193 @ ( sK138_SY2337 @ SV837 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV837
= ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4372]) ).
thf(4414,plain,
! [SV422: $i > $o,SV837: $i,SV193: $i > $o] :
( ( ( ! [SY3284: $i] :
( ~ ( SV193 @ SY3284 )
| ( ( sK138_SY2337 @ SV837 @ SV422 @ SV193 )
= SY3284 ) ) )
= $true )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV837
= ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4373]) ).
thf(4415,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( ~ ( in @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4376]) ).
thf(4416,plain,
! [SV825: $i,SV747: $i,SV147: $i] :
( ( ( ~ ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SV747 ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4376]) ).
thf(4417,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( ! [SY3261: $i] :
~ ~ ( ~ ( in @ SY3261 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
| ~ ( in @ SY3261 @ SV747 ) ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4377]) ).
thf(4418,plain,
! [SV147: $i,SV747: $i,SV825: $i,SV860: $i,SV868: $i] :
( ( ( ~ ( in @ SV868 @ SV860 )
| ( in @ SV868 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) ) )
= $true )
| ( ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SV860 )
= $true )
| ( ( in @ SV860 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4378]) ).
thf(4419,plain,
! [SV147: $i,SV747: $i,SV820: $i] :
( ( ( in @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4379]) ).
thf(4420,plain,
! [SV820: $i,SV747: $i,SV147: $i] :
( ( ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SV747 )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4380]) ).
thf(4421,plain,
! [SV147: $i,SV747: $i,SV820: $i,SV869: $i] :
( ( ( ~ ~ ( ~ ( in @ SV869 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
| ~ ( in @ SV869 @ SV747 ) ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4381]) ).
thf(4422,plain,
! [SV147: $i,SV747: $i,SV820: $i,SV854: $i,SV867: $i] :
( ( ( ~ ( in @ SV867 @ SV854 ) )
= $true )
| ( ( in @ SV867 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
= $true )
| ( ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SV854 )
= $true )
| ( ( in @ SV854 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4382]) ).
thf(4423,plain,
! [SV828: $i,SV183: $i > $o,SV866: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV866 ) )
= $true )
| ( ( ~ ! [SY3295: $i] :
( ~ ( SV411 @ SY3295 )
| ( SV866 = SY3295 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV183 @ ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4383]) ).
thf(4424,plain,
! [SV828: $i,SV183: $i > $o,SV861: $i,SV411: $i > $o] :
( ( ( SV411 @ SV861 )
= $false )
| ( ( ~ ! [SY3286: $i] :
( ~ ( SV411 @ SY3286 )
| ( SV861 = SY3286 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV828
= ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4384]) ).
thf(4425,plain,
! [SV821: $i,SV183: $i > $o,SV862: $i,SV411: $i > $o] :
( ( ( SV411 @ SV862 )
= $false )
| ( ( ~ ! [SY3287: $i] :
( ~ ( SV411 @ SY3287 )
| ( SV862 = SY3287 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV183 @ ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4385]) ).
thf(4426,plain,
! [SV821: $i,SV183: $i > $o,SV855: $i,SV411: $i > $o] :
( ( ( ! [SY3280: $i] :
( ~ ( SV411 @ SY3280 )
| ( SV855 = SY3280 ) ) )
= $false )
| ( ( SV411 @ SV855 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV821
= ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4386]) ).
thf(4427,plain,
! [SV822: $i,SV183: $i > $o,SV863: $i,SV411: $i > $o] :
( ( ( SV411 @ SV863 )
= $false )
| ( ( ~ ! [SY3288: $i] :
( ~ ( SV411 @ SY3288 )
| ( SV863 = SY3288 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV183 @ ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4387]) ).
thf(4428,plain,
! [SV822: $i,SV183: $i > $o,SV856: $i,SV411: $i > $o] :
( ( ( ! [SY3281: $i] :
( ~ ( SV411 @ SY3281 )
| ( SV856 = SY3281 ) ) )
= $false )
| ( ( SV411 @ SV856 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV822
= ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4388]) ).
thf(4429,plain,
! [SV817: $i,SV183: $i > $o,SV857: $i,SV411: $i > $o] :
( ( ( ! [SY3282: $i] :
( ~ ( SV411 @ SY3282 )
| ( SV857 = SY3282 ) ) )
= $false )
| ( ( SV411 @ SV857 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV183 @ ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4389]) ).
thf(4430,plain,
! [SV853: $i,SV183: $i > $o,SV817: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK154_SY3278 @ SV817 @ SV183 @ SV853 @ SV411 ) )
| ( SV853
= ( sK154_SY3278 @ SV817 @ SV183 @ SV853 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV853 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV817
= ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4390]) ).
thf(4431,plain,
! [SV193: $i > $o,SV846: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK152_SY2770 @ SV846 @ SV193 @ SV422 ) )
| ~ ! [SY3302: $i] :
( ~ ( SV422 @ SY3302 )
| ( ( sK152_SY2770 @ SV846 @ SV193 @ SV422 )
= SY3302 ) ) )
= $false )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV193 @ ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4391]) ).
thf(4432,plain,
! [SV193: $i > $o,SV846: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK146_SY2770 @ SV846 @ SV193 @ SV422 ) ) )
= $false )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV846
= ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4392]) ).
thf(4433,plain,
! [SV193: $i > $o,SV846: $i,SV422: $i > $o] :
( ( ( ~ ! [SY3296: $i] :
( ~ ( SV422 @ SY3296 )
| ( ( sK146_SY2770 @ SV846 @ SV193 @ SV422 )
= SY3296 ) ) )
= $false )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV846
= ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4392]) ).
thf(4434,plain,
! [SV422: $i > $o,SV847: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK153_SY2337 @ SV847 @ SV422 @ SV193 ) )
| ~ ! [SY3303: $i] :
( ~ ( SV193 @ SY3303 )
| ( ( sK153_SY2337 @ SV847 @ SV422 @ SV193 )
= SY3303 ) ) )
= $false )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV422 @ ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4393]) ).
thf(4435,plain,
! [SV422: $i > $o,SV847: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK147_SY2337 @ SV847 @ SV422 @ SV193 ) ) )
= $false )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV847
= ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4394]) ).
thf(4436,plain,
! [SV422: $i > $o,SV847: $i,SV193: $i > $o] :
( ( ( ~ ! [SY3297: $i] :
( ~ ( SV193 @ SY3297 )
| ( ( sK147_SY2337 @ SV847 @ SV422 @ SV193 )
= SY3297 ) ) )
= $false )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV847
= ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4394]) ).
thf(4437,plain,
! [SV193: $i > $o,SV841: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK148_SY2770 @ SV841 @ SV193 @ SV422 ) ) )
= $false )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV193 @ ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4395]) ).
thf(4438,plain,
! [SV193: $i > $o,SV841: $i,SV422: $i > $o] :
( ( ( ~ ! [SY3298: $i] :
( ~ ( SV422 @ SY3298 )
| ( ( sK148_SY2770 @ SV841 @ SV193 @ SV422 )
= SY3298 ) ) )
= $false )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV193 @ ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4395]) ).
thf(4439,plain,
! [SV193: $i > $o,SV841: $i,SV422: $i > $o] :
( ( ( SV422 @ ( sK140_SY2770 @ SV841 @ SV193 @ SV422 ) )
= $true )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV841
= ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4396]) ).
thf(4440,plain,
! [SV193: $i > $o,SV841: $i,SV422: $i > $o] :
( ( ( ! [SY3289: $i] :
( ~ ( SV422 @ SY3289 )
| ( ( sK140_SY2770 @ SV841 @ SV193 @ SV422 )
= SY3289 ) ) )
= $true )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV841
= ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4397]) ).
thf(4441,plain,
! [SV422: $i > $o,SV842: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK149_SY2337 @ SV842 @ SV422 @ SV193 ) ) )
= $false )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV422 @ ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4398]) ).
thf(4442,plain,
! [SV422: $i > $o,SV842: $i,SV193: $i > $o] :
( ( ( ~ ! [SY3299: $i] :
( ~ ( SV193 @ SY3299 )
| ( ( sK149_SY2337 @ SV842 @ SV422 @ SV193 )
= SY3299 ) ) )
= $false )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV422 @ ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4398]) ).
thf(4443,plain,
! [SV422: $i > $o,SV842: $i,SV193: $i > $o] :
( ( ( SV193 @ ( sK141_SY2337 @ SV842 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV842
= ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4399]) ).
thf(4444,plain,
! [SV422: $i > $o,SV842: $i,SV193: $i > $o] :
( ( ( ! [SY3290: $i] :
( ~ ( SV193 @ SY3290 )
| ( ( sK141_SY2337 @ SV842 @ SV422 @ SV193 )
= SY3290 ) ) )
= $true )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV842
= ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4400]) ).
thf(4445,plain,
! [SV193: $i > $o,SV843: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK150_SY2770 @ SV843 @ SV193 @ SV422 ) ) )
= $false )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV193 @ ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4401]) ).
thf(4446,plain,
! [SV193: $i > $o,SV843: $i,SV422: $i > $o] :
( ( ( ~ ! [SY3300: $i] :
( ~ ( SV422 @ SY3300 )
| ( ( sK150_SY2770 @ SV843 @ SV193 @ SV422 )
= SY3300 ) ) )
= $false )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV193 @ ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4401]) ).
thf(4447,plain,
! [SV193: $i > $o,SV843: $i,SV422: $i > $o] :
( ( ( SV422 @ ( sK142_SY2770 @ SV843 @ SV193 @ SV422 ) )
= $true )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV843
= ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4402]) ).
thf(4448,plain,
! [SV193: $i > $o,SV843: $i,SV422: $i > $o] :
( ( ( ! [SY3291: $i] :
( ~ ( SV422 @ SY3291 )
| ( ( sK142_SY2770 @ SV843 @ SV193 @ SV422 )
= SY3291 ) ) )
= $true )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV843
= ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4403]) ).
thf(4449,plain,
! [SV422: $i > $o,SV844: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK151_SY2337 @ SV844 @ SV422 @ SV193 ) ) )
= $false )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV422 @ ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4404]) ).
thf(4450,plain,
! [SV422: $i > $o,SV844: $i,SV193: $i > $o] :
( ( ( ~ ! [SY3301: $i] :
( ~ ( SV193 @ SY3301 )
| ( ( sK151_SY2337 @ SV844 @ SV422 @ SV193 )
= SY3301 ) ) )
= $false )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV422 @ ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4404]) ).
thf(4451,plain,
! [SV422: $i > $o,SV844: $i,SV193: $i > $o] :
( ( ( SV193 @ ( sK143_SY2337 @ SV844 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV844
= ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4405]) ).
thf(4452,plain,
! [SV422: $i > $o,SV844: $i,SV193: $i > $o] :
( ( ( ! [SY3292: $i] :
( ~ ( SV193 @ SY3292 )
| ( ( sK143_SY2337 @ SV844 @ SV422 @ SV193 )
= SY3292 ) ) )
= $true )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV844
= ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4406]) ).
thf(4453,plain,
! [SV193: $i > $o,SV836: $i,SV422: $i > $o] :
( ( ( SV422 @ ( sK144_SY2770 @ SV836 @ SV193 @ SV422 ) )
= $true )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV193 @ ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4407]) ).
thf(4454,plain,
! [SV193: $i > $o,SV836: $i,SV422: $i > $o] :
( ( ( ! [SY3293: $i] :
( ~ ( SV422 @ SY3293 )
| ( ( sK144_SY2770 @ SV836 @ SV193 @ SV422 )
= SY3293 ) ) )
= $true )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV193 @ ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4408]) ).
thf(4455,plain,
! [SV193: $i > $o,SV836: $i,SV870: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV870 )
| ( ( sK137_SY2770 @ SV836 @ SV193 @ SV422 )
= SV870 ) )
= $true )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV836
= ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4410]) ).
thf(4456,plain,
! [SV422: $i > $o,SV837: $i,SV193: $i > $o] :
( ( ( SV193 @ ( sK145_SY2337 @ SV837 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV422 @ ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4411]) ).
thf(4457,plain,
! [SV422: $i > $o,SV837: $i,SV193: $i > $o] :
( ( ( ! [SY3294: $i] :
( ~ ( SV193 @ SY3294 )
| ( ( sK145_SY2337 @ SV837 @ SV422 @ SV193 )
= SY3294 ) ) )
= $true )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV422 @ ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4412]) ).
thf(4458,plain,
! [SV422: $i > $o,SV837: $i,SV871: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV871 )
| ( ( sK138_SY2337 @ SV837 @ SV422 @ SV193 )
= SV871 ) )
= $true )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV837
= ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4414]) ).
thf(4459,plain,
! [SV147: $i,SV747: $i,SV825: $i] :
( ( ( in @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) @ ( sK3_SY2186 @ SV147 ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4415]) ).
thf(4460,plain,
! [SV825: $i,SV747: $i,SV147: $i] :
( ( ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SV747 )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4416]) ).
thf(4461,plain,
! [SV147: $i,SV747: $i,SV825: $i,SV872: $i] :
( ( ( ~ ~ ( ~ ( in @ SV872 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
| ~ ( in @ SV872 @ SV747 ) ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4417]) ).
thf(4462,plain,
! [SV147: $i,SV747: $i,SV825: $i,SV860: $i,SV868: $i] :
( ( ( ~ ( in @ SV868 @ SV860 ) )
= $true )
| ( ( in @ SV868 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
= $true )
| ( ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SV860 )
= $true )
| ( ( in @ SV860 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4418]) ).
thf(4463,plain,
! [SV147: $i,SV747: $i,SV820: $i,SV869: $i] :
( ( ( ~ ( ~ ( in @ SV869 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
| ~ ( in @ SV869 @ SV747 ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4421]) ).
thf(4464,plain,
! [SV147: $i,SV747: $i,SV820: $i,SV854: $i,SV867: $i] :
( ( ( in @ SV867 @ SV854 )
= $false )
| ( ( in @ SV867 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
= $true )
| ( ( in @ ( sK117_SY3252 @ SV147 @ SV747 @ SV820 ) @ SV854 )
= $true )
| ( ( in @ SV854 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4422]) ).
thf(4465,plain,
! [SV828: $i,SV183: $i > $o,SV866: $i,SV411: $i > $o] :
( ( ( SV411 @ SV866 )
= $false )
| ( ( ~ ! [SY3295: $i] :
( ~ ( SV411 @ SY3295 )
| ( SV866 = SY3295 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV183 @ ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4423]) ).
thf(4466,plain,
! [SV828: $i,SV183: $i > $o,SV861: $i,SV411: $i > $o] :
( ( ( ! [SY3286: $i] :
( ~ ( SV411 @ SY3286 )
| ( SV861 = SY3286 ) ) )
= $false )
| ( ( SV411 @ SV861 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV828
= ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4424]) ).
thf(4467,plain,
! [SV821: $i,SV183: $i > $o,SV862: $i,SV411: $i > $o] :
( ( ( ! [SY3287: $i] :
( ~ ( SV411 @ SY3287 )
| ( SV862 = SY3287 ) ) )
= $false )
| ( ( SV411 @ SV862 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV183 @ ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4425]) ).
thf(4468,plain,
! [SV855: $i,SV183: $i > $o,SV821: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK155_SY3280 @ SV821 @ SV183 @ SV855 @ SV411 ) )
| ( SV855
= ( sK155_SY3280 @ SV821 @ SV183 @ SV855 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV855 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV821
= ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4426]) ).
thf(4469,plain,
! [SV822: $i,SV183: $i > $o,SV863: $i,SV411: $i > $o] :
( ( ( ! [SY3288: $i] :
( ~ ( SV411 @ SY3288 )
| ( SV863 = SY3288 ) ) )
= $false )
| ( ( SV411 @ SV863 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV183 @ ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4427]) ).
thf(4470,plain,
! [SV856: $i,SV183: $i > $o,SV822: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK156_SY3281 @ SV822 @ SV183 @ SV856 @ SV411 ) )
| ( SV856
= ( sK156_SY3281 @ SV822 @ SV183 @ SV856 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV856 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV822
= ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4428]) ).
thf(4471,plain,
! [SV857: $i,SV183: $i > $o,SV817: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK157_SY3282 @ SV817 @ SV183 @ SV857 @ SV411 ) )
| ( SV857
= ( sK157_SY3282 @ SV817 @ SV183 @ SV857 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV857 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV183 @ ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4429]) ).
thf(4472,plain,
! [SV853: $i,SV183: $i > $o,SV817: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK154_SY3278 @ SV817 @ SV183 @ SV853 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV853 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV817
= ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4430]) ).
thf(4473,plain,
! [SV411: $i > $o,SV183: $i > $o,SV817: $i,SV853: $i] :
( ( ( SV853
= ( sK154_SY3278 @ SV817 @ SV183 @ SV853 @ SV411 ) )
= $false )
| ( ( SV411 @ SV853 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV817
= ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4430]) ).
thf(4474,plain,
! [SV193: $i > $o,SV846: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ ( sK152_SY2770 @ SV846 @ SV193 @ SV422 ) ) )
= $false )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV193 @ ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4431]) ).
thf(4475,plain,
! [SV193: $i > $o,SV846: $i,SV422: $i > $o] :
( ( ( ~ ! [SY3302: $i] :
( ~ ( SV422 @ SY3302 )
| ( ( sK152_SY2770 @ SV846 @ SV193 @ SV422 )
= SY3302 ) ) )
= $false )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV193 @ ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4431]) ).
thf(4476,plain,
! [SV193: $i > $o,SV846: $i,SV422: $i > $o] :
( ( ( SV422 @ ( sK146_SY2770 @ SV846 @ SV193 @ SV422 ) )
= $true )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV846
= ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4432]) ).
thf(4477,plain,
! [SV193: $i > $o,SV846: $i,SV422: $i > $o] :
( ( ( ! [SY3296: $i] :
( ~ ( SV422 @ SY3296 )
| ( ( sK146_SY2770 @ SV846 @ SV193 @ SV422 )
= SY3296 ) ) )
= $true )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV846
= ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4433]) ).
thf(4478,plain,
! [SV422: $i > $o,SV847: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK153_SY2337 @ SV847 @ SV422 @ SV193 ) ) )
= $false )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV422 @ ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4434]) ).
thf(4479,plain,
! [SV422: $i > $o,SV847: $i,SV193: $i > $o] :
( ( ( ~ ! [SY3303: $i] :
( ~ ( SV193 @ SY3303 )
| ( ( sK153_SY2337 @ SV847 @ SV422 @ SV193 )
= SY3303 ) ) )
= $false )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV422 @ ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4434]) ).
thf(4480,plain,
! [SV422: $i > $o,SV847: $i,SV193: $i > $o] :
( ( ( SV193 @ ( sK147_SY2337 @ SV847 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV847
= ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4435]) ).
thf(4481,plain,
! [SV422: $i > $o,SV847: $i,SV193: $i > $o] :
( ( ( ! [SY3297: $i] :
( ~ ( SV193 @ SY3297 )
| ( ( sK147_SY2337 @ SV847 @ SV422 @ SV193 )
= SY3297 ) ) )
= $true )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV847
= ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4436]) ).
thf(4482,plain,
! [SV193: $i > $o,SV841: $i,SV422: $i > $o] :
( ( ( SV422 @ ( sK148_SY2770 @ SV841 @ SV193 @ SV422 ) )
= $true )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV193 @ ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4437]) ).
thf(4483,plain,
! [SV193: $i > $o,SV841: $i,SV422: $i > $o] :
( ( ( ! [SY3298: $i] :
( ~ ( SV422 @ SY3298 )
| ( ( sK148_SY2770 @ SV841 @ SV193 @ SV422 )
= SY3298 ) ) )
= $true )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV193 @ ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4438]) ).
thf(4484,plain,
! [SV193: $i > $o,SV841: $i,SV873: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV873 )
| ( ( sK140_SY2770 @ SV841 @ SV193 @ SV422 )
= SV873 ) )
= $true )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV841
= ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4440]) ).
thf(4485,plain,
! [SV422: $i > $o,SV842: $i,SV193: $i > $o] :
( ( ( SV193 @ ( sK149_SY2337 @ SV842 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV422 @ ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4441]) ).
thf(4486,plain,
! [SV422: $i > $o,SV842: $i,SV193: $i > $o] :
( ( ( ! [SY3299: $i] :
( ~ ( SV193 @ SY3299 )
| ( ( sK149_SY2337 @ SV842 @ SV422 @ SV193 )
= SY3299 ) ) )
= $true )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV422 @ ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4442]) ).
thf(4487,plain,
! [SV422: $i > $o,SV842: $i,SV874: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV874 )
| ( ( sK141_SY2337 @ SV842 @ SV422 @ SV193 )
= SV874 ) )
= $true )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV842
= ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4444]) ).
thf(4488,plain,
! [SV193: $i > $o,SV843: $i,SV422: $i > $o] :
( ( ( SV422 @ ( sK150_SY2770 @ SV843 @ SV193 @ SV422 ) )
= $true )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV193 @ ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4445]) ).
thf(4489,plain,
! [SV193: $i > $o,SV843: $i,SV422: $i > $o] :
( ( ( ! [SY3300: $i] :
( ~ ( SV422 @ SY3300 )
| ( ( sK150_SY2770 @ SV843 @ SV193 @ SV422 )
= SY3300 ) ) )
= $true )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV193 @ ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4446]) ).
thf(4490,plain,
! [SV193: $i > $o,SV843: $i,SV875: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV875 )
| ( ( sK142_SY2770 @ SV843 @ SV193 @ SV422 )
= SV875 ) )
= $true )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV843
= ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4448]) ).
thf(4491,plain,
! [SV422: $i > $o,SV844: $i,SV193: $i > $o] :
( ( ( SV193 @ ( sK151_SY2337 @ SV844 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV422 @ ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4449]) ).
thf(4492,plain,
! [SV422: $i > $o,SV844: $i,SV193: $i > $o] :
( ( ( ! [SY3301: $i] :
( ~ ( SV193 @ SY3301 )
| ( ( sK151_SY2337 @ SV844 @ SV422 @ SV193 )
= SY3301 ) ) )
= $true )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV422 @ ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4450]) ).
thf(4493,plain,
! [SV422: $i > $o,SV844: $i,SV876: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV876 )
| ( ( sK143_SY2337 @ SV844 @ SV422 @ SV193 )
= SV876 ) )
= $true )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV844
= ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4452]) ).
thf(4494,plain,
! [SV193: $i > $o,SV836: $i,SV877: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV877 )
| ( ( sK144_SY2770 @ SV836 @ SV193 @ SV422 )
= SV877 ) )
= $true )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV193 @ ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4454]) ).
thf(4495,plain,
! [SV193: $i > $o,SV836: $i,SV870: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV870 ) )
= $true )
| ( ( ( sK137_SY2770 @ SV836 @ SV193 @ SV422 )
= SV870 )
= $true )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV836
= ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4455]) ).
thf(4496,plain,
! [SV422: $i > $o,SV837: $i,SV878: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV878 )
| ( ( sK145_SY2337 @ SV837 @ SV422 @ SV193 )
= SV878 ) )
= $true )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV422 @ ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4457]) ).
thf(4497,plain,
! [SV422: $i > $o,SV837: $i,SV871: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV871 ) )
= $true )
| ( ( ( sK138_SY2337 @ SV837 @ SV422 @ SV193 )
= SV871 )
= $true )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV837
= ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4458]) ).
thf(4498,plain,
! [SV147: $i,SV747: $i,SV825: $i,SV872: $i] :
( ( ( ~ ( ~ ( in @ SV872 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
| ~ ( in @ SV872 @ SV747 ) ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4461]) ).
thf(4499,plain,
! [SV147: $i,SV747: $i,SV825: $i,SV860: $i,SV868: $i] :
( ( ( in @ SV868 @ SV860 )
= $false )
| ( ( in @ SV868 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
= $true )
| ( ( in @ ( sK122_SY3260 @ SV147 @ SV747 @ SV825 ) @ SV860 )
= $true )
| ( ( in @ SV860 @ ( sK3_SY2186 @ SV147 ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4462]) ).
thf(4500,plain,
! [SV147: $i,SV747: $i,SV820: $i,SV869: $i] :
( ( ( ~ ( in @ SV869 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
| ~ ( in @ SV869 @ SV747 ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4463]) ).
thf(4501,plain,
! [SV828: $i,SV183: $i > $o,SV866: $i,SV411: $i > $o] :
( ( ( ! [SY3295: $i] :
( ~ ( SV411 @ SY3295 )
| ( SV866 = SY3295 ) ) )
= $false )
| ( ( SV411 @ SV866 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV183 @ ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4465]) ).
thf(4502,plain,
! [SV861: $i,SV183: $i > $o,SV828: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK158_SY3286 @ SV828 @ SV183 @ SV861 @ SV411 ) )
| ( SV861
= ( sK158_SY3286 @ SV828 @ SV183 @ SV861 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV861 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV828
= ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4466]) ).
thf(4503,plain,
! [SV862: $i,SV183: $i > $o,SV821: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK159_SY3287 @ SV821 @ SV183 @ SV862 @ SV411 ) )
| ( SV862
= ( sK159_SY3287 @ SV821 @ SV183 @ SV862 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV862 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV183 @ ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4467]) ).
thf(4504,plain,
! [SV855: $i,SV183: $i > $o,SV821: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK155_SY3280 @ SV821 @ SV183 @ SV855 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV855 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV821
= ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4468]) ).
thf(4505,plain,
! [SV411: $i > $o,SV183: $i > $o,SV821: $i,SV855: $i] :
( ( ( SV855
= ( sK155_SY3280 @ SV821 @ SV183 @ SV855 @ SV411 ) )
= $false )
| ( ( SV411 @ SV855 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV821
= ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4468]) ).
thf(4506,plain,
! [SV863: $i,SV183: $i > $o,SV822: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK160_SY3288 @ SV822 @ SV183 @ SV863 @ SV411 ) )
| ( SV863
= ( sK160_SY3288 @ SV822 @ SV183 @ SV863 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV863 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV183 @ ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4469]) ).
thf(4507,plain,
! [SV856: $i,SV183: $i > $o,SV822: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK156_SY3281 @ SV822 @ SV183 @ SV856 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV856 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV822
= ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4470]) ).
thf(4508,plain,
! [SV411: $i > $o,SV183: $i > $o,SV822: $i,SV856: $i] :
( ( ( SV856
= ( sK156_SY3281 @ SV822 @ SV183 @ SV856 @ SV411 ) )
= $false )
| ( ( SV411 @ SV856 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV822
= ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4470]) ).
thf(4509,plain,
! [SV857: $i,SV183: $i > $o,SV817: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK157_SY3282 @ SV817 @ SV183 @ SV857 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV857 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV183 @ ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4471]) ).
thf(4510,plain,
! [SV411: $i > $o,SV183: $i > $o,SV817: $i,SV857: $i] :
( ( ( SV857
= ( sK157_SY3282 @ SV817 @ SV183 @ SV857 @ SV411 ) )
= $false )
| ( ( SV411 @ SV857 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV183 @ ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4471]) ).
thf(4511,plain,
! [SV853: $i,SV183: $i > $o,SV817: $i,SV411: $i > $o] :
( ( ( SV411 @ ( sK154_SY3278 @ SV817 @ SV183 @ SV853 @ SV411 ) )
= $true )
| ( ( SV411 @ SV853 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV817
= ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4472]) ).
thf(4512,plain,
! [SV193: $i > $o,SV846: $i,SV422: $i > $o] :
( ( ( SV422 @ ( sK152_SY2770 @ SV846 @ SV193 @ SV422 ) )
= $true )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV193 @ ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4474]) ).
thf(4513,plain,
! [SV193: $i > $o,SV846: $i,SV422: $i > $o] :
( ( ( ! [SY3302: $i] :
( ~ ( SV422 @ SY3302 )
| ( ( sK152_SY2770 @ SV846 @ SV193 @ SV422 )
= SY3302 ) ) )
= $true )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV193 @ ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4475]) ).
thf(4514,plain,
! [SV193: $i > $o,SV846: $i,SV879: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV879 )
| ( ( sK146_SY2770 @ SV846 @ SV193 @ SV422 )
= SV879 ) )
= $true )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV846
= ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4477]) ).
thf(4515,plain,
! [SV422: $i > $o,SV847: $i,SV193: $i > $o] :
( ( ( SV193 @ ( sK153_SY2337 @ SV847 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV422 @ ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4478]) ).
thf(4516,plain,
! [SV422: $i > $o,SV847: $i,SV193: $i > $o] :
( ( ( ! [SY3303: $i] :
( ~ ( SV193 @ SY3303 )
| ( ( sK153_SY2337 @ SV847 @ SV422 @ SV193 )
= SY3303 ) ) )
= $true )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV422 @ ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4479]) ).
thf(4517,plain,
! [SV422: $i > $o,SV847: $i,SV880: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV880 )
| ( ( sK147_SY2337 @ SV847 @ SV422 @ SV193 )
= SV880 ) )
= $true )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV847
= ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4481]) ).
thf(4518,plain,
! [SV193: $i > $o,SV841: $i,SV881: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV881 )
| ( ( sK148_SY2770 @ SV841 @ SV193 @ SV422 )
= SV881 ) )
= $true )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV193 @ ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4483]) ).
thf(4519,plain,
! [SV193: $i > $o,SV841: $i,SV873: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV873 ) )
= $true )
| ( ( ( sK140_SY2770 @ SV841 @ SV193 @ SV422 )
= SV873 )
= $true )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV841
= ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4484]) ).
thf(4520,plain,
! [SV422: $i > $o,SV842: $i,SV882: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV882 )
| ( ( sK149_SY2337 @ SV842 @ SV422 @ SV193 )
= SV882 ) )
= $true )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV422 @ ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4486]) ).
thf(4521,plain,
! [SV422: $i > $o,SV842: $i,SV874: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV874 ) )
= $true )
| ( ( ( sK141_SY2337 @ SV842 @ SV422 @ SV193 )
= SV874 )
= $true )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV842
= ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4487]) ).
thf(4522,plain,
! [SV193: $i > $o,SV843: $i,SV883: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV883 )
| ( ( sK150_SY2770 @ SV843 @ SV193 @ SV422 )
= SV883 ) )
= $true )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV193 @ ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4489]) ).
thf(4523,plain,
! [SV193: $i > $o,SV843: $i,SV875: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV875 ) )
= $true )
| ( ( ( sK142_SY2770 @ SV843 @ SV193 @ SV422 )
= SV875 )
= $true )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV843
= ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4490]) ).
thf(4524,plain,
! [SV422: $i > $o,SV844: $i,SV884: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV884 )
| ( ( sK151_SY2337 @ SV844 @ SV422 @ SV193 )
= SV884 ) )
= $true )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV422 @ ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4492]) ).
thf(4525,plain,
! [SV422: $i > $o,SV844: $i,SV876: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV876 ) )
= $true )
| ( ( ( sK143_SY2337 @ SV844 @ SV422 @ SV193 )
= SV876 )
= $true )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV844
= ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4493]) ).
thf(4526,plain,
! [SV193: $i > $o,SV836: $i,SV877: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV877 ) )
= $true )
| ( ( ( sK144_SY2770 @ SV836 @ SV193 @ SV422 )
= SV877 )
= $true )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV193 @ ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4494]) ).
thf(4527,plain,
! [SV193: $i > $o,SV836: $i,SV870: $i,SV422: $i > $o] :
( ( ( SV422 @ SV870 )
= $false )
| ( ( ( sK137_SY2770 @ SV836 @ SV193 @ SV422 )
= SV870 )
= $true )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV836
= ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4495]) ).
thf(4528,plain,
! [SV422: $i > $o,SV837: $i,SV878: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV878 ) )
= $true )
| ( ( ( sK145_SY2337 @ SV837 @ SV422 @ SV193 )
= SV878 )
= $true )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV422 @ ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4496]) ).
thf(4529,plain,
! [SV422: $i > $o,SV837: $i,SV871: $i,SV193: $i > $o] :
( ( ( SV193 @ SV871 )
= $false )
| ( ( ( sK138_SY2337 @ SV837 @ SV422 @ SV193 )
= SV871 )
= $true )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV837
= ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4497]) ).
thf(4530,plain,
! [SV147: $i,SV747: $i,SV825: $i,SV872: $i] :
( ( ( ~ ( in @ SV872 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
| ~ ( in @ SV872 @ SV747 ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4498]) ).
thf(4531,plain,
! [SV147: $i,SV747: $i,SV820: $i,SV869: $i] :
( ( ( ~ ( in @ SV869 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) ) )
= $true )
| ( ( ~ ( in @ SV869 @ SV747 ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4500]) ).
thf(4532,plain,
! [SV866: $i,SV183: $i > $o,SV828: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK161_SY3295 @ SV828 @ SV183 @ SV866 @ SV411 ) )
| ( SV866
= ( sK161_SY3295 @ SV828 @ SV183 @ SV866 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV866 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV183 @ ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4501]) ).
thf(4533,plain,
! [SV861: $i,SV183: $i > $o,SV828: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK158_SY3286 @ SV828 @ SV183 @ SV861 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV861 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV828
= ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4502]) ).
thf(4534,plain,
! [SV411: $i > $o,SV183: $i > $o,SV828: $i,SV861: $i] :
( ( ( SV861
= ( sK158_SY3286 @ SV828 @ SV183 @ SV861 @ SV411 ) )
= $false )
| ( ( SV411 @ SV861 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV828
= ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4502]) ).
thf(4535,plain,
! [SV862: $i,SV183: $i > $o,SV821: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK159_SY3287 @ SV821 @ SV183 @ SV862 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV862 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV183 @ ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4503]) ).
thf(4536,plain,
! [SV411: $i > $o,SV183: $i > $o,SV821: $i,SV862: $i] :
( ( ( SV862
= ( sK159_SY3287 @ SV821 @ SV183 @ SV862 @ SV411 ) )
= $false )
| ( ( SV411 @ SV862 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV183 @ ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4503]) ).
thf(4537,plain,
! [SV855: $i,SV183: $i > $o,SV821: $i,SV411: $i > $o] :
( ( ( SV411 @ ( sK155_SY3280 @ SV821 @ SV183 @ SV855 @ SV411 ) )
= $true )
| ( ( SV411 @ SV855 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV821
= ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4504]) ).
thf(4538,plain,
! [SV863: $i,SV183: $i > $o,SV822: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK160_SY3288 @ SV822 @ SV183 @ SV863 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV863 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV183 @ ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4506]) ).
thf(4539,plain,
! [SV411: $i > $o,SV183: $i > $o,SV822: $i,SV863: $i] :
( ( ( SV863
= ( sK160_SY3288 @ SV822 @ SV183 @ SV863 @ SV411 ) )
= $false )
| ( ( SV411 @ SV863 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV183 @ ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4506]) ).
thf(4540,plain,
! [SV856: $i,SV183: $i > $o,SV822: $i,SV411: $i > $o] :
( ( ( SV411 @ ( sK156_SY3281 @ SV822 @ SV183 @ SV856 @ SV411 ) )
= $true )
| ( ( SV411 @ SV856 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV822
= ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4507]) ).
thf(4541,plain,
! [SV857: $i,SV183: $i > $o,SV817: $i,SV411: $i > $o] :
( ( ( SV411 @ ( sK157_SY3282 @ SV817 @ SV183 @ SV857 @ SV411 ) )
= $true )
| ( ( SV411 @ SV857 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV817 )
= $false )
| ( ( SV183 @ ( sK115_SY3233 @ SV411 @ SV817 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4509]) ).
thf(4542,plain,
! [SV193: $i > $o,SV846: $i,SV885: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV885 )
| ( ( sK152_SY2770 @ SV846 @ SV193 @ SV422 )
= SV885 ) )
= $true )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV193 @ ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4513]) ).
thf(4543,plain,
! [SV193: $i > $o,SV846: $i,SV879: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV879 ) )
= $true )
| ( ( ( sK146_SY2770 @ SV846 @ SV193 @ SV422 )
= SV879 )
= $true )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV846
= ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4514]) ).
thf(4544,plain,
! [SV422: $i > $o,SV847: $i,SV886: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV886 )
| ( ( sK153_SY2337 @ SV847 @ SV422 @ SV193 )
= SV886 ) )
= $true )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV422 @ ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4516]) ).
thf(4545,plain,
! [SV422: $i > $o,SV847: $i,SV880: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV880 ) )
= $true )
| ( ( ( sK147_SY2337 @ SV847 @ SV422 @ SV193 )
= SV880 )
= $true )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV847
= ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4517]) ).
thf(4546,plain,
! [SV193: $i > $o,SV841: $i,SV881: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV881 ) )
= $true )
| ( ( ( sK148_SY2770 @ SV841 @ SV193 @ SV422 )
= SV881 )
= $true )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV193 @ ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4518]) ).
thf(4547,plain,
! [SV193: $i > $o,SV841: $i,SV873: $i,SV422: $i > $o] :
( ( ( SV422 @ SV873 )
= $false )
| ( ( ( sK140_SY2770 @ SV841 @ SV193 @ SV422 )
= SV873 )
= $true )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV841
= ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4519]) ).
thf(4548,plain,
! [SV422: $i > $o,SV842: $i,SV882: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV882 ) )
= $true )
| ( ( ( sK149_SY2337 @ SV842 @ SV422 @ SV193 )
= SV882 )
= $true )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV422 @ ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4520]) ).
thf(4549,plain,
! [SV422: $i > $o,SV842: $i,SV874: $i,SV193: $i > $o] :
( ( ( SV193 @ SV874 )
= $false )
| ( ( ( sK141_SY2337 @ SV842 @ SV422 @ SV193 )
= SV874 )
= $true )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV842
= ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4521]) ).
thf(4550,plain,
! [SV193: $i > $o,SV843: $i,SV883: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV883 ) )
= $true )
| ( ( ( sK150_SY2770 @ SV843 @ SV193 @ SV422 )
= SV883 )
= $true )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV193 @ ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4522]) ).
thf(4551,plain,
! [SV193: $i > $o,SV843: $i,SV875: $i,SV422: $i > $o] :
( ( ( SV422 @ SV875 )
= $false )
| ( ( ( sK142_SY2770 @ SV843 @ SV193 @ SV422 )
= SV875 )
= $true )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV843
= ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4523]) ).
thf(4552,plain,
! [SV422: $i > $o,SV844: $i,SV884: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV884 ) )
= $true )
| ( ( ( sK151_SY2337 @ SV844 @ SV422 @ SV193 )
= SV884 )
= $true )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV422 @ ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4524]) ).
thf(4553,plain,
! [SV422: $i > $o,SV844: $i,SV876: $i,SV193: $i > $o] :
( ( ( SV193 @ SV876 )
= $false )
| ( ( ( sK143_SY2337 @ SV844 @ SV422 @ SV193 )
= SV876 )
= $true )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV844
= ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4525]) ).
thf(4554,plain,
! [SV193: $i > $o,SV836: $i,SV877: $i,SV422: $i > $o] :
( ( ( SV422 @ SV877 )
= $false )
| ( ( ( sK144_SY2770 @ SV836 @ SV193 @ SV422 )
= SV877 )
= $true )
| ( ( SV193 @ SV836 )
= $false )
| ( ( SV193 @ ( sK126_SY3248 @ SV422 @ SV836 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4526]) ).
thf(4555,plain,
! [SV422: $i > $o,SV837: $i,SV878: $i,SV193: $i > $o] :
( ( ( SV193 @ SV878 )
= $false )
| ( ( ( sK145_SY2337 @ SV837 @ SV422 @ SV193 )
= SV878 )
= $true )
| ( ( SV422 @ SV837 )
= $false )
| ( ( SV422 @ ( sK127_SY3249 @ SV193 @ SV837 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4528]) ).
thf(4556,plain,
! [SV147: $i,SV747: $i,SV825: $i,SV872: $i] :
( ( ( ~ ( in @ SV872 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) ) )
= $true )
| ( ( ~ ( in @ SV872 @ SV747 ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4530]) ).
thf(4557,plain,
! [SV147: $i,SV747: $i,SV820: $i,SV869: $i] :
( ( ( in @ SV869 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
= $false )
| ( ( ~ ( in @ SV869 @ SV747 ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4531]) ).
thf(4558,plain,
! [SV866: $i,SV183: $i > $o,SV828: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ ( sK161_SY3295 @ SV828 @ SV183 @ SV866 @ SV411 ) ) )
= $false )
| ( ( SV411 @ SV866 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV183 @ ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4532]) ).
thf(4559,plain,
! [SV411: $i > $o,SV183: $i > $o,SV828: $i,SV866: $i] :
( ( ( SV866
= ( sK161_SY3295 @ SV828 @ SV183 @ SV866 @ SV411 ) )
= $false )
| ( ( SV411 @ SV866 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV183 @ ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4532]) ).
thf(4560,plain,
! [SV861: $i,SV183: $i > $o,SV828: $i,SV411: $i > $o] :
( ( ( SV411 @ ( sK158_SY3286 @ SV828 @ SV183 @ SV861 @ SV411 ) )
= $true )
| ( ( SV411 @ SV861 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV828
= ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $false )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4533]) ).
thf(4561,plain,
! [SV862: $i,SV183: $i > $o,SV821: $i,SV411: $i > $o] :
( ( ( SV411 @ ( sK159_SY3287 @ SV821 @ SV183 @ SV862 @ SV411 ) )
= $true )
| ( ( SV411 @ SV862 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV821 )
= $false )
| ( ( SV183 @ ( sK118_SY3237 @ SV411 @ SV821 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4535]) ).
thf(4562,plain,
! [SV863: $i,SV183: $i > $o,SV822: $i,SV411: $i > $o] :
( ( ( SV411 @ ( sK160_SY3288 @ SV822 @ SV183 @ SV863 @ SV411 ) )
= $true )
| ( ( SV411 @ SV863 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV822 )
= $false )
| ( ( SV183 @ ( sK119_SY3238 @ SV411 @ SV822 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $false )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4538]) ).
thf(4563,plain,
! [SV193: $i > $o,SV846: $i,SV885: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV885 ) )
= $true )
| ( ( ( sK152_SY2770 @ SV846 @ SV193 @ SV422 )
= SV885 )
= $true )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV193 @ ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4542]) ).
thf(4564,plain,
! [SV193: $i > $o,SV846: $i,SV879: $i,SV422: $i > $o] :
( ( ( SV422 @ SV879 )
= $false )
| ( ( ( sK146_SY2770 @ SV846 @ SV193 @ SV422 )
= SV879 )
= $true )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV846
= ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4543]) ).
thf(4565,plain,
! [SV422: $i > $o,SV847: $i,SV886: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV886 ) )
= $true )
| ( ( ( sK153_SY2337 @ SV847 @ SV422 @ SV193 )
= SV886 )
= $true )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV422 @ ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4544]) ).
thf(4566,plain,
! [SV422: $i > $o,SV847: $i,SV880: $i,SV193: $i > $o] :
( ( ( SV193 @ SV880 )
= $false )
| ( ( ( sK147_SY2337 @ SV847 @ SV422 @ SV193 )
= SV880 )
= $true )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV847
= ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $false )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4545]) ).
thf(4567,plain,
! [SV193: $i > $o,SV841: $i,SV881: $i,SV422: $i > $o] :
( ( ( SV422 @ SV881 )
= $false )
| ( ( ( sK148_SY2770 @ SV841 @ SV193 @ SV422 )
= SV881 )
= $true )
| ( ( SV193 @ SV841 )
= $false )
| ( ( SV193 @ ( sK129_SY3256 @ SV422 @ SV841 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4546]) ).
thf(4568,plain,
! [SV422: $i > $o,SV842: $i,SV882: $i,SV193: $i > $o] :
( ( ( SV193 @ SV882 )
= $false )
| ( ( ( sK149_SY2337 @ SV842 @ SV422 @ SV193 )
= SV882 )
= $true )
| ( ( SV422 @ SV842 )
= $false )
| ( ( SV422 @ ( sK130_SY3257 @ SV193 @ SV842 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4548]) ).
thf(4569,plain,
! [SV193: $i > $o,SV843: $i,SV883: $i,SV422: $i > $o] :
( ( ( SV422 @ SV883 )
= $false )
| ( ( ( sK150_SY2770 @ SV843 @ SV193 @ SV422 )
= SV883 )
= $true )
| ( ( SV193 @ SV843 )
= $false )
| ( ( SV193 @ ( sK131_SY3258 @ SV422 @ SV843 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4550]) ).
thf(4570,plain,
! [SV422: $i > $o,SV844: $i,SV884: $i,SV193: $i > $o] :
( ( ( SV193 @ SV884 )
= $false )
| ( ( ( sK151_SY2337 @ SV844 @ SV422 @ SV193 )
= SV884 )
= $true )
| ( ( SV422 @ SV844 )
= $false )
| ( ( SV422 @ ( sK132_SY3259 @ SV193 @ SV844 @ SV422 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $false )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4552]) ).
thf(4571,plain,
! [SV147: $i,SV747: $i,SV825: $i,SV872: $i] :
( ( ( in @ SV872 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
= $false )
| ( ( ~ ( in @ SV872 @ SV747 ) )
= $true )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4556]) ).
thf(4572,plain,
! [SV147: $i,SV820: $i,SV747: $i,SV869: $i] :
( ( ( in @ SV869 @ SV747 )
= $false )
| ( ( in @ SV869 @ ( sK110_SY3178 @ SV820 @ SV747 @ SV147 ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV147 )
= $false )
| ( ( in @ SV820 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4557]) ).
thf(4573,plain,
! [SV866: $i,SV183: $i > $o,SV828: $i,SV411: $i > $o] :
( ( ( SV411 @ ( sK161_SY3295 @ SV828 @ SV183 @ SV866 @ SV411 ) )
= $true )
| ( ( SV411 @ SV866 )
= $false )
| ( ( ( descr
@ ^ [SY2300: $i] : ( SV183 @ SY2300 ) )
= ( descr
@ ^ [SY2751: $i] : ( SV411 @ SY2751 ) ) )
= $true )
| ( ( SV183 @ SV828 )
= $false )
| ( ( SV183 @ ( sK123_SY3244 @ SV411 @ SV828 @ SV183 ) )
= $true )
| ( ( SV183 @ ( sK13_SY2744 @ SV411 @ SV183 ) )
= $true )
| ( ( SV411 @ ( sK22_SY3113 @ SV183 @ SV411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4558]) ).
thf(4574,plain,
! [SV193: $i > $o,SV846: $i,SV885: $i,SV422: $i > $o] :
( ( ( SV422 @ SV885 )
= $false )
| ( ( ( sK152_SY2770 @ SV846 @ SV193 @ SV422 )
= SV885 )
= $true )
| ( ( SV193 @ SV846 )
= $false )
| ( ( SV193 @ ( sK134_SY3264 @ SV422 @ SV846 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4563]) ).
thf(4575,plain,
! [SV422: $i > $o,SV847: $i,SV886: $i,SV193: $i > $o] :
( ( ( SV193 @ SV886 )
= $false )
| ( ( ( sK153_SY2337 @ SV847 @ SV422 @ SV193 )
= SV886 )
= $true )
| ( ( SV422 @ SV847 )
= $false )
| ( ( SV422 @ ( sK135_SY3265 @ SV193 @ SV847 @ SV422 ) )
= $true )
| ( ( SV193 @ ( sK14_SY2766 @ SV422 @ SV193 ) )
= $true )
| ( ( SV422 @ ( sK23_SY3119 @ SV193 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4565]) ).
thf(4576,plain,
! [SV147: $i,SV825: $i,SV747: $i,SV872: $i] :
( ( ( in @ SV872 @ SV747 )
= $false )
| ( ( in @ SV872 @ ( sK114_SY3178 @ SV825 @ SV747 @ SV147 ) )
= $false )
| ( ( in @ ( sK80_SY3176 @ SV147 @ SV747 ) @ SV747 )
= $true )
| ( ( in @ SV825 @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4571]) ).
thf(4577,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[458,4576,4575,4574,4573,4572,4570,4569,4568,4567,4566,4564,4562,4561,4560,4559,4555,4554,4553,4551,4549,4547,4541,4540,4539,4537,4536,4534,4529,4527,4515,4512,4511,4510,4508,4505,4499,4491,4488,4485,4482,4480,4476,4473,4464,4460,4459,4456,4453,4451,4447,4443,4439,4420,4419,4413,4409,4375,4374,4355,4354,4345,4338,4337,4335,4333,4332,4315,4313,4303,4302,4294,4290,4289,4257,4224,4221,4185,4181,4100,4072,4065,4041,4036,4035,4034,4032,4031,4008,4007,4005,4004,3998,3997,3996,3994,3991,3989,3976,3969,3964,3960,3959,3958,3949,3945,3942,3931,3923,3921,3912,3911,3910,3900,3898,3896,3892,3891,3889,3870,3862,3859,3857,3854,3853,3839,3837,3817,3816,3809,3807,3804,3798,3797,3796,3793,3787,3782,3769,3764,3752,3749,3748,3746,3745,3736,3734,3730,3724,3722,3711,3696,3690,3689,3675,3673,3670,3668,3646,3642,3641,3640,3639,3638,3637,3619,3618,3613,3612,3611,3609,3577,3568,3567,3564,3562,3561,3557,3554,3551,3526,3509,3490,3489,3482,3481,3480,3479,3478,3471,3470,3468,3465,3463,3462,3461,3460,3457,3456,3455,3454,3451,3450,3449,3448,3445,3444,3439,3438,3427,3415,3378,3377,3376,3375,3374,3373,3372,3370,3359,3357,3351,3350,3349,3348,3347,3343,3339,3336,3332,3329,3325,3322,3321,3313,3308,3307,3300,3299,3272,3262,3261,3251,3247,3246,3244,3243,3241,3240,3229,3220,3218,3212,3211,3209,3208,3206,3205,3185,3184,3182,3181,3179,3171,3170,3158,3157,3155,3153,3118,3116,3106,3104,3101,3099,3096,3093,3082,3075,3072,3070,3065,3062,3059,3056,3052,3040,3038,3019,3018,3017,3013,3012,3011,3009,3008,3007,3006,3003,3001,2993,2987,2968,2967,2966,2953,2952,2951,2928,2923,2922,2887,2869,2867,2866,2865,2864,2863,2862,2861,2858,2857,2846,2840,2839,2838,2820,2819,2813,2804,2802,2801,2799,2798,2796,2792,2778,2771,2769,2768,2767,2766,2765,2762,2728,2727,2726,2701,2665,2664,2656,2639,2636,2608,2594,2581,2580,2579,2571,2569,2566,2555,2544,2541,2538,2537,2536,2534,2532,2528,2525,2524,2516,2512,2510,2500,2499,2493,2492,2491,2490,2485,2483,2477,2467,2462,2450,2441,2422,2419,2418,2417,2416,2415,2414,2413,2410,2399,2390,2384,2378,2352,2351,2328,2319,2309,2308,2304,2302,2283,2282,2275,2271,2269,2264,2263,2261,2243,2242,2236,2229,2228,2216,2204,2189,2188,2187,2177,2173,2146,2142,2129,2109,2107,2106,2099,2098,2081,2061,2036,2031,2015,1985,1968,1931,1907,1901,1897,1894,1893,1886,1884,1877,1865,1858,1856,1838,1833,1830,1822,1818,1814,1813,1808,1793,1783,1782,1778,1777,1771,1770,1739,1736,1734,1733,1732,1731,1725,1716,1715,1714,1706,1704,1701,1677,1670,1667,1662,1632,1630,1622,1611,1608,1607,1604,1599,1597,1567,1564,1552,1487,1484,1437,1413,1390,1325,1324,1319,1318,1317,1311,1310,1309,1298,1297,1296,1045,1044,1043,1042,1041,1040,1039,1038,1037,1036,1035,1034,1033,1031,1030,1029,1028,1027,1026,1025,1024,786,785,784,781,780,778,763,762,761,524,500,462]) ).
thf(4578,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[4577]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU746^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/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 15:36:12 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 77.00/13.12 .
% 77.00/13.12
% 77.00/13.12 No.of.Axioms: 0
% 77.00/13.12
% 77.00/13.12 Length.of.Defs: 61656
% 77.00/13.12
% 77.00/13.12 Contains.Choice.Funs: true
% 77.00/13.12 ...............................................................................................................................................................................................
% 77.00/13.12
% 77.00/13.12 ********************************
% 77.00/13.12 * All subproblems solved! *
% 77.00/13.12 ********************************
% 77.00/13.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:262,ps:0,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:4577,loop_count:0,foatp_calls:1,translation:fof_full)
% 77.00/13.12
% 77.00/13.12 %**** Beginning of derivation protocol ****
% 77.00/13.12 % SZS output start CNFRefutation
% See solution above
% 77.00/13.15
% 77.00/13.15 %**** End of derivation protocol ****
% 77.00/13.15 %**** no. of clauses in derivation: 4578 ****
% 77.00/13.15 %**** clause counter: 4577 ****
% 77.00/13.15
% 77.00/13.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:262,ps:0,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:4577,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------