%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU813^1 : 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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:48:43 AM UTC 2026
% Result : Theorem 159.46s 26.85s
% Output : CNFRefutation 159.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 333
% Syntax : Number of formulae : 6170 (2158 unt; 0 typ; 332 def)
% Number of atoms : 56993 (20711 equ; 0 cnn)
% Maximal formula atoms : 332 ( 9 avg)
% Number of connectives : 124747 (20398 ~;20689 |; 261 &;79391 @)
% ( 71 <=>;3937 =>; 0 <=; 0 <~>)
% Maximal formula depth : 337 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3049 (3049 >; 0 *; 0 +; 0 <<)
% Number of symbols : 585 ( 582 usr; 336 con; 0-6 aty)
% Number of variables : 26230 (1494 ^;24515 !; 221 ?;26230 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric,type,
antisymmetric: $i > $i > $o ).
thf(tp_ap,type,
ap: $i > $i > $i > $i > $i ).
thf(tp_ap2apEq1,type,
ap2apEq1: $o ).
thf(tp_ap2apEq2,type,
ap2apEq2: $o ).
thf(tp_ap2p,type,
ap2p: $o ).
thf(tp_apProp,type,
apProp: $o ).
thf(tp_app,type,
app: $o ).
thf(tp_atleast2p,type,
atleast2p: $i > $o ).
thf(tp_atmost1p,type,
atmost1p: $i > $o ).
thf(tp_atmost2p,type,
atmost2p: $i > $o ).
thf(tp_beta1,type,
beta1: $o ).
thf(tp_beta2,type,
beta2: $o ).
thf(tp_binintersect,type,
binintersect: $i > $i > $i ).
thf(tp_binintersectEL,type,
binintersectEL: $o ).
thf(tp_binintersectER,type,
binintersectER: $o ).
thf(tp_binintersectI,type,
binintersectI: $o ).
thf(tp_binintersectLsub,type,
binintersectLsub: $o ).
thf(tp_binintersectRsub,type,
binintersectRsub: $o ).
thf(tp_binintersectSubset1,type,
binintersectSubset1: $o ).
thf(tp_binintersectSubset2,type,
binintersectSubset2: $o ).
thf(tp_binintersectSubset3,type,
binintersectSubset3: $o ).
thf(tp_binintersectSubset4,type,
binintersectSubset4: $o ).
thf(tp_binintersectSubset5,type,
binintersectSubset5: $o ).
thf(tp_binintersectTELcontra,type,
binintersectTELcontra: $o ).
thf(tp_binintersectTERcontra,type,
binintersectTERcontra: $o ).
thf(tp_binintersectT_lem,type,
binintersectT_lem: $o ).
thf(tp_binunion,type,
binunion: $i > $i > $i ).
thf(tp_binunionE,type,
binunionE: $o ).
thf(tp_binunionEcases,type,
binunionEcases: $o ).
thf(tp_binunionIL,type,
binunionIL: $o ).
thf(tp_binunionIR,type,
binunionIR: $o ).
thf(tp_binunionLsub,type,
binunionLsub: $o ).
thf(tp_binunionRsub,type,
binunionRsub: $o ).
thf(tp_binunionTE,type,
binunionTE: $o ).
thf(tp_binunionTEcontra,type,
binunionTEcontra: $o ).
thf(tp_binunionTILcontra,type,
binunionTILcontra: $o ).
thf(tp_binunionTIRcontra,type,
binunionTIRcontra: $o ).
thf(tp_binunionT_lem,type,
binunionT_lem: $o ).
thf(tp_breln,type,
breln: $i > $i > $i > $o ).
thf(tp_breln1,type,
breln1: $i > $i > $o ).
thf(tp_breln1Set,type,
breln1Set: $i > $i ).
thf(tp_breln1SetBreln1,type,
breln1SetBreln1: $o ).
thf(tp_breln1all1,type,
breln1all1: $o ).
thf(tp_breln1all2,type,
breln1all2: $o ).
thf(tp_breln1compE,type,
breln1compE: $o ).
thf(tp_breln1compEex,type,
breln1compEex: $o ).
thf(tp_breln1compI,type,
breln1compI: $o ).
thf(tp_breln1compprop,type,
breln1compprop: $o ).
thf(tp_breln1compset,type,
breln1compset: $i > $i > $i > $i ).
thf(tp_breln1invE,type,
breln1invE: $o ).
thf(tp_breln1invI,type,
breln1invI: $o ).
thf(tp_breln1invprop,type,
breln1invprop: $o ).
thf(tp_breln1invset,type,
breln1invset: $i > $i > $i ).
thf(tp_breln1unionCommutes,type,
breln1unionCommutes: $o ).
thf(tp_breln1unionE,type,
breln1unionE: $o ).
thf(tp_breln1unionEcases,type,
breln1unionEcases: $o ).
thf(tp_breln1unionI,type,
breln1unionI: $o ).
thf(tp_breln1unionIL,type,
breln1unionIL: $o ).
thf(tp_breln1unionIR,type,
breln1unionIR: $o ).
thf(tp_breln1unionprop,type,
breln1unionprop: $o ).
thf(tp_brelnall1,type,
brelnall1: $o ).
thf(tp_brelnall2,type,
brelnall2: $o ).
thf(tp_bs114d,type,
bs114d: $o ).
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_cartprodfstin,type,
cartprodfstin: $o ).
thf(tp_cartprodfstpairEq,type,
cartprodfstpairEq: $o ).
thf(tp_cartprodmempair,type,
cartprodmempair: $o ).
thf(tp_cartprodmempair1,type,
cartprodmempair1: $o ).
thf(tp_cartprodmempaircEq,type,
cartprodmempaircEq: $o ).
thf(tp_cartprodpairin,type,
cartprodpairin: $o ).
thf(tp_cartprodpairmemEL,type,
cartprodpairmemEL: $o ).
thf(tp_cartprodpairmemER,type,
cartprodpairmemER: $o ).
thf(tp_cartprodpairsurjEq,type,
cartprodpairsurjEq: $o ).
thf(tp_cartprodsndin,type,
cartprodsndin: $o ).
thf(tp_cartprodsndpairEq,type,
cartprodsndpairEq: $o ).
thf(tp_choice2fnsingleton,type,
choice2fnsingleton: $o ).
thf(tp_complementImpComplementIntersect,type,
complementImpComplementIntersect: $o ).
thf(tp_complementInPowersetComplementIntersect,type,
complementInPowersetComplementIntersect: $o ).
thf(tp_complementSubsetComplementIntersect,type,
complementSubsetComplementIntersect: $o ).
thf(tp_complementTE1,type,
complementTE1: $o ).
thf(tp_complementTI1,type,
complementTI1: $o ).
thf(tp_complementT_lem,type,
complementT_lem: $o ).
thf(tp_complementTcontraSubset,type,
complementTcontraSubset: $o ).
thf(tp_complementTnotintersectT,type,
complementTnotintersectT: $o ).
thf(tp_complementUnionInPowersetComplement,type,
complementUnionInPowersetComplement: $o ).
thf(tp_contraSubsetComplement,type,
contraSubsetComplement: $o ).
thf(tp_contrasubsetT,type,
contrasubsetT: $o ).
thf(tp_contrasubsetT1,type,
contrasubsetT1: $o ).
thf(tp_contrasubsetT2,type,
contrasubsetT2: $o ).
thf(tp_contrasubsetT3,type,
contrasubsetT3: $o ).
thf(tp_demorgan1,type,
demorgan1: $o ).
thf(tp_demorgan1a,type,
demorgan1a: $o ).
thf(tp_demorgan1b,type,
demorgan1b: $o ).
thf(tp_demorgan2,type,
demorgan2: $o ).
thf(tp_demorgan2a,type,
demorgan2a: $o ).
thf(tp_demorgan2a1,type,
demorgan2a1: $o ).
thf(tp_demorgan2a2,type,
demorgan2a2: $o ).
thf(tp_demorgan2b,type,
demorgan2b: $o ).
thf(tp_demorgan2b2,type,
demorgan2b2: $o ).
thf(tp_descr,type,
descr: ( $i > $o ) > $i ).
thf(tp_descr__Cong,type,
descr__Cong: $o ).
thf(tp_descrp,type,
descrp: $o ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_disjointsetsI1,type,
disjointsetsI1: $o ).
thf(tp_doubleComplementE1,type,
doubleComplementE1: $o ).
thf(tp_doubleComplementEq,type,
doubleComplementEq: $o ).
thf(tp_doubleComplementI1,type,
doubleComplementI1: $o ).
thf(tp_doubleComplementSub1,type,
doubleComplementSub1: $o ).
thf(tp_doubleComplementSub2,type,
doubleComplementSub2: $o ).
thf(tp_dpsetconstr,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_dpsetconstrEL1,type,
dpsetconstrEL1: $o ).
thf(tp_dpsetconstrEL2,type,
dpsetconstrEL2: $o ).
thf(tp_dpsetconstrER,type,
dpsetconstrER: $o ).
thf(tp_dpsetconstrERa,type,
dpsetconstrERa: $o ).
thf(tp_dpsetconstrI,type,
dpsetconstrI: $o ).
thf(tp_dpsetconstrSub,type,
dpsetconstrSub: $o ).
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrEL,type,
dsetconstrEL: $o ).
thf(tp_dsetconstrER,type,
dsetconstrER: $o ).
thf(tp_dsetconstrI,type,
dsetconstrI: $o ).
thf(tp_dsetconstr__Cong,type,
dsetconstr__Cong: $o ).
thf(tp_emptyE1,type,
emptyE1: $o ).
thf(tp_emptyI,type,
emptyI: $o ).
thf(tp_emptyInPowerset,type,
emptyInPowerset: $o ).
thf(tp_emptyinPowerset,type,
emptyinPowerset: $o ).
thf(tp_emptyinunitempty,type,
emptyinunitempty: $o ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_emptysetAx,type,
emptysetAx: $o ).
thf(tp_emptysetE,type,
emptysetE: $o ).
thf(tp_emptyset__Cong,type,
emptyset__Cong: $o ).
thf(tp_emptysetimpfalse,type,
emptysetimpfalse: $o ).
thf(tp_emptysetsubset,type,
emptysetsubset: $o ).
thf(tp_eqbreln,type,
eqbreln: $o ).
thf(tp_eqbreln1,type,
eqbreln1: $o ).
thf(tp_eqimpsubset1,type,
eqimpsubset1: $o ).
thf(tp_eqimpsubset2,type,
eqimpsubset2: $o ).
thf(tp_eqinunit,type,
eqinunit: $o ).
thf(tp_eta1,type,
eta1: $o ).
thf(tp_eta2,type,
eta2: $o ).
thf(tp_ex1,type,
ex1: $i > ( $i > $o ) > $o ).
thf(tp_ex1E1,type,
ex1E1: $o ).
thf(tp_ex1E2,type,
ex1E2: $o ).
thf(tp_ex1I,type,
ex1I: $o ).
thf(tp_ex1I2,type,
ex1I2: $o ).
thf(tp_exu,type,
exu: ( $i > $o ) > $o ).
thf(tp_exuE1,type,
exuE1: $o ).
thf(tp_exuE2,type,
exuE2: $o ).
thf(tp_exuE3e,type,
exuE3e: $o ).
thf(tp_exuE3u,type,
exuE3u: $o ).
thf(tp_exuEu,type,
exuEu: $o ).
thf(tp_exuI1,type,
exuI1: $o ).
thf(tp_exuI2,type,
exuI2: $o ).
thf(tp_exuI3,type,
exuI3: $o ).
thf(tp_exu__Cong,type,
exu__Cong: $o ).
thf(tp_foundation2,type,
foundation2: $o ).
thf(tp_foundationAx,type,
foundationAx: $o ).
thf(tp_func,type,
func: $i > $i > $i > $o ).
thf(tp_funcGraphProp1,type,
funcGraphProp1: $o ).
thf(tp_funcGraphProp2,type,
funcGraphProp2: $o ).
thf(tp_funcGraphProp3,type,
funcGraphProp3: $o ).
thf(tp_funcGraphProp4,type,
funcGraphProp4: $o ).
thf(tp_funcImageSingleton,type,
funcImageSingleton: $o ).
thf(tp_funcSet,type,
funcSet: $i > $i > $i ).
thf(tp_funcext,type,
funcext: $o ).
thf(tp_funcext2,type,
funcext2: $o ).
thf(tp_funcextLem,type,
funcextLem: $o ).
thf(tp_funcinfuncset,type,
funcinfuncset: $o ).
thf(tp_if,type,
if: $i > $o > $i > $i > $i ).
thf(tp_ifSingleton,type,
ifSingleton: $o ).
thf(tp_iffalse,type,
iffalse: $o ).
thf(tp_iffalseProp1,type,
iffalseProp1: $o ).
thf(tp_iffalseProp2,type,
iffalseProp2: $o ).
thf(tp_ifp,type,
ifp: $o ).
thf(tp_iftrue,type,
iftrue: $o ).
thf(tp_iftrueProp1,type,
iftrueProp1: $o ).
thf(tp_iftrueProp2,type,
iftrueProp2: $o ).
thf(tp_iftrueorfalse,type,
iftrueorfalse: $o ).
thf(tp_image1,type,
image1: $i > ( $i > $i ) > $i ).
thf(tp_image1E,type,
image1E: $o ).
thf(tp_image1Equiv,type,
image1Equiv: $o ).
thf(tp_image1Ex,type,
image1Ex: $o ).
thf(tp_image1Ex1,type,
image1Ex1: $o ).
thf(tp_image1I,type,
image1I: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_inComplementUnionImpInComplement1,type,
inComplementUnionImpInComplement1: $o ).
thf(tp_inComplementUnionImpNotIn1,type,
inComplementUnionImpNotIn1: $o ).
thf(tp_inCongP,type,
inCongP: $o ).
thf(tp_inIntersectImpInIntersectUnions,type,
inIntersectImpInIntersectUnions: $o ).
thf(tp_inIntersectImpInUnion,type,
inIntersectImpInUnion: $o ).
thf(tp_inIntersectImpInUnion2,type,
inIntersectImpInUnion2: $o ).
thf(tp_inPowerset,type,
inPowerset: $o ).
thf(tp_in__Cong,type,
in__Cong: $o ).
thf(tp_infuncsetfunc,type,
infuncsetfunc: $o ).
thf(tp_injFuncInInjFuncSet,type,
injFuncInInjFuncSet: $o ).
thf(tp_injFuncSet,type,
injFuncSet: $i > $i > $i ).
thf(tp_injFuncSetFuncIn,type,
injFuncSetFuncIn: $o ).
thf(tp_injFuncSetFuncInj,type,
injFuncSetFuncInj: $o ).
thf(tp_injective,type,
injective: $i > $i > $i > $o ).
thf(tp_intersectInPowersetIntersectUnions,type,
intersectInPowersetIntersectUnions: $o ).
thf(tp_iskpair,type,
iskpair: $i > $o ).
thf(tp_kfst,type,
kfst: $i > $i ).
thf(tp_kfstpairEq,type,
kfstpairEq: $o ).
thf(tp_kfstsingleton,type,
kfstsingleton: $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_kpairiskpair,type,
kpairiskpair: $o ).
thf(tp_kpairp,type,
kpairp: $o ).
thf(tp_kpairsurjEq,type,
kpairsurjEq: $o ).
thf(tp_ksnd,type,
ksnd: $i > $i ).
thf(tp_ksndpairEq,type,
ksndpairEq: $o ).
thf(tp_ksndsingleton,type,
ksndsingleton: $o ).
thf(tp_lam,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(tp_lam2lamEq,type,
lam2lamEq: $o ).
thf(tp_lam2p,type,
lam2p: $o ).
thf(tp_lamProp,type,
lamProp: $o ).
thf(tp_lamp,type,
lamp: $o ).
thf(tp_leftInvIsSurj,type,
leftInvIsSurj: $o ).
thf(tp_noeltsimpempty,type,
noeltsimpempty: $o ).
thf(tp_nonempty,type,
nonempty: $i > $o ).
thf(tp_nonemptyE1,type,
nonemptyE1: $o ).
thf(tp_nonemptyI,type,
nonemptyI: $o ).
thf(tp_nonemptyI1,type,
nonemptyI1: $o ).
thf(tp_nonemptyImpWitness,type,
nonemptyImpWitness: $o ).
thf(tp_notdallE,type,
notdallE: $o ).
thf(tp_notdexE,type,
notdexE: $o ).
thf(tp_notequalI1,type,
notequalI1: $o ).
thf(tp_notequalI2,type,
notequalI2: $o ).
thf(tp_notinemptyset,type,
notinemptyset: $o ).
thf(tp_notinself,type,
notinself: $o ).
thf(tp_notinself2,type,
notinself2: $o ).
thf(tp_notinsingleton,type,
notinsingleton: $o ).
thf(tp_notsubsetI,type,
notsubsetI: $o ).
thf(tp_omega,type,
omega: $i ).
thf(tp_omega0Ax,type,
omega0Ax: $o ).
thf(tp_omegaIndAx,type,
omegaIndAx: $o ).
thf(tp_omegaS,type,
omegaS: $i > $i ).
thf(tp_omegaSAx,type,
omegaSAx: $o ).
thf(tp_omegaSclos,type,
omegaSclos: $o ).
thf(tp_omegaSp,type,
omegaSp: $o ).
thf(tp_omega__Cong,type,
omega__Cong: $o ).
thf(tp_peano,type,
peano: $i > $i > $i > $o ).
thf(tp_peano0notS,type,
peano0notS: $o ).
thf(tp_peano3,type,
peano3: $i > $i > $i > $o ).
thf(tp_peano4,type,
peano4: $i > $i > $i > $o ).
thf(tp_peano5,type,
peano5: $i > $i > $i > $o ).
thf(tp_peanoSinj,type,
peanoSinj: $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetAx,type,
powersetAx: $o ).
thf(tp_powersetE,type,
powersetE: $o ).
thf(tp_powersetE1,type,
powersetE1: $o ).
thf(tp_powersetI,type,
powersetI: $o ).
thf(tp_powersetI1,type,
powersetI1: $o ).
thf(tp_powersetTE1,type,
powersetTE1: $o ).
thf(tp_powersetTI1,type,
powersetTI1: $o ).
thf(tp_powersetT_lem,type,
powersetT_lem: $o ).
thf(tp_powerset__Cong,type,
powerset__Cong: $o ).
thf(tp_powersetsubset,type,
powersetsubset: $o ).
thf(tp_prop2set,type,
prop2set: $o > $i ).
thf(tp_prop2set2propI,type,
prop2set2propI: $o ).
thf(tp_prop2setE,type,
prop2setE: $o ).
thf(tp_prop2setI,type,
prop2setI: $o ).
thf(tp_quantDeMorgan1,type,
quantDeMorgan1: $o ).
thf(tp_quantDeMorgan2,type,
quantDeMorgan2: $o ).
thf(tp_quantDeMorgan3,type,
quantDeMorgan3: $o ).
thf(tp_quantDeMorgan4,type,
quantDeMorgan4: $o ).
thf(tp_reflexive,type,
reflexive: $i > $i > $o ).
thf(tp_refllinearorder,type,
refllinearorder: $i > $i > $o ).
thf(tp_refltransitive,type,
refltransitive: $i > $i > $o ).
thf(tp_reflwellordering,type,
reflwellordering: $i > $i > $o ).
thf(tp_regular,type,
regular: $i > $o ).
thf(tp_replAx,type,
replAx: $o ).
thf(tp_sK100_SY4134,type,
sK100_SY4134: ( $i > $i ) > $i > $i > $i > $i ).
thf(tp_sK101_SY2855,type,
sK101_SY2855: $i > ( $i > $o ) > $i ).
thf(tp_sK102_SY4114,type,
sK102_SY4114: $i > $i > $i ).
thf(tp_sK103_SY4121,type,
sK103_SY4121: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK104_SY3190,type,
sK104_SY3190: $i > ( $i > $o ) > $i ).
thf(tp_sK105_SY2411,type,
sK105_SY2411: $i > ( $i > $o ) > $i ).
thf(tp_sK106_SY2468,type,
sK106_SY2468: $i > ( $i > $o ) > $i ).
thf(tp_sK107_SY2472,type,
sK107_SY2472: $i > ( $i > $o ) > $i ).
thf(tp_sK108_SY2565,type,
sK108_SY2565: $i > ( $i > $o ) > $i ).
thf(tp_sK109_SY2855,type,
sK109_SY2855: $i > ( $i > $o ) > $i ).
thf(tp_sK10_SY3275,type,
sK10_SY3275: $i > $i > $i ).
thf(tp_sK110_SY4022,type,
sK110_SY4022: $i > $i > $i > $i ).
thf(tp_sK111_SY4036,type,
sK111_SY4036: $i > $i > $i > $i ).
thf(tp_sK112_SY4036,type,
sK112_SY4036: $i > $i > $i > $i ).
thf(tp_sK113_SY3190,type,
sK113_SY3190: $i > ( $i > $o ) > $i ).
thf(tp_sK114_SY2468,type,
sK114_SY2468: $i > ( $i > $o ) > $i ).
thf(tp_sK115_SY2468,type,
sK115_SY2468: $i > ( $i > $o ) > $i ).
thf(tp_sK116_SY4061,type,
sK116_SY4061: $i > $i > $i > $i > $i ).
thf(tp_sK117_SY4135,type,
sK117_SY4135: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK118_SY4036,type,
sK118_SY4036: $i > $i > $i > $i ).
thf(tp_sK119_SY2468,type,
sK119_SY2468: $i > ( $i > $o ) > $i ).
thf(tp_sK11_SY3407,type,
sK11_SY3407: ( $i > $o ) > $i > $i ).
thf(tp_sK120_SY4151,type,
sK120_SY4151: $i > $i > $i > $i > $i > $i ).
thf(tp_sK121_SY3585,type,
sK121_SY3585: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK122_SY4194,type,
sK122_SY4194: $i > $i > $i > $i ).
thf(tp_sK123_SY4022,type,
sK123_SY4022: $i > $i > $i > $i ).
thf(tp_sK124_SY4022,type,
sK124_SY4022: $i > $i > $i > $i ).
thf(tp_sK125_SY4198,type,
sK125_SY4198: $i > $i > $i > $i > $i ).
thf(tp_sK126_SY4061,type,
sK126_SY4061: $i > $i > $i > $i > $i ).
thf(tp_sK127_SY4061,type,
sK127_SY4061: $i > $i > $i > $i > $i ).
thf(tp_sK128_SY4163,type,
sK128_SY4163: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK129_SY4159,type,
sK129_SY4159: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK12_SY3425,type,
sK12_SY3425: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK130_SY3585,type,
sK130_SY3585: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK131_SY4022,type,
sK131_SY4022: $i > $i > $i > $i ).
thf(tp_sK132_SY4061,type,
sK132_SY4061: $i > $i > $i > $i > $i ).
thf(tp_sK133_SY4205,type,
sK133_SY4205: $i > $i > $i > $i ).
thf(tp_sK134_SY4206,type,
sK134_SY4206: $i > $i > $i > $i ).
thf(tp_sK135_SY4199,type,
sK135_SY4199: $o > $i > $i > $i > $i > $i > $i ).
thf(tp_sK136_SX0,type,
sK136_SX0: $i > $i > $i > $i > $i > $i ).
thf(tp_sK137_SX0,type,
sK137_SX0: $i > $i > $i > $i > $i > $i ).
thf(tp_sK138_SY4207,type,
sK138_SY4207: $i > $i > $i > $i > $i ).
thf(tp_sK139_SY4208,type,
sK139_SY4208: $i > $i > $i > $i > $i ).
thf(tp_sK13_SY3515,type,
sK13_SY3515: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK140_SY4214,type,
sK140_SY4214: $i > $i > $i > $i ).
thf(tp_sK141_SY4215,type,
sK141_SY4215: $i > $i > $i > $i > $i ).
thf(tp_sK142_SY4191,type,
sK142_SY4191: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK143_SY4192,type,
sK143_SY4192: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK144_SY4116,type,
sK144_SY4116: $i > $i > $i > $i ).
thf(tp_sK145_SY4165,type,
sK145_SY4165: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK146_SY4116,type,
sK146_SY4116: $i > $i > $i > $i ).
thf(tp_sK147_SY4201,type,
sK147_SY4201: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK148_SY4209,type,
sK148_SY4209: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK149_SY4210,type,
sK149_SY4210: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK14_SY3582,type,
sK14_SY3582: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK150_SY3519,type,
sK150_SY3519: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK151_SY2866,type,
sK151_SY2866: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK152_SY4193,type,
sK152_SY4193: $i > $i > $i > $i ).
thf(tp_sK153_SY4229,type,
sK153_SY4229: $i > $i > $i > $i ).
thf(tp_sK154_SY4216,type,
sK154_SY4216: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK155_SY3519,type,
sK155_SY3519: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK156_SY2866,type,
sK156_SY2866: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK157_SY4235,type,
sK157_SY4235: $i > $i > $i > $i ).
thf(tp_sK158_SY4221,type,
sK158_SY4221: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK159_SY4222,type,
sK159_SY4222: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK15_SY3598,type,
sK15_SY3598: $i > $i > $i ).
thf(tp_sK160_SY4217,type,
sK160_SY4217: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK161_SY4225,type,
sK161_SY4225: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK162_SY4226,type,
sK162_SY4226: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK163_SY4227,type,
sK163_SY4227: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK164_SY4228,type,
sK164_SY4228: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK165_SY4223,type,
sK165_SY4223: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK166_SY4165,type,
sK166_SY4165: $i > $i > ( $i > $i ) > $i > $i ).
thf(tp_sK167_SY4233,type,
sK167_SY4233: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK168_SY4234,type,
sK168_SY4234: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK169_SY4239,type,
sK169_SY4239: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK16_SY3653,type,
sK16_SY3653: ( $i > $o ) > $i > $i ).
thf(tp_sK170_SY3519,type,
sK170_SY3519: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK171_SY2866,type,
sK171_SY2866: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK172_SY4240,type,
sK172_SY4240: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK173_SY3519,type,
sK173_SY3519: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK174_SY2866,type,
sK174_SY2866: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK175_SY3519,type,
sK175_SY3519: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK176_SY2866,type,
sK176_SY2866: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK177_SY3519,type,
sK177_SY3519: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK178_SY2866,type,
sK178_SY2866: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK179_SY3519,type,
sK179_SY3519: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK17_SY3657,type,
sK17_SY3657: $i > $i > $i ).
thf(tp_sK180_SY2866,type,
sK180_SY2866: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK181_SY3519,type,
sK181_SY3519: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK182_SY2866,type,
sK182_SY2866: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK183_SY3519,type,
sK183_SY3519: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK184_SY2866,type,
sK184_SY2866: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK185_SY3519,type,
sK185_SY3519: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK186_SY2866,type,
sK186_SY2866: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK187_SY4251,type,
sK187_SY4251: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK188_SY4252,type,
sK188_SY4252: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK189_SY4253,type,
sK189_SY4253: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK18_SY3721,type,
sK18_SY3721: $i > $i > $i ).
thf(tp_sK190_SY4254,type,
sK190_SY4254: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK191_SY4258,type,
sK191_SY4258: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK192_SY4259,type,
sK192_SY4259: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK193_SY4260,type,
sK193_SY4260: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK194_SY4268,type,
sK194_SY4268: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK19_SY3726,type,
sK19_SY3726: $i > $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK20_SY2402,type,
sK20_SY2402: $i > $i ).
thf(tp_sK21_SY3733,type,
sK21_SY3733: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK22_SY3742,type,
sK22_SY3742: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK23_SY3745,type,
sK23_SY3745: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK24_SY3770,type,
sK24_SY3770: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK25_SY2669,type,
sK25_SY2669: $i > $i ).
thf(tp_sK26_SY3786,type,
sK26_SY3786: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK27_SY3417,type,
sK27_SY3417: ( $i > $o ) > $i > $i ).
thf(tp_sK28_SY3994,type,
sK28_SY3994: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK29_SY3805,type,
sK29_SY3805: ( $i > $i > $o ) > $i > $i > $i ).
thf(tp_sK2_SY2943,type,
sK2_SY2943: $i > $i ).
thf(tp_sK30_SY3812,type,
sK30_SY3812: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK31_SY3934,type,
sK31_SY3934: $i ).
thf(tp_sK32_SY4003,type,
sK32_SY4003: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK33_SY3826,type,
sK33_SY3826: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK34_SY3599,type,
sK34_SY3599: $i > $i > $i ).
thf(tp_sK35_SY3006,type,
sK35_SY3006: $i > $i ).
thf(tp_sK36_SY3943,type,
sK36_SY3943: ( $i > $o ) > $i > $i ).
thf(tp_sK37_SY3950,type,
sK37_SY3950: $i > ( $i > $o ) > $i ).
thf(tp_sK38_SY3987,type,
sK38_SY3987: ( $i > $o ) > $i > $i ).
thf(tp_sK39_SY3820,type,
sK39_SY3820: $i > $i > $i > $i ).
thf(tp_sK3_SY3462,type,
sK3_SY3462: ( $i > $i ) > $i > $i ).
thf(tp_sK40_SY3540,type,
sK40_SY3540: ( $i > $o ) > $i > $i ).
thf(tp_sK41_SY3843,type,
sK41_SY3843: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK42_SY3668,type,
sK42_SY3668: $i > $i > $i ).
thf(tp_sK43_SY3670,type,
sK43_SY3670: ( $i > $o ) > $i > $i ).
thf(tp_sK44_SY2577,type,
sK44_SY2577: $i > $i ).
thf(tp_sK45_SY3375,type,
sK45_SY3375: $i > $i > $i ).
thf(tp_sK46_SY4001,type,
sK46_SY4001: $o > $i > $i > $i ).
thf(tp_sK47_SX0,type,
sK47_SX0: $i > $i > $i ).
thf(tp_sK48_SX0,type,
sK48_SX0: $i > $i > $i ).
thf(tp_sK49_SY4014,type,
sK49_SY4014: ( $i > $o ) > $i > $i > $i ).
thf(tp_sK4_SY3504,type,
sK4_SY3504: ( $i > $i ) > $i > $i ).
thf(tp_sK50_SY4026,type,
sK50_SY4026: ( $i > $o ) > $i > $i > $i ).
thf(tp_sK51_SY3211,type,
sK51_SY3211: $i > $i > $i ).
thf(tp_sK52_SY3265,type,
sK52_SY3265: $i > $i > $i ).
thf(tp_sK53_SY2563,type,
sK53_SY2563: $i > ( $i > $o ) > $i ).
thf(tp_sK54_SY4052,type,
sK54_SY4052: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(tp_sK55_SY4072,type,
sK55_SY4072: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK56_SY3585,type,
sK56_SY3585: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK57_SY3658,type,
sK57_SY3658: $i > $i > $i ).
thf(tp_sK58_SY4090,type,
sK58_SY4090: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK59_SY3268,type,
sK59_SY3268: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK5_SY3512,type,
sK5_SY3512: $i ).
thf(tp_sK60_SY3750,type,
sK60_SY3750: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK61_SY4131,type,
sK61_SY4131: $i > ( $i > $o ) > $i ).
thf(tp_sK62_SY3965,type,
sK62_SY3965: $i > $i > $i > $i ).
thf(tp_sK63_SY3768,type,
sK63_SY3768: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK64_SY3983,type,
sK64_SY3983: $i > $i > $i > $i ).
thf(tp_sK65_SY3497,type,
sK65_SY3497: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK66_SY4122,type,
sK66_SY4122: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK67_SY4020,type,
sK67_SY4020: $i > $i > $i > $i ).
thf(tp_sK68_SY4124,type,
sK68_SY4124: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK69_SY3658,type,
sK69_SY3658: $i > $i > $i ).
thf(tp_sK6_SY2868,type,
sK6_SY2868: $i > $i ).
thf(tp_sK70_SY4035,type,
sK70_SY4035: $i > $i > $i > $i ).
thf(tp_sK71_SY4042,type,
sK71_SY4042: $i > $i > $i > $i ).
thf(tp_sK72_SY3941,type,
sK72_SY3941: $i > ( $i > $o ) > $i ).
thf(tp_sK73_SY3942,type,
sK73_SY3942: $i > ( $i > $o ) > $i ).
thf(tp_sK74_SY4050,type,
sK74_SY4050: $i > $i > $i > $i > $i ).
thf(tp_sK75_SY3949,type,
sK75_SY3949: $i > ( $i > $o ) > $i ).
thf(tp_sK76_SY3951,type,
sK76_SY3951: $i > ( $i > $o ) > $i ).
thf(tp_sK77_SY4133,type,
sK77_SY4133: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(tp_sK78_SY4059,type,
sK78_SY4059: $i > $i > $i > $i > $i ).
thf(tp_sK79_SY4066,type,
sK79_SY4066: $i > $i > $i > $i > $i ).
thf(tp_sK7_SY3023,type,
sK7_SY3023: $i > $i ).
thf(tp_sK80_SY4002,type,
sK80_SY4002: $i > ( $i > $o ) > $i ).
thf(tp_sK81_SY4144,type,
sK81_SY4144: $i > $i > ( $i > $o ) > $i > $i ).
thf(tp_sK82_SY4081,type,
sK82_SY4081: $i > $i > $i > $i > $i ).
thf(tp_sK83_SY4034,type,
sK83_SY4034: $i > ( $i > $o ) > $i ).
thf(tp_sK84_SY4087,type,
sK84_SY4087: $i > $i > $i > $i > $i ).
thf(tp_sK85_SY4045,type,
sK85_SY4045: $i > ( $i > $o ) > $i ).
thf(tp_sK86_SY4148,type,
sK86_SY4148: $i > $i > ( $i > $o ) > $i > $i ).
thf(tp_sK87_SY4149,type,
sK87_SY4149: $i > $i > $i > $i ).
thf(tp_sK88_SY4137,type,
sK88_SY4137: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK89_SY4150,type,
sK89_SY4150: $i > $i > $i > $i ).
thf(tp_sK8_SY3165,type,
sK8_SY3165: $i > $i ).
thf(tp_sK90_SY4153,type,
sK90_SY4153: $i > $i > $i > $i > $i ).
thf(tp_sK91_SY4108,type,
sK91_SY4108: ( $i > $i ) > $i > $i > $i > $i ).
thf(tp_sK92_SY4154,type,
sK92_SY4154: $i > $i > $i > $i > $i ).
thf(tp_sK93_SY4070,type,
sK93_SY4070: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK94_SY4093,type,
sK94_SY4093: $i > $i > $i > $i ).
thf(tp_sK95_SY2411,type,
sK95_SY2411: $i > ( $i > $o ) > $i ).
thf(tp_sK96_SY2472,type,
sK96_SY2472: $i > ( $i > $o ) > $i ).
thf(tp_sK97_SY2565,type,
sK97_SY2565: $i > ( $i > $o ) > $i ).
thf(tp_sK98_SY2565,type,
sK98_SY2565: $i > ( $i > $o ) > $i ).
thf(tp_sK99_SY3324,type,
sK99_SY3324: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK9_SY3238,type,
sK9_SY3238: ( $i > $o ) > $i > $i ).
thf(tp_secondinupair,type,
secondinupair: $o ).
thf(tp_sepInPowerset,type,
sepInPowerset: $o ).
thf(tp_sepSubset,type,
sepSubset: $o ).
thf(tp_set2prop,type,
set2prop: $i > $o ).
thf(tp_setOfPairsIsBReln,type,
setOfPairsIsBReln: $o ).
thf(tp_setOfPairsIsBReln1,type,
setOfPairsIsBReln1: $o ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinAx,type,
setadjoinAx: $o ).
thf(tp_setadjoinE,type,
setadjoinE: $o ).
thf(tp_setadjoinIL,type,
setadjoinIL: $o ).
thf(tp_setadjoinIR,type,
setadjoinIR: $o ).
thf(tp_setadjoinOr,type,
setadjoinOr: $o ).
thf(tp_setadjoinSub,type,
setadjoinSub: $o ).
thf(tp_setadjoinSub2,type,
setadjoinSub2: $o ).
thf(tp_setadjoin__Cong,type,
setadjoin__Cong: $o ).
thf(tp_setbeta,type,
setbeta: $o ).
thf(tp_setext,type,
setext: $o ).
thf(tp_setextAx,type,
setextAx: $o ).
thf(tp_setextT,type,
setextT: $o ).
thf(tp_setextsub,type,
setextsub: $o ).
thf(tp_setminus,type,
setminus: $i > $i > $i ).
thf(tp_setminusEL,type,
setminusEL: $o ).
thf(tp_setminusELneg,type,
setminusELneg: $o ).
thf(tp_setminusER,type,
setminusER: $o ).
thf(tp_setminusERneg,type,
setminusERneg: $o ).
thf(tp_setminusI,type,
setminusI: $o ).
thf(tp_setminusILneg,type,
setminusILneg: $o ).
thf(tp_setminusIRneg,type,
setminusIRneg: $o ).
thf(tp_setminusLsub,type,
setminusLsub: $o ).
thf(tp_setminusSubset1,type,
setminusSubset1: $o ).
thf(tp_setminusSubset2,type,
setminusSubset2: $o ).
thf(tp_setminusT_lem,type,
setminusT_lem: $o ).
thf(tp_setoftrueEq,type,
setoftrueEq: $o ).
thf(tp_setsmeet,type,
setsmeet: $i > $i > $o ).
thf(tp_setukpairIL,type,
setukpairIL: $o ).
thf(tp_setukpairIR,type,
setukpairIR: $o ).
thf(tp_setukpairinjL,type,
setukpairinjL: $o ).
thf(tp_setukpairinjL1,type,
setukpairinjL1: $o ).
thf(tp_setukpairinjL2,type,
setukpairinjL2: $o ).
thf(tp_setukpairinjR,type,
setukpairinjR: $o ).
thf(tp_setukpairinjR1,type,
setukpairinjR1: $o ).
thf(tp_setukpairinjR11,type,
setukpairinjR11: $o ).
thf(tp_setukpairinjR12,type,
setukpairinjR12: $o ).
thf(tp_setukpairinjR2,type,
setukpairinjR2: $o ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunionAx,type,
setunionAx: $o ).
thf(tp_setunionE,type,
setunionE: $o ).
thf(tp_setunionE2,type,
setunionE2: $o ).
thf(tp_setunionI,type,
setunionI: $o ).
thf(tp_setunion__Cong,type,
setunion__Cong: $o ).
thf(tp_setunionsingleton,type,
setunionsingleton: $o ).
thf(tp_setunionsingleton1,type,
setunionsingleton1: $o ).
thf(tp_setunionsingleton2,type,
setunionsingleton2: $o ).
thf(tp_singleton,type,
singleton: $i > $o ).
thf(tp_singletoninpowerset,type,
singletoninpowerset: $o ).
thf(tp_singletoninpowunion,type,
singletoninpowunion: $o ).
thf(tp_singletonprop,type,
singletonprop: $o ).
thf(tp_singletonsswitch,type,
singletonsswitch: $o ).
thf(tp_singletonsubset,type,
singletonsubset: $o ).
thf(tp_singletonsuniq,type,
singletonsuniq: $o ).
thf(tp_subPowSU,type,
subPowSU: $o ).
thf(tp_subbreln,type,
subbreln: $o ).
thf(tp_subbreln1,type,
subbreln1: $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset2powerset,type,
subset2powerset: $o ).
thf(tp_subsetE,type,
subsetE: $o ).
thf(tp_subsetE2,type,
subsetE2: $o ).
thf(tp_subsetI1,type,
subsetI1: $o ).
thf(tp_subsetI2,type,
subsetI2: $o ).
thf(tp_subsetRefl,type,
subsetRefl: $o ).
thf(tp_subsetTI,type,
subsetTI: $o ).
thf(tp_subsetTrans,type,
subsetTrans: $o ).
thf(tp_subsetemptysetimpeq,type,
subsetemptysetimpeq: $o ).
thf(tp_surjCantorThm,type,
surjCantorThm: $o ).
thf(tp_surjFuncSet,type,
surjFuncSet: $i > $i > $i ).
thf(tp_surjFuncSetFuncIn,type,
surjFuncSetFuncIn: $o ).
thf(tp_surjFuncSetFuncSurj,type,
surjFuncSetFuncSurj: $o ).
thf(tp_surjective,type,
surjective: $i > $i > $i > $o ).
thf(tp_symdiff,type,
symdiff: $i > $i > $i ).
thf(tp_symdiffE,type,
symdiffE: $o ).
thf(tp_symdiffI1,type,
symdiffI1: $o ).
thf(tp_symdiffI2,type,
symdiffI2: $o ).
thf(tp_symdiffIneg1,type,
symdiffIneg1: $o ).
thf(tp_symdiffIneg2,type,
symdiffIneg2: $o ).
thf(tp_theeq,type,
theeq: $o ).
thf(tp_theprop,type,
theprop: $o ).
thf(tp_transitive,type,
transitive: $i > $i > $o ).
thf(tp_transitiveset,type,
transitiveset: $i > $o ).
thf(tp_transitivesetOp1,type,
transitivesetOp1: $o ).
thf(tp_ubforcartprodlem1,type,
ubforcartprodlem1: $o ).
thf(tp_ubforcartprodlem2,type,
ubforcartprodlem2: $o ).
thf(tp_ubforcartprodlem3,type,
ubforcartprodlem3: $o ).
thf(tp_uniqinunit,type,
uniqinunit: $o ).
thf(tp_upairequniteq,type,
upairequniteq: $o ).
thf(tp_upairinpowunion,type,
upairinpowunion: $o ).
thf(tp_upairset2E,type,
upairset2E: $o ).
thf(tp_upairset2IR,type,
upairset2IR: $o ).
thf(tp_upairsetE,type,
upairsetE: $o ).
thf(tp_upairsetIL,type,
upairsetIL: $o ).
thf(tp_upairsetIR,type,
upairsetIR: $o ).
thf(tp_upairsetp,type,
upairsetp: $i > $o ).
thf(tp_upairsubunion,type,
upairsubunion: $o ).
thf(tp_vacuousDall,type,
vacuousDall: $o ).
thf(tp_wellorderingAx,type,
wellorderingAx: $o ).
thf(tp_woz13rule0,type,
woz13rule0: $o ).
thf(tp_woz13rule1,type,
woz13rule1: $o ).
thf(tp_woz13rule2,type,
woz13rule2: $o ).
thf(tp_woz13rule3,type,
woz13rule3: $o ).
thf(tp_woz13rule4,type,
woz13rule4: $o ).
thf(tp_woz1_1,type,
woz1_1: $o ).
thf(tp_woz1_2,type,
woz1_2: $o ).
thf(tp_woz1_3,type,
woz1_3: $o ).
thf(tp_woz1_4,type,
woz1_4: $o ).
thf(tp_woz1_5,type,
woz1_5: $o ).
thf(tp_woz2A,type,
woz2A: $o ).
thf(tp_woz2B,type,
woz2B: $o ).
thf(tp_woz2Ex,type,
woz2Ex: $o ).
thf(tp_woz2W,type,
woz2W: $o ).
thf(ap2apEq1,definition,
( ap2apEq1
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/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(binunionTE,definition,
( binunionTE
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binunion @ X @ Y ) )
=> ( ( ( in @ Xx @ X )
=> Xphi )
=> ( ( ( in @ Xx @ Y )
=> Xphi )
=> Xphi ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTE) ).
thf(binunionTEcontra,definition,
( binunionTEcontra
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ X )
=> ( ~ ( in @ Xx @ Y )
=> ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTEcontra) ).
thf(binunionTILcontra,definition,
( binunionTILcontra
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
=> ~ ( in @ Xx @ X ) ) ) ) ) ) ),
file('/export/starexec/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(breln1SetBreln1,definition,
( breln1SetBreln1
= ( ! [A: $i,R: $i] :
( ( in @ R @ ( breln1Set @ A ) )
=> ( breln1 @ A @ R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1SetBreln1) ).
thf(breln1all1,definition,
( breln1all1
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1all1) ).
thf(breln1all2,definition,
( breln1all2
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1all2) ).
thf(breln1compE,definition,
( breln1compE
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
=> ? [Xz: $i] :
( ( in @ Xz @ A )
& ( in @ ( kpair @ Xx @ Xz ) @ R )
& ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compE) ).
thf(breln1compEex,definition,
( breln1compEex
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
=> ! [Xphi: $o] :
( ! [Xz: $i] :
( ( in @ Xz @ A )
=> ( ( in @ ( kpair @ Xx @ Xz ) @ R )
=> ( ( in @ ( kpair @ Xz @ Xy ) @ S )
=> Xphi ) ) )
=> Xphi ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compEex) ).
thf(breln1compI,definition,
( breln1compI
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ! [Xz: $i] :
( ( in @ Xz @ A )
=> ( ( in @ ( kpair @ Xx @ Xz ) @ R )
=> ( ( in @ ( kpair @ Xz @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compI) ).
thf(breln1compprop,definition,
( breln1compprop
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compprop) ).
thf(breln1invE,definition,
( breln1invE
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1invE) ).
thf(breln1invI,definition,
( breln1invI
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1invI) ).
thf(breln1invprop,definition,
( breln1invprop
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1invprop) ).
thf(breln1unionCommutes,definition,
( breln1unionCommutes
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ( binunion @ R @ S )
= ( binunion @ S @ R ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionCommutes) ).
thf(breln1unionE,definition,
( breln1unionE
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionE) ).
thf(breln1unionEcases,definition,
( breln1unionEcases
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
=> ! [Xphi: $o] :
( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> Xphi )
=> ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> Xphi )
=> Xphi ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionEcases) ).
thf(breln1unionI,definition,
( breln1unionI
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionI) ).
thf(breln1unionIL,definition,
( breln1unionIL
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionIL) ).
thf(breln1unionIR,definition,
( breln1unionIR
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionIR) ).
thf(breln1unionprop,definition,
( breln1unionprop
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionprop) ).
thf(brelnall1,definition,
( brelnall1
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/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(choice2fnsingleton,definition,
( choice2fnsingleton
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xphi @ Xx @ Xy ) ) )
=> ! [R: $i] :
( ( in @ R @ ( breln1Set @ B ) )
=> ( ( reflwellordering @ B @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] :
( ( Xphi @ Xx @ Xy )
& ! [Xz: $i] :
( ( in @ Xz @ B )
=> ( ( Xphi @ Xx @ Xz )
=> ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice2fnsingleton) ).
thf(complementImpComplementIntersect,definition,
( complementImpComplementIntersect
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ X ) )
=> ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/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(complementUnionInPowersetComplement,definition,
( complementUnionInPowersetComplement
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementUnionInPowersetComplement) ).
thf(contraSubsetComplement,definition,
( contraSubsetComplement
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ Y )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ),
file('/export/starexec/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(demorgan1,definition,
( demorgan1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ X @ Y ) )
= ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan1) ).
thf(demorgan1a,definition,
( demorgan1a
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
=> ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan1a) ).
thf(demorgan1b,definition,
( demorgan1b
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan1b) ).
thf(demorgan2,definition,
( demorgan2
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binunion @ X @ Y ) )
= ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2) ).
thf(demorgan2a,definition,
( demorgan2a
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2a) ).
thf(demorgan2a1,definition,
( demorgan2a1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2a1) ).
thf(demorgan2a2,definition,
( demorgan2a2
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2a2) ).
thf(demorgan2b,definition,
( demorgan2b
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2b) ).
thf(demorgan2b2,definition,
( demorgan2b2
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ X ) )
=> ( ( in @ Xx @ ( setminus @ A @ Y ) )
=> ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2b2) ).
thf(descr__Cong,definition,
( descr__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) )
=> ( ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ),
file('/export/starexec/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(eqbreln1,definition,
( eqbreln1
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
=> ( R = S ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqbreln1) ).
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(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(foundation2,definition,
( foundation2
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [X: $i] :
( ( in @ X @ A )
& ( ( binintersect @ X @ A )
= emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundation2) ).
thf(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/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(image1E,definition,
( image1E
= ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) )
=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image1E) ).
thf(image1Equiv,definition,
( image1Equiv
= ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image1Equiv) ).
thf(image1Ex,definition,
( image1Ex
= ( ! [A: $i,Xf: $i > $i] :
? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image1Ex) ).
thf(image1Ex1,definition,
( image1Ex1
= ( ! [A: $i,Xf: $i > $i] :
( exu
@ ^ [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image1Ex1) ).
thf(image1I,definition,
( image1I
= ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) )
=> ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image1I) ).
thf(inComplementUnionImpInComplement1,definition,
( inComplementUnionImpInComplement1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ),
file('/export/starexec/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(injFuncInInjFuncSet,definition,
( injFuncInInjFuncSet
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( ( injective @ A @ B @ Xf )
=> ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injFuncInInjFuncSet) ).
thf(injFuncSetFuncIn,definition,
( injFuncSetFuncIn
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( injFuncSet @ A @ B ) )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injFuncSetFuncIn) ).
thf(injFuncSetFuncInj,definition,
( injFuncSetFuncInj
= ( ! [Xx: $i,Xy: $i,Xf: $i] :
( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
=> ( injective @ Xx @ Xy @ Xf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injFuncSetFuncInj) ).
thf(intersectInPowersetIntersectUnions,definition,
( intersectInPowersetIntersectUnions
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ),
file('/export/starexec/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(leftInvIsSurj,definition,
( leftInvIsSurj
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ B @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
= Xx ) )
=> ( surjective @ B @ A @ Xg ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leftInvIsSurj) ).
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(notinself,definition,
( notinself
= ( ! [A: $i] :
~ ( in @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinself) ).
thf(notinself2,definition,
( notinself2
= ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinself2) ).
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(omegaSclos,definition,
( omegaSclos
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSclos) ).
thf(omegaSp,definition,
( omegaSp
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( omegaS @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSp) ).
thf(omega__Cong,definition,
( omega__Cong
= ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).
thf(peano0notS,definition,
( peano0notS
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( ( omegaS @ Xx )
!= emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',peano0notS) ).
thf(peanoSinj,definition,
( peanoSinj
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ! [Xy: $i] :
( ( in @ Xy @ omega )
=> ( ( ( omegaS @ Xx )
= ( omegaS @ Xy ) )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',peanoSinj) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/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(setOfPairsIsBReln1,definition,
( setOfPairsIsBReln1
= ( ! [A: $i,Xphi: $i > $i > $o] :
( breln1 @ A
@ ( dpsetconstr @ A @ A
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln1) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/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(subbreln1,definition,
( subbreln1
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( subset @ R @ S ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subbreln1) ).
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(surjCantorThm,definition,
( surjCantorThm
= ( ! [A: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ ( powerset @ A ) ) )
=> ~ ( surjective @ A @ ( powerset @ A ) @ Xf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjCantorThm) ).
thf(surjFuncSetFuncIn,definition,
( surjFuncSetFuncIn
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjFuncSetFuncIn) ).
thf(surjFuncSetFuncSurj,definition,
( surjFuncSetFuncSurj
= ( ! [Xx: $i,Xy: $i,Xf: $i] :
( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
=> ( surjective @ Xx @ Xy @ Xf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjFuncSetFuncSurj) ).
thf(symdiffE,definition,
( symdiffE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) ) ),
file('/export/starexec/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(transitiveset,definition,
( transitiveset
= ( ^ [A: $i] :
! [X: $i] :
( ( in @ X @ A )
=> ( subset @ X @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitiveset) ).
thf(transitivesetOp1,definition,
( transitivesetOp1
= ( ! [X: $i] :
( ( transitiveset @ X )
=> ! [A: $i] :
( ( in @ A @ X )
=> ( subset @ A @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivesetOp1) ).
thf(ubforcartprodlem1,definition,
( ubforcartprodlem1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/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(woz13rule0,definition,
( woz13rule0
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule0) ).
thf(woz13rule1,definition,
( woz13rule1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ X @ Z )
=> ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule1) ).
thf(woz13rule2,definition,
( woz13rule2
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ Y @ Z )
=> ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule2) ).
thf(woz13rule3,definition,
( woz13rule3
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ X @ Y )
=> ( ( subset @ X @ Z )
=> ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule3) ).
thf(woz13rule4,definition,
( woz13rule4
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( subset @ X @ Z )
=> ( ( subset @ Y @ W )
=> ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule4) ).
thf(woz1_1,definition,
( woz1_1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz1_1) ).
thf(woz1_2,definition,
( woz1_2
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
= ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz1_2) ).
thf(woz1_3,definition,
( woz1_3
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz1_3) ).
thf(woz1_4,definition,
( woz1_4
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz1_4) ).
thf(woz1_5,definition,
( woz1_5
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz1_5) ).
thf(woz2A,definition,
( woz2A
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [T: $i] :
( ( breln1 @ A @ T )
=> ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
= ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz2A) ).
thf(woz2B,definition,
( woz2B
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [T: $i] :
( ( breln1 @ A @ T )
=> ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
= ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz2B) ).
thf(woz2Ex,definition,
( woz2Ex
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( R
= ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz2Ex) ).
thf(woz2W,definition,
( woz2W
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
= ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz2W) ).
thf(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ( surjFuncSetFuncSurj
=> ( leftInvIsSurj
=> ( surjCantorThm
=> ( foundation2
=> ( notinself
=> ( notinself2
=> ( omegaSp
=> ( omegaSclos
=> ( peano0notS
=> ( peanoSinj
=> ( transitivesetOp1
=> ! [X: $i] :
( ( transitiveset @ X )
=> ! [Y: $i] :
( ( transitiveset @ Y )
=> ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintTransitive) ).
thf(2,negated_conjecture,
( ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ( surjFuncSetFuncSurj
=> ( leftInvIsSurj
=> ( surjCantorThm
=> ( foundation2
=> ( notinself
=> ( notinself2
=> ( omegaSp
=> ( omegaSclos
=> ( peano0notS
=> ( peanoSinj
=> ( transitivesetOp1
=> ! [X: $i] :
( ( transitiveset @ X )
=> ! [Y: $i] :
( ( transitiveset @ Y )
=> ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) )
=> ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) )
=> ( ! [SY22: $i > $i > $o,SY23: $i] :
( ! [SY24: $i] :
( ( in @ SY24 @ SY23 )
=> ? [SY26: $i] :
( ( SY22 @ SY24 @ SY26 )
& ! [SY27: $i] :
( ( SY22 @ SY24 @ SY27 )
=> ( SY26 = SY27 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY23 )
& ( SY22 @ Xy @ Xx ) ) ) )
=> ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) )
=> ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) )
=> ( ! [SY54: $i > $o] :
( ? [SY56: $i] :
( ( SY54 @ SY56 )
& ! [SY57: $i] :
( ( SY54 @ SY57 )
=> ( SY56 = SY57 ) ) )
=> ( SY54
@ ( descr
@ ^ [Xx: $i] : ( SY54 @ Xx ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) )
=> ( ! [SY71: $i > $o] :
( ? [SY73: $i] :
( ( SY71 @ SY73 )
& ! [SY74: $i] :
( ( SY71 @ SY74 )
=> ( SY73 = SY74 ) ) )
=> ? [Xx: $i] :
( ( SY71 @ Xx )
& ! [Xy: $i] :
( ( SY71 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [SY83: $i > $o] :
( ? [SY85: $i] :
( ( SY83 @ SY85 )
& ! [SY86: $i] :
( ( SY83 @ SY86 )
=> ( SY85 = SY86 ) ) )
=> ? [Xx: $i] : ( SY83 @ Xx ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) )
=> ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) )
=> ( ! [SY100: $i] :
( ( SY100 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY100 ) )
=> ( ! [SY102: $i,SY103: $i > $o,SY104: $i] :
( ( in @ SY104 @ SY102 )
=> ( ( SY103 @ SY104 )
=> ( ( dsetconstr @ SY102
@ ^ [Xy: $i] : ( SY103 @ Xy ) )
!= emptyset ) ) )
=> ( ! [SY106: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY106 )
=> ( SY106 != emptyset ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
=> ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) )
=> ( ! [SY139: $i > $o] :
( ? [SY141: $i] :
( ( SY139 @ SY141 )
& ! [SY142: $i] :
( ( SY139 @ SY142 )
=> ( SY141 = SY142 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY139 @ Xy )
<=> ( Xy = Xx ) ) )
=> ( ! [SY145: $i] :
( ( SY145 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY145 )
& $true ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) )
=> ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) )
=> ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) )
=> ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) )
=> ( ! [SY194: $i > $o] :
( ? [Xx: $i] :
( ( SY194 @ Xx )
& ! [Xy: $i] :
( ( SY194 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY198: $i] :
( ( SY194 @ SY198 )
& ! [SY199: $i] :
( ( SY194 @ SY199 )
=> ( SY198 = SY199 ) ) ) )
=> ( ! [SY200: $i > $o] :
( ? [Xx: $i] : ( SY200 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY200 @ Xx )
=> ( ( SY200 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY205: $i] :
( ( SY200 @ SY205 )
& ! [SY206: $i] :
( ( SY200 @ SY206 )
=> ( SY205 = SY206 ) ) ) ) )
=> ( ! [SY207: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY207 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY211: $i] :
( ( SY207 @ SY211 )
& ! [SY212: $i] :
( ( SY207 @ SY212 )
=> ( SY211 = SY212 ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) )
=> ( ! [SY221: $i > $o] :
( ? [SY223: $i] :
( ( SY221 @ SY223 )
& ! [SY224: $i] :
( ( SY221 @ SY224 )
=> ( SY223 = SY224 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY221 @ Xx )
=> ( ( SY221 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY227: $i > $o,SY228: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY227 @ Xx )
<=> ( SY228 @ Xy ) ) )
=> ( ? [SY232: $i] :
( ( SY227 @ SY232 )
& ! [SY233: $i] :
( ( SY227 @ SY233 )
=> ( SY232 = SY233 ) ) )
<=> ? [SY235: $i] :
( ( SY228 @ SY235 )
& ! [SY236: $i] :
( ( SY228 @ SY236 )
=> ( SY235 = SY236 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) )
=> ( ( omega = omega )
=> ( ! [SY245: $i > $o] :
( ? [SY247: $i] :
( ( SY245 @ SY247 )
& ! [SY248: $i] :
( ( SY245 @ SY248 )
=> ( SY247 = SY248 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY245 @ Xx )
=> ( ( SY245 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY251: $i > $o,SY252: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY251 @ Xx )
<=> ( SY252 @ Xy ) ) )
=> ( ? [SY256: $i] :
( ( SY251 @ SY256 )
& ! [SY257: $i] :
( ( SY251 @ SY257 )
=> ( SY256 = SY257 ) ) )
=> ( ? [SY259: $i] :
( ( SY252 @ SY259 )
& ! [SY260: $i] :
( ( SY252 @ SY260 )
=> ( SY259 = SY260 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY251 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY252 @ Xx ) ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i] : ( subset @ emptyset @ A )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) )
=> ( ! [A: $i] : ( subset @ A @ A )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) )
=> ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) )
=> ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) )
=> ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) )
=> ( ! [A: $i] : ( in @ A @ ( powerset @ A ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) )
=> ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) )
=> ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) )
=> ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B )
=> ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) )
=> ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A )
=> ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) )
=> ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) )
=> ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A )
=> ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) )
=> ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx )
=> ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xy )
=> ( Xy = Xx ) ) )
=> ( ex1 @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) )
=> ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) )
=> ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx )
=> ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xy = Xu ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) )
=> ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy )
=> ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) )
=> ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( ksnd @ Xu ) @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) )
=> ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) )
=> ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xphi @ Xx @ Xy )
=> ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) )
=> ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( subset
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
@ ( cartprod @ A @ B ) )
=> ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( breln @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) )
=> ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( in @ Xy @ B ) )
=> ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in
@ ( setunion
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
@ B ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) )
=> ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] :
( ( Xf @ Xx )
= Xy ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( in
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
@ ( funcSet @ A @ B ) ) )
=> ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) )
=> ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
=> ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) )
=> ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( subset @ R @ S ) ) ) )
=> ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
=> ( R = S ) ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ A @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) )
=> ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
= ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( in @ Xy
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xy @ emptyset ) ) ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) )
=> ( ! [X: $i] :
( ( singleton @ X )
=> ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ( setunion @ X )
= Xx ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xy ) ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ Y )
=> ( in @ Xx @ X ) ) )
=> ( X = Y ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) )
=> ( subset @ X @ Y ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) )
=> ( in @ X @ ( powerset @ Y ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ X @ ( powerset @ Y ) )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
=> ( in @ Xx @ X ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ X )
=> ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ Y )
=> ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( ( in @ Xx @ Y )
=> ~ ( in @ Xx @ X ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( subset @ X @ Y )
=> ( ~ ( in @ Xx @ Y )
=> ~ ( in @ Xx @ X ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ Y )
=> ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
=> ( subset @ X @ Y ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
=> ( in @ Xx @ X ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( X
= ( setminus @ A @ ( setminus @ A @ X ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ X ) )
=> ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ X ) )
=> ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ Y )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
=> ~ ( in @ Xx @ X ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
=> ~ ( in @ Xx @ Y ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ~ ( in @ Xx @ X ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binunion @ X @ Y ) )
=> ( ( ( in @ Xx @ X )
=> Xphi )
=> ( ( ( in @ Xx @ Y )
=> Xphi )
=> Xphi ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ X )
=> ( ~ ( in @ Xx @ Y )
=> ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
=> ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ X @ Y ) )
= ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ X ) )
=> ( ( in @ Xx @ ( setminus @ A @ Y ) )
=> ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binunion @ X @ Y ) )
= ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ A ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ X @ Z )
=> ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ Y @ Z )
=> ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ X @ Y )
=> ( ( subset @ X @ Z )
=> ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( subset @ X @ Z )
=> ( ( subset @ Y @ W )
=> ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
= ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( in @ R @ ( breln1Set @ A ) )
=> ( breln1 @ A @ R ) )
=> ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xphi @ Xx @ Xy ) ) )
=> ! [R: $i] :
( ( in @ R @ ( breln1Set @ B ) )
=> ( ( reflwellordering @ B @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] :
( ( Xphi @ Xx @ Xy )
& ! [Xz: $i] :
( ( in @ Xz @ B )
=> ( ( Xphi @ Xx @ Xz )
=> ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) )
=> ( ! [A: $i,Xphi: $i > $i > $o] :
( breln1 @ A
@ ( dpsetconstr @ A @ A
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( subset @ R @ S ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
=> ( R = S ) ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( breln1 @ A @ ( breln1invset @ A @ R ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ! [Xz: $i] :
( ( in @ Xz @ A )
=> ( ( in @ ( kpair @ Xx @ Xz ) @ R )
=> ( ( in @ ( kpair @ Xz @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
=> ? [Xz: $i] :
( ( in @ Xz @ A )
& ( in @ ( kpair @ Xx @ Xz ) @ R )
& ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
=> ! [Xphi: $o] :
( ! [Xz: $i] :
( ( in @ Xz @ A )
=> ( ( in @ ( kpair @ Xx @ Xz ) @ R )
=> ( ( in @ ( kpair @ Xz @ Xy ) @ S )
=> Xphi ) ) )
=> Xphi ) ) ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( binunion @ R @ S ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
=> ! [Xphi: $o] :
( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> Xphi )
=> ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> Xphi )
=> Xphi ) ) ) ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ( binunion @ R @ S )
= ( binunion @ S @ R ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( R
= ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
= ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [T: $i] :
( ( breln1 @ A @ T )
=> ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
= ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [T: $i] :
( ( breln1 @ A @ T )
=> ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
= ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) )
=> ( ! [A: $i,Xf: $i > $i] :
? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) )
=> ( ! [SY1127: $i,SY1128: $i > $i] :
? [SY1132: $i] :
( ! [SY1133: $i] :
( ( in @ SY1133 @ SY1132 )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY1127 )
& ( SY1133
= ( SY1128 @ Xy ) ) ) )
& ! [SY1135: $i] :
( ! [SY1136: $i] :
( ( in @ SY1136 @ SY1135 )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY1127 )
& ( SY1136
= ( SY1128 @ Xy ) ) ) )
=> ( SY1132 = SY1135 ) ) )
=> ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) )
=> ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) )
=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) )
=> ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) )
=> ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( ( injective @ A @ B @ Xf )
=> ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( injFuncSet @ A @ B ) )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) )
=> ( ! [Xx: $i,Xy: $i,Xf: $i] :
( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
=> ( injective @ Xx @ Xy @ Xf ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) )
=> ( ! [Xx: $i,Xy: $i,Xf: $i] :
( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
=> ( surjective @ Xx @ Xy @ Xf ) )
=> ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ B @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
= Xx ) )
=> ( surjective @ B @ A @ Xg ) ) ) )
=> ( ! [A: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ ( powerset @ A ) ) )
=> ~ ( surjective @ A @ ( powerset @ A ) @ Xf ) )
=> ( ! [SY1176: $i] :
( ( SY1176 != emptyset )
=> ? [X: $i] :
( ( in @ X @ SY1176 )
& ( ( binintersect @ X @ SY1176 )
= emptyset ) ) )
=> ( ! [A: $i] :
~ ( in @ A @ A )
=> ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( omegaS @ Xx ) @ omega ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( ( omegaS @ Xx )
!= emptyset ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ! [Xy: $i] :
( ( in @ Xy @ omega )
=> ( ( ( omegaS @ Xx )
= ( omegaS @ Xy ) )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY1186: $i] :
( ! [SY1187: $i] :
( ( in @ SY1187 @ SY1186 )
=> ( subset @ SY1187 @ SY1186 ) )
=> ! [A: $i] :
( ( in @ A @ SY1186 )
=> ( subset @ A @ SY1186 ) ) )
=> ! [SY0: $i] :
( ! [SY1: $i] :
( ( in @ SY1 @ SY0 )
=> ( subset @ SY1 @ SY0 ) )
=> ! [SY2: $i] :
( ! [SY3: $i] :
( ( in @ SY3 @ SY2 )
=> ( subset @ SY3 @ SY2 ) )
=> ! [SY4: $i] :
( ( in @ SY4 @ ( binintersect @ SY0 @ SY2 ) )
=> ( subset @ SY4 @ ( binintersect @ SY0 @ SY2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [SY22: $i > $i > $o,SY23: $i] :
( ! [SY24: $i] :
( ( in @ SY24 @ SY23 )
=> ? [SY26: $i] :
( ( SY22 @ SY24 @ SY26 )
& ! [SY27: $i] :
( ( SY22 @ SY24 @ SY27 )
=> ( SY26 = SY27 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY23 )
& ( SY22 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [SY54: $i > $o] :
( ? [SY56: $i] :
( ( SY54 @ SY56 )
& ! [SY57: $i] :
( ( SY54 @ SY57 )
=> ( SY56 = SY57 ) ) )
=> ( SY54
@ ( descr
@ ^ [Xx: $i] : ( SY54 @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [SY71: $i > $o] :
( ? [SY73: $i] :
( ( SY71 @ SY73 )
& ! [SY74: $i] :
( ( SY71 @ SY74 )
=> ( SY73 = SY74 ) ) )
=> ? [Xx: $i] :
( ( SY71 @ Xx )
& ! [Xy: $i] :
( ( SY71 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(24,plain,
( ( ! [SY83: $i > $o] :
( ? [SY85: $i] :
( ( SY83 @ SY85 )
& ! [SY86: $i] :
( ( SY83 @ SY86 )
=> ( SY85 = SY86 ) ) )
=> ? [Xx: $i] : ( SY83 @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(27,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(29,plain,
( ( ! [SY100: $i] :
( ( SY100 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY100 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [SY102: $i,SY103: $i > $o,SY104: $i] :
( ( in @ SY104 @ SY102 )
=> ( ( SY103 @ SY104 )
=> ( ( dsetconstr @ SY102
@ ^ [Xy: $i] : ( SY103 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [SY106: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY106 )
=> ( SY106 != emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(32,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(33,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(34,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(35,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(36,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(39,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(40,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(41,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(42,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(43,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(44,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(45,plain,
( ( ! [SY139: $i > $o] :
( ? [SY141: $i] :
( ( SY139 @ SY141 )
& ! [SY142: $i] :
( ( SY139 @ SY142 )
=> ( SY141 = SY142 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY139 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(46,plain,
( ( ! [SY145: $i] :
( ( SY145 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY145 )
& $true ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(47,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(48,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(49,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(50,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(51,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(52,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(53,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(54,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(55,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(56,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(57,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(58,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(59,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(60,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(61,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(62,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(63,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(64,plain,
( ( ! [SY194: $i > $o] :
( ? [Xx: $i] :
( ( SY194 @ Xx )
& ! [Xy: $i] :
( ( SY194 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY198: $i] :
( ( SY194 @ SY198 )
& ! [SY199: $i] :
( ( SY194 @ SY199 )
=> ( SY198 = SY199 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(65,plain,
( ( ! [SY200: $i > $o] :
( ? [Xx: $i] : ( SY200 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY200 @ Xx )
=> ( ( SY200 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY205: $i] :
( ( SY200 @ SY205 )
& ! [SY206: $i] :
( ( SY200 @ SY206 )
=> ( SY205 = SY206 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(66,plain,
( ( ! [SY207: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY207 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY211: $i] :
( ( SY207 @ SY211 )
& ! [SY212: $i] :
( ( SY207 @ SY212 )
=> ( SY211 = SY212 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(68,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(69,plain,
( ( ! [SY221: $i > $o] :
( ? [SY223: $i] :
( ( SY221 @ SY223 )
& ! [SY224: $i] :
( ( SY221 @ SY224 )
=> ( SY223 = SY224 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY221 @ Xx )
=> ( ( SY221 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(70,plain,
( ( ! [SY227: $i > $o,SY228: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY227 @ Xx )
<=> ( SY228 @ Xy ) ) )
=> ( ? [SY232: $i] :
( ( SY227 @ SY232 )
& ! [SY233: $i] :
( ( SY227 @ SY233 )
=> ( SY232 = SY233 ) ) )
<=> ? [SY235: $i] :
( ( SY228 @ SY235 )
& ! [SY236: $i] :
( ( SY228 @ SY236 )
=> ( SY235 = SY236 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(71,plain,
( ( emptyset = emptyset )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(72,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(73,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(74,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(75,plain,
( ( omega = omega )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(76,plain,
( ( ! [SY245: $i > $o] :
( ? [SY247: $i] :
( ( SY245 @ SY247 )
& ! [SY248: $i] :
( ( SY245 @ SY248 )
=> ( SY247 = SY248 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY245 @ Xx )
=> ( ( SY245 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(77,plain,
( ( ! [SY251: $i > $o,SY252: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY251 @ Xx )
<=> ( SY252 @ Xy ) ) )
=> ( ? [SY256: $i] :
( ( SY251 @ SY256 )
& ! [SY257: $i] :
( ( SY251 @ SY257 )
=> ( SY256 = SY257 ) ) )
=> ( ? [SY259: $i] :
( ( SY252 @ SY259 )
& ! [SY260: $i] :
( ( SY252 @ SY260 )
=> ( SY259 = SY260 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY251 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY252 @ Xx ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(82,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(83,plain,
( ( ! [A: $i] : ( subset @ emptyset @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(84,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(85,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(86,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(87,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(88,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(89,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(90,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(91,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(92,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(95,plain,
( ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(98,plain,
( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(99,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(100,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(101,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(102,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(103,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(104,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(105,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(106,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(107,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(109,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(110,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(111,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(113,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(114,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(115,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(116,plain,
( ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(117,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(118,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(119,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(120,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(121,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(122,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(123,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(124,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(125,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(126,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(127,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(128,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(129,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(130,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(131,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(132,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(133,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(134,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(135,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(136,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(137,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(138,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(139,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(140,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(141,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(142,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(143,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(144,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(145,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(146,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(147,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(148,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(149,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(150,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(151,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(152,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(153,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(154,plain,
( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(155,plain,
( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(156,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(157,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(158,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(159,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xy )
=> ( Xy = Xx ) ) )
=> ( ex1 @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(160,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(161,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(162,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(163,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(164,plain,
( ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(165,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(166,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(167,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(168,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(169,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(170,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(171,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(172,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(173,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xy = Xu ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(174,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(175,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(176,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(177,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(178,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( ksnd @ Xu ) @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(179,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(180,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(181,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(182,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(183,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(184,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(185,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xphi @ Xx @ Xy )
=> ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(186,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( subset
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
@ ( cartprod @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(187,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( breln @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(188,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(189,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(190,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( in @ Xy @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(191,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(192,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(193,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in
@ ( setunion
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
@ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(194,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(195,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(196,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(197,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(198,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] :
( ( Xf @ Xx )
= Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(199,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(200,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( in
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
@ ( funcSet @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(201,plain,
( ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(202,plain,
( ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(203,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(204,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(205,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(206,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(207,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
=> ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(208,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(209,plain,
( ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( subset @ R @ S ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(210,plain,
( ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
=> ( R = S ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(211,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(212,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ A @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(213,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(214,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(215,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(216,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(217,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
= ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(218,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(219,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(220,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( in @ Xy
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(221,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xy @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(222,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(223,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(224,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(225,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(226,plain,
( ( ! [X: $i] :
( ( singleton @ X )
=> ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ( setunion @ X )
= Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(227,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(228,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(229,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(230,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(231,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(232,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(233,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(234,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(235,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ Y )
=> ( in @ Xx @ X ) ) )
=> ( X = Y ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(236,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) )
=> ( subset @ X @ Y ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(237,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) )
=> ( in @ X @ ( powerset @ Y ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(238,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ X @ ( powerset @ Y ) )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(239,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(240,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
=> ( in @ Xx @ X ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(241,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ X )
=> ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(242,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ Y )
=> ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(243,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( ( in @ Xx @ Y )
=> ~ ( in @ Xx @ X ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(244,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( subset @ X @ Y )
=> ( ~ ( in @ Xx @ Y )
=> ~ ( in @ Xx @ X ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(245,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ Y )
=> ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(246,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
=> ( subset @ X @ Y ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(247,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(248,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
=> ( in @ Xx @ X ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(249,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(250,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(251,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( X
= ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(252,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ X ) )
=> ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(253,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ X ) )
=> ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(254,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(255,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(256,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ Y )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(257,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(258,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
=> ~ ( in @ Xx @ X ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(259,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
=> ~ ( in @ Xx @ Y ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(260,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(261,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(262,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(263,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(264,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ~ ( in @ Xx @ X ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(265,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(266,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binunion @ X @ Y ) )
=> ( ( ( in @ Xx @ X )
=> Xphi )
=> ( ( ( in @ Xx @ Y )
=> Xphi )
=> Xphi ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(267,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ X )
=> ( ~ ( in @ Xx @ Y )
=> ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(268,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(269,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(270,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(271,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
=> ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(272,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(273,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ X @ Y ) )
= ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(274,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(275,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ X ) )
=> ( ( in @ Xx @ ( setminus @ A @ Y ) )
=> ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(276,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(277,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binunion @ X @ Y ) )
= ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(278,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(279,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ X @ Z )
=> ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(280,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ Y @ Z )
=> ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(281,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ X @ Y )
=> ( ( subset @ X @ Z )
=> ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(282,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( subset @ X @ Z )
=> ( ( subset @ Y @ W )
=> ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(283,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(284,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
= ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(285,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(286,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(287,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(288,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(289,plain,
( ( ! [A: $i,R: $i] :
( ( in @ R @ ( breln1Set @ A ) )
=> ( breln1 @ A @ R ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(290,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xphi @ Xx @ Xy ) ) )
=> ! [R: $i] :
( ( in @ R @ ( breln1Set @ B ) )
=> ( ( reflwellordering @ B @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] :
( ( Xphi @ Xx @ Xy )
& ! [Xz: $i] :
( ( in @ Xz @ B )
=> ( ( Xphi @ Xx @ Xz )
=> ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(291,plain,
( ( ! [A: $i,Xphi: $i > $i > $o] :
( breln1 @ A
@ ( dpsetconstr @ A @ A
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(292,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(293,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( subset @ R @ S ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(294,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
=> ( R = S ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(295,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(296,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(297,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(298,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(299,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ! [Xz: $i] :
( ( in @ Xz @ A )
=> ( ( in @ ( kpair @ Xx @ Xz ) @ R )
=> ( ( in @ ( kpair @ Xz @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(300,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
=> ? [Xz: $i] :
( ( in @ Xz @ A )
& ( in @ ( kpair @ Xx @ Xz ) @ R )
& ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(301,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
=> ! [Xphi: $o] :
( ! [Xz: $i] :
( ( in @ Xz @ A )
=> ( ( in @ ( kpair @ Xx @ Xz ) @ R )
=> ( ( in @ ( kpair @ Xz @ Xy ) @ S )
=> Xphi ) ) )
=> Xphi ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(302,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(303,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(304,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(305,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(306,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(307,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
=> ! [Xphi: $o] :
( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> Xphi )
=> ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> Xphi )
=> Xphi ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(308,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ( binunion @ R @ S )
= ( binunion @ S @ R ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(309,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( R
= ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(310,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
= ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(311,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [T: $i] :
( ( breln1 @ A @ T )
=> ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
= ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(312,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [T: $i] :
( ( breln1 @ A @ T )
=> ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
= ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(313,plain,
( ( ! [A: $i,Xf: $i > $i] :
? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(314,plain,
( ( ! [SY1127: $i,SY1128: $i > $i] :
? [SY1132: $i] :
( ! [SY1133: $i] :
( ( in @ SY1133 @ SY1132 )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY1127 )
& ( SY1133
= ( SY1128 @ Xy ) ) ) )
& ! [SY1135: $i] :
( ! [SY1136: $i] :
( ( in @ SY1136 @ SY1135 )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY1127 )
& ( SY1136
= ( SY1128 @ Xy ) ) ) )
=> ( SY1132 = SY1135 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(315,plain,
( ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(316,plain,
( ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) )
=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(317,plain,
( ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) )
=> ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(318,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( ( injective @ A @ B @ Xf )
=> ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(319,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( injFuncSet @ A @ B ) )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(320,plain,
( ( ! [Xx: $i,Xy: $i,Xf: $i] :
( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
=> ( injective @ Xx @ Xy @ Xf ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(321,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(322,plain,
( ( ! [Xx: $i,Xy: $i,Xf: $i] :
( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
=> ( surjective @ Xx @ Xy @ Xf ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(323,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ B @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
= Xx ) )
=> ( surjective @ B @ A @ Xg ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(324,plain,
( ( ! [A: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ ( powerset @ A ) ) )
=> ~ ( surjective @ A @ ( powerset @ A ) @ Xf ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(325,plain,
( ( ! [SY1176: $i] :
( ( SY1176 != emptyset )
=> ? [X: $i] :
( ( in @ X @ SY1176 )
& ( ( binintersect @ X @ SY1176 )
= emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(326,plain,
( ( ! [A: $i] :
~ ( in @ A @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(327,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(328,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( omegaS @ Xx ) @ omega ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(329,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(330,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( ( omegaS @ Xx )
!= emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(331,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ! [Xy: $i] :
( ( in @ Xy @ omega )
=> ( ( ( omegaS @ Xx )
= ( omegaS @ Xy ) )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(332,plain,
( ( ! [SY1186: $i] :
( ! [SY1187: $i] :
( ( in @ SY1187 @ SY1186 )
=> ( subset @ SY1187 @ SY1186 ) )
=> ! [A: $i] :
( ( in @ A @ SY1186 )
=> ( subset @ A @ SY1186 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(333,plain,
( ( ! [SY0: $i] :
( ! [SY1: $i] :
( ( in @ SY1 @ SY0 )
=> ( subset @ SY1 @ SY0 ) )
=> ! [SY2: $i] :
( ! [SY3: $i] :
( ( in @ SY3 @ SY2 )
=> ( subset @ SY3 @ SY2 ) )
=> ! [SY4: $i] :
( ( in @ SY4 @ ( binintersect @ SY0 @ SY2 ) )
=> ( subset @ SY4 @ ( binintersect @ SY0 @ SY2 ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(334,plain,
( ( ~ ! [SY0: $i] :
( ! [SY1: $i] :
( ( in @ SY1 @ SY0 )
=> ( subset @ SY1 @ SY0 ) )
=> ! [SY2: $i] :
( ! [SY3: $i] :
( ( in @ SY3 @ SY2 )
=> ( subset @ SY3 @ SY2 ) )
=> ! [SY4: $i] :
( ( in @ SY4 @ ( binintersect @ SY0 @ SY2 ) )
=> ( subset @ SY4 @ ( binintersect @ SY0 @ SY2 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[333]) ).
thf(335,plain,
( ( ! [SY1186: $i] :
( ! [SY1187: $i] :
( ( in @ SY1187 @ SY1186 )
=> ( subset @ SY1187 @ SY1186 ) )
=> ! [A: $i] :
( ( in @ A @ SY1186 )
=> ( subset @ A @ SY1186 ) ) ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(336,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ! [Xy: $i] :
( ( in @ Xy @ omega )
=> ( ( ( omegaS @ Xx )
= ( omegaS @ Xy ) )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(337,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( ( omegaS @ Xx )
!= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(338,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(339,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( omegaS @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(340,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(341,plain,
( ( ! [A: $i] :
~ ( in @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(342,plain,
( ( ! [SY1176: $i] :
( ( SY1176 != emptyset )
=> ? [X: $i] :
( ( in @ X @ SY1176 )
& ( ( binintersect @ X @ SY1176 )
= emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(343,plain,
( ( ! [A: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ ( powerset @ A ) ) )
=> ~ ( surjective @ A @ ( powerset @ A ) @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(344,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ B @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
= Xx ) )
=> ( surjective @ B @ A @ Xg ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(345,plain,
( ( ! [Xx: $i,Xy: $i,Xf: $i] :
( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
=> ( surjective @ Xx @ Xy @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(346,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(347,plain,
( ( ! [Xx: $i,Xy: $i,Xf: $i] :
( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
=> ( injective @ Xx @ Xy @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(348,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( injFuncSet @ A @ B ) )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(349,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( ( injective @ A @ B @ Xf )
=> ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[318]) ).
thf(350,plain,
( ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) )
=> ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(351,plain,
( ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) )
=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(352,plain,
( ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(353,plain,
( ( ! [SY1127: $i,SY1128: $i > $i] :
? [SY1132: $i] :
( ! [SY1133: $i] :
( ( in @ SY1133 @ SY1132 )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY1127 )
& ( SY1133
= ( SY1128 @ Xy ) ) ) )
& ! [SY1135: $i] :
( ! [SY1136: $i] :
( ( in @ SY1136 @ SY1135 )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY1127 )
& ( SY1136
= ( SY1128 @ Xy ) ) ) )
=> ( SY1132 = SY1135 ) ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(354,plain,
( ( ! [A: $i,Xf: $i > $i] :
? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(355,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [T: $i] :
( ( breln1 @ A @ T )
=> ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
= ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(356,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [T: $i] :
( ( breln1 @ A @ T )
=> ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
= ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(357,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
= ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(358,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( R
= ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[309]) ).
thf(359,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ( binunion @ R @ S )
= ( binunion @ S @ R ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(360,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
=> ! [Xphi: $o] :
( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> Xphi )
=> ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> Xphi )
=> Xphi ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[307]) ).
thf(361,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[306]) ).
thf(362,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[305]) ).
thf(363,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[304]) ).
thf(364,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(365,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(366,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
=> ! [Xphi: $o] :
( ! [Xz: $i] :
( ( in @ Xz @ A )
=> ( ( in @ ( kpair @ Xx @ Xz ) @ R )
=> ( ( in @ ( kpair @ Xz @ Xy ) @ S )
=> Xphi ) ) )
=> Xphi ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[301]) ).
thf(367,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
=> ? [Xz: $i] :
( ( in @ Xz @ A )
& ( in @ ( kpair @ Xx @ Xz ) @ R )
& ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(368,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ! [Xz: $i] :
( ( in @ Xz @ A )
=> ( ( in @ ( kpair @ Xx @ Xz ) @ R )
=> ( ( in @ ( kpair @ Xz @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[299]) ).
thf(369,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[298]) ).
thf(370,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(371,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(372,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[295]) ).
thf(373,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
=> ( R = S ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(374,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( subset @ R @ S ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[293]) ).
thf(375,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(376,plain,
( ( ! [A: $i,Xphi: $i > $i > $o] :
( breln1 @ A
@ ( dpsetconstr @ A @ A
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(377,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xphi @ Xx @ Xy ) ) )
=> ! [R: $i] :
( ( in @ R @ ( breln1Set @ B ) )
=> ( ( reflwellordering @ B @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] :
( ( Xphi @ Xx @ Xy )
& ! [Xz: $i] :
( ( in @ Xz @ B )
=> ( ( Xphi @ Xx @ Xz )
=> ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(378,plain,
( ( ! [A: $i,R: $i] :
( ( in @ R @ ( breln1Set @ A ) )
=> ( breln1 @ A @ R ) ) )
= $true ),
inference(copy,[status(thm)],[289]) ).
thf(379,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[288]) ).
thf(380,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[287]) ).
thf(381,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(382,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[285]) ).
thf(383,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
= ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(384,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(385,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( subset @ X @ Z )
=> ( ( subset @ Y @ W )
=> ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(386,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ X @ Y )
=> ( ( subset @ X @ Z )
=> ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[281]) ).
thf(387,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ Y @ Z )
=> ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(388,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ X @ Z )
=> ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(389,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(390,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binunion @ X @ Y ) )
= ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(391,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(392,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ X ) )
=> ( ( in @ Xx @ ( setminus @ A @ Y ) )
=> ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(393,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(394,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ X @ Y ) )
= ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[273]) ).
thf(395,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(396,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
=> ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(397,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(398,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(399,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(400,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ X )
=> ( ~ ( in @ Xx @ Y )
=> ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(401,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binunion @ X @ Y ) )
=> ( ( ( in @ Xx @ X )
=> Xphi )
=> ( ( ( in @ Xx @ Y )
=> Xphi )
=> Xphi ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(402,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(403,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(404,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(405,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(406,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(407,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(408,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(409,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(410,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(411,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(412,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(413,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(414,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(415,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(416,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( X
= ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(417,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(418,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(419,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(420,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(421,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(422,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(423,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(424,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(425,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(426,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(427,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(428,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(429,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(430,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(431,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(432,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(433,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(434,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(435,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(436,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(437,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(438,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(439,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(440,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(441,plain,
( ( ! [X: $i] :
( ( singleton @ X )
=> ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ( setunion @ X )
= Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(442,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(443,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(444,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(445,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(446,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(447,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(448,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(449,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(450,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(451,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(452,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(453,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(454,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(455,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(456,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(457,plain,
( ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
=> ( R = S ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(458,plain,
( ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( subset @ R @ S ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(459,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(460,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(461,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(462,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(463,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(464,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(465,plain,
( ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(466,plain,
( ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(467,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(468,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(469,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(470,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(471,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(472,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(473,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(474,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(475,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(476,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(477,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(478,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(479,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(480,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( breln @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(481,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(482,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(483,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(484,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(485,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(486,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(487,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(488,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(489,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( ksnd @ Xu ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(490,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(491,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(492,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(493,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(494,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(495,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(496,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(497,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(498,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(499,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(500,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(501,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(502,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(503,plain,
( ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(504,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(505,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(506,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(507,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(508,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xy )
=> ( Xy = Xx ) ) )
=> ( ex1 @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(509,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(510,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(511,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(512,plain,
( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(513,plain,
( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(514,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(515,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(516,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(517,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(518,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(519,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(520,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(521,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(522,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(523,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(524,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(525,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(526,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(527,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(528,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(529,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(530,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(531,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(532,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(533,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(534,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(535,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(536,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(537,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(538,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(539,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(540,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(541,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(542,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(543,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(544,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(545,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(546,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(547,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(548,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(549,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(550,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(551,plain,
( ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(552,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(553,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(554,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(555,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(556,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(557,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(558,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(559,plain,
( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(560,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(561,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(562,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(563,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(564,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(565,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(566,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(567,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(568,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(569,plain,
( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(570,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(571,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(572,plain,
( ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(573,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(574,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(575,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(576,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(577,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(578,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(579,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(580,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(581,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(582,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(583,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(584,plain,
( ( ! [A: $i] : ( subset @ emptyset @ A ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(585,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(586,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(587,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(588,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(589,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(590,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(591,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(592,plain,
( ( omega = omega )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(593,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(594,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(595,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(596,plain,
( ( emptyset = emptyset )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(597,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(598,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(599,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(600,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(601,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(602,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(603,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(604,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(605,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(606,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(607,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(608,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(609,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(610,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(611,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(612,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(613,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(614,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(615,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(616,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(617,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(618,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(619,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(620,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(621,plain,
( ( ! [SY145: $i] :
( ( SY145 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY145 )
& $true ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(622,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(623,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(624,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(625,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(626,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(627,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(628,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(629,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(630,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(631,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(632,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(633,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(634,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(635,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(636,plain,
( ( ! [SY106: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY106 )
=> ( SY106 != emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(637,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(638,plain,
( ( ! [SY100: $i] :
( ( SY100 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY100 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(639,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(640,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(641,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(642,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(643,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(644,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(645,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(646,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(647,plain,
( ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(648,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(649,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(650,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(651,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(652,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(653,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(654,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(655,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(656,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(657,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(658,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(659,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(660,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(661,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(662,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(663,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(664,plain,
( ( ~ ! [SY0: $i] :
( ! [SY1: $i] :
( ( in @ SY1 @ SY0 )
=> ( subset @ SY1 @ SY0 ) )
=> ! [SY2: $i] :
( ! [SY3: $i] :
( ( in @ SY3 @ SY2 )
=> ( subset @ SY3 @ SY2 ) )
=> ! [SY4: $i] :
( ( in @ SY4 @ ( binintersect @ SY0 @ SY2 ) )
=> ( subset @ SY4 @ ( binintersect @ SY0 @ SY2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(665,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[620,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(666,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[621,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(667,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ omega )
| ( ( omegaS @ SX0 )
!= ( omegaS @ SX1 ) )
| ( 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,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(668,plain,
( ( ! [SX0: $i,SX1: $i,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)],[469,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(669,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(670,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( ( kpair @ SX2 @ SX3 )
= ( kpair @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(671,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ( SX0
@ ( descr
@ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[652,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(672,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( powerset @ SX0 )
= ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[594,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(673,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ 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)],[510,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(674,plain,
( ( ! [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)],[455,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(675,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( setadjoin @ SX2 @ emptyset ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(676,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( 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)],[462,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(677,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,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)],[494,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(678,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(679,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ( ( setadjoin @ SX0 @ SX2 )
= ( setadjoin @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[595,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(680,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ( func @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(681,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[406,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(682,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( ( binintersect @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[549,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(683,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $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)],[467,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(684,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ ( setminus @ SX0 @ SX2 ) )
| ( subset @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(685,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ ( powerset @ SX0 ) )
| ( ( setminus @ SX0 @ ( binintersect @ ( binunion @ SX1 @ SX2 ) @ ( binunion @ SX3 @ SX4 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SX0 @ SX1 ) @ ( setminus @ SX0 @ SX2 ) ) @ ( binintersect @ ( setminus @ SX0 @ SX3 ) @ ( setminus @ SX0 @ SX4 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(686,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( 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)],[659,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(687,plain,
( ( ! [SX0: $i > $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)],[598,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(688,plain,
( ( ! [SX0: $i > $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)],[601,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(689,plain,
( ( ! [SX0: $i > $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)],[648,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(690,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[611,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(691,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ( in @ SX1 @ emptyset )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[612,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(692,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(693,plain,
( ( ! [SX0: $i,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)],[450,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(694,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[663,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(695,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| ! [SX1: $o] : SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[646,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(696,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ emptyset )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[572,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(697,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[411,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(698,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ ( setminus @ SX0 @ ( binintersect @ SX1 @ SX2 ) ) )
| ( in @ SX3 @ ( binunion @ ( setminus @ SX0 @ SX1 ) @ ( setminus @ SX0 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(699,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[618,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(700,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( binunion @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(701,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ! [SX3: $o] :
( ~ ( ( SX2 != SX0 )
| SX3 )
| ~ ( ~ ( in @ SX2 @ SX1 )
| SX3 )
| SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[632,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(702,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ( breln1 @ SX0 @ ( breln1compset @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(703,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ( SX1
= ( breln1invset @ SX0 @ ( breln1invset @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(704,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) ) )
| ( in @ SX3 @ ( setminus @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(705,plain,
( ( ! [SX0: $i,SX1: $i > $i,SX2: $i] :
~ ( ~ ( ~ ( in @ SX2
@ ( image1 @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX0 )
| ( SX2
!= ( SX1 @ SX3 ) ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX0 )
| ( SX2
!= ( SX1 @ SX3 ) ) )
| ( in @ SX2
@ ( image1 @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(706,plain,
( ( ! [SX0: $i,SX1: $i > $i,SX2: $i] :
( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX0 )
| ( SX2
!= ( SX1 @ SX3 ) ) )
| ( in @ SX2
@ ( image1 @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(707,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ ( breln1compset @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX5 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX5 ) @ SX1 ) )
| ~ ( in @ ( kpair @ SX5 @ SX4 ) @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(708,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ ( kfst @ SX2 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(709,plain,
( ( ! [SX0: $i,SX1: $i,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)],[661,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(710,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[633,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(711,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ ( binunion @ SX1 @ SX2 ) )
| ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(712,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(713,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(714,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( ( setminus @ SX0 @ ( binintersect @ SX1 @ SX2 ) )
= ( binunion @ ( setminus @ SX0 @ SX1 ) @ ( setminus @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(715,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( 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)],[424,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(716,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[423,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(717,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[413,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(718,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ SX1 @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(719,plain,
( ( ! [SX0: $i,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)],[405,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(720,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( in @ emptyset @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[607,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(721,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(722,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ ( setadjoin @ SX1 @ emptyset ) @ ( powerset @ 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,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(723,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( set2prop @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[606,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(724,plain,
( ( ! [SX0: $i,SX1: $i,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)],[454,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(725,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(726,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( iskpair @ 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,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(727,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( powerset @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(728,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[402,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(729,plain,
( ( ! [SX0: $i > $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)],[602,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(730,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setadjoin @ SX0 @ emptyset )
!= ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(731,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(732,plain,
( ( ! [SX0: $i,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)],[448,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(733,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(734,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( funcSet @ SX0 @ ( powerset @ SX0 ) ) )
| ~ ( surjective @ SX0 @ ( powerset @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(735,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( 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)],[656,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(736,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX1: $i] : ( in @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(737,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( 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)],[475,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(738,plain,
( ( ! [SX0: $i,SX1: $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)],[431,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(739,plain,
( ( ! [SX0: $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)],[426,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(740,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ ( ksnd @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(741,plain,
( ( ! [SX0: $i,SX1: $i,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)],[520,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(742,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[414,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(743,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(744,plain,
( ( ! [SX0: $i,SX1: $i,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)],[478,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(745,plain,
( ( ! [SX0: $i,SX1: $i,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)],[477,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(746,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(747,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX3 )
| ( SX3 = SX2 ) )
| ( ex1 @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(748,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setminus @ SX0 @ SX1 )
!= emptyset )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(749,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[532,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(750,plain,
( ( ! [SX0: $i,SX1: $i,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)],[452,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(751,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( 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)],[589,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(752,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ex1 @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(753,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(754,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ ( binunion @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(755,plain,
( ( ! [SX0: $i,SX1: $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)],[447,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(756,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[631,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(757,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(758,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 != emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[636,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(759,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( 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)],[660,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(760,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX5 ) @ SX1 )
| ~ ( in @ ( kpair @ SX5 @ SX4 ) @ SX2 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ ( breln1compset @ SX0 @ SX1 @ SX2 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(761,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) ) @ ( powerset @ ( setminus @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(762,plain,
( ( ! [SX0: $i,SX1: $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)],[505,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(763,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
!= ( setadjoin @ SX2 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(764,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) ) )
| ( subset @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(765,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ( ( binintersect @ SX1 @ SX0 )
!= emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(766,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( ( kpair @ ( kfst @ SX2 ) @ ( ksnd @ SX2 ) )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(767,plain,
( ( ! [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)],[599,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(768,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ SX3 )
| ( subset @ ( binintersect @ SX1 @ SX2 ) @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(769,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( breln @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( breln @ SX0 @ SX1 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
| ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 ) ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 )
| ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(770,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(771,plain,
( ( ! [SX0: $i,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)],[518,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(772,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(773,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( SX2 @ SX3 ) @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( funcSet @ SX1 @ SX0 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ( ( ap @ SX1 @ SX0 @ SX3 @ ( SX2 @ SX4 ) )
= SX4 ) )
| ( surjective @ SX1 @ SX0 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(774,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(775,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ( ex1 @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(776,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[415,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(777,plain,
( ( ! [SX0: $i,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)],[407,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(778,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ex1 @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(779,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( breln1 @ SX0 @ SX3 )
| ( ( breln1compset @ SX0 @ ( binunion @ SX1 @ SX2 ) @ SX3 )
= ( binunion @ ( breln1compset @ SX0 @ SX1 @ SX3 ) @ ( breln1compset @ SX0 @ SX2 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(780,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $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)],[476,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(781,plain,
( ( ! [SX0: $i > $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)],[590,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(782,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(783,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(784,plain,
( ( ! [SX0: $i,SX1: $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)],[446,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(785,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[626,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(786,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ ( kpair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( kpair @ SX3 @ SX2 ) @ ( breln1invset @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(787,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[577,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(788,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[637,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(789,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[583,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(790,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(791,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) ) @ ( powerset @ ( setminus @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(792,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX2 @ SX3 )
| ( subset @ ( binintersect @ SX1 @ SX2 ) @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(793,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(794,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setunion @ SX0 )
= ( setunion @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[593,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(795,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(796,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(797,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( breln @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( breln @ SX0 @ SX1 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
| ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 ) ) )
| ( subset @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(798,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( breln1 @ SX0 @ SX3 )
| ( ( breln1compset @ SX0 @ ( binunion @ SX1 @ SX2 ) @ SX3 )
= ( binunion @ ( breln1invset @ SX0 @ ( breln1compset @ SX0 @ ( breln1invset @ SX0 @ SX3 ) @ ( breln1invset @ SX0 @ SX2 ) ) ) @ ( breln1invset @ SX0 @ ( breln1compset @ SX0 @ ( breln1invset @ SX0 @ SX3 ) @ ( breln1invset @ SX0 @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(799,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( ( kpair @ ( kfst @ SX0 ) @ ( ksnd @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(800,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( binintersect @ SX1 @ SX2 ) )
| ( in @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(801,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(802,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[381,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(803,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(804,plain,
( ( ! [SX0: $i,SX1: $i > $i] :
~ ! [SX2: $i] :
~ ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX0 )
| ( SX3
!= ( SX1 @ SX4 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX0 )
| ( SX3
!= ( SX1 @ SX4 ) ) )
| ( in @ SX3 @ SX2 ) ) )
| ~ ! [SX3: $i] :
( ~ ! [SX4: $i] :
~ ( ~ ( ~ ( in @ SX4 @ SX3 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX0 )
| ( SX4
!= ( SX1 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX0 )
| ( SX4
!= ( SX1 @ SX5 ) ) )
| ( in @ SX4 @ SX3 ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(805,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( setminus @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(806,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ~ ( injective @ SX0 @ SX1 @ SX2 )
| ( in @ SX2 @ ( injFuncSet @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(807,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ( ( breln1invset @ SX0 @ ( breln1compset @ SX0 @ SX1 @ SX2 ) )
= ( breln1compset @ SX0 @ ( breln1invset @ SX0 @ SX2 ) @ ( breln1invset @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(808,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[650,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(809,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ~ ( SX2 @ SX3 @ SX4 ) ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( breln1Set @ SX1 ) )
| ~ ( reflwellordering @ SX1 @ SX3 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ( singleton
@ ( dsetconstr @ SX1
@ ^ [SX5: $i] :
~ ( ~ ( SX2 @ SX4 @ SX5 )
| ~ ! [SX6: $i] :
( ~ ( in @ SX6 @ SX1 )
| ~ ( SX2 @ SX4 @ SX6 )
| ( in @ ( kpair @ SX5 @ SX6 ) @ SX3 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(810,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( 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)],[519,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(811,plain,
( ( ! [SX0: $i,SX1: $i,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)],[449,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(812,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(813,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[579,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(814,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( binintersect @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(815,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[429,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(816,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX0 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(817,plain,
( ( ! [SX0: $i,SX1: $i > $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)],[639,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(818,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[604,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(819,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ! [SX2: $o] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX1 @ SX3 )
| ~ ( in @ SX3 @ SX0 )
| SX2 )
| SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[624,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(820,plain,
( ( ! [SX0: $i,SX1: $i,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)],[459,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(821,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ~ ( subset @ SX2 @ SX1 )
| ( subset @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[557,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(822,plain,
( ( ! [SX0: $i,SX1: $i > $i] :
~ ! [SX2: $i] :
~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX0 )
| ( SX3
!= ( SX1 @ SX4 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX0 )
| ( SX3
!= ( SX1 @ SX4 ) ) )
| ( in @ SX3 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(823,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ( 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,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(824,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ( ( lam @ SX0 @ SX1
@ ^ [SX3: $i] : ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(825,plain,
( ( ~ ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) )
| ! [SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX1 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( subset @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[664,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(826,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(827,plain,
( ( ! [SX0: $i > $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)],[597,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(828,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[641,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(829,plain,
( ( ! [SX0: $i,SX1: $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)],[516,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(830,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[408,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(831,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(832,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( if @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(833,plain,
( ( ! [SX0: $i,SX1: $i,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)],[536,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(834,plain,
( ( ! [SX0: $i,SX1: $i,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)],[468,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(835,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX2 )
| ( subset @ SX0 @ ( setadjoin @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(836,plain,
( ( ! [SX0: $i,SX1: $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)],[438,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(837,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(838,plain,
( ( ! [SX0: $i,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)],[401,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(839,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( breln @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i > $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)],[466,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(840,plain,
( ( ! [SX0: $i,SX1: $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)],[445,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(841,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[657,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(842,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(843,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,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)],[500,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(844,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( injFuncSet @ SX0 @ SX1 ) )
| ( injective @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(845,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(846,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ ( binunion @ SX1 @ SX2 ) )
| ! [SX5: $o] :
( ~ ( ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| SX5 )
| ~ ( ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 )
| SX5 )
| SX5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(847,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) ) )
| ( in @ SX3 @ ( binintersect @ ( setminus @ SX0 @ SX1 ) @ ( setminus @ SX0 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(848,plain,
( ( ! [SX0: $i,SX1: $i > $i,SX2: $i] :
( ~ ( in @ SX2
@ ( image1 @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX0 )
| ( SX2
!= ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(849,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( ( omegaS @ SX0 )
!= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(850,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[616,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(851,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( surjFuncSet @ SX0 @ SX1 ) )
| ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(852,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( in @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[574,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(853,plain,
( ( ! [SX0: $i,SX1: $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)],[443,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(854,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[422,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(855,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(856,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [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)],[653,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(857,plain,
( ( ! [SX0: $i,SX1: $i,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)],[479,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(858,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[625,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(859,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ ( binunion @ SX1 @ SX2 ) )
| ~ ( in @ SX3 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(860,plain,
( ( ! [SX0: $i > $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)],[655,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(861,plain,
( ( ! [SX0: $i,SX1: $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)],[456,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(862,plain,
( ( ! [SX0: $i,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)],[440,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(863,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i > $o] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| ( SX2 @ ( kpair @ SX3 @ SX4 ) ) ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(864,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[629,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(865,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ 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,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(866,plain,
( ( ! [SX0: $i] :
( ~ ( singleton @ SX0 )
| ( in @ ( setunion @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(867,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(868,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(869,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(870,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( kpair @ SX3 @ ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(871,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( setminus @ SX0 @ SX1 ) @ ( powerset @ ( setminus @ SX0 @ ( binintersect @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(872,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[638,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(873,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[382,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(874,plain,
( ( ! [SX0: $i,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)],[419,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(875,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ( ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[613,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(876,plain,
( ( ! [SX0: $i,SX1: $i,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)],[474,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(877,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX2 ) @ ( breln1invset @ SX0 @ SX1 ) )
| ( in @ ( kpair @ SX2 @ SX3 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(878,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[553,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(879,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(880,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(881,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 )
| ~ ~ ( in @ SX3 @ SX2 )
| ~ ( in @ SX3 @ ( binunion @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(882,plain,
( ( ! [SX0: $i,SX1: $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)],[444,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(883,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( breln1Set @ SX0 ) )
| ( breln1 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(884,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( 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)],[453,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(885,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( powerset @ SX0 ) @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[568,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(886,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,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)],[496,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(887,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[570,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(888,plain,
( ( ! [SX0: $o,SX1: $i] :
( ~ ( in @ SX1 @ ( prop2set @ SX0 ) )
| SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[647,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(889,plain,
( ( ! [SX0: $i,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)],[461,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(890,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 ) ) )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(891,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ( breln1 @ SX0 @ ( breln1invset @ 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,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(892,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[649,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(893,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[558,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(894,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) )
| ( in @ ( kpair @ SX3 @ SX4 ) @ ( binunion @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(895,plain,
( ( ! [SX0: $i,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)],[522,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(896,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[384,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(897,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( injFuncSet @ SX0 @ SX1 ) )
| ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(898,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( surjFuncSet @ SX0 @ SX1 ) )
| ( surjective @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(899,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( omegaS @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(900,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) )
= ( binintersect @ ( setminus @ SX0 @ SX1 ) @ ( setminus @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(901,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i > $o] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| ( SX2 @ ( kpair @ SX3 @ SX4 ) ) ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(902,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(903,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( ( kfst @ ( kpair @ SX2 @ SX3 ) )
= SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(904,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[421,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(905,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(906,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( setminus @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(907,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[399,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(908,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[642,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(909,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[556,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(910,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ ( breln1compset @ SX0 @ SX1 @ SX2 ) )
| ! [SX5: $o] :
( ~ ! [SX6: $i] :
( ~ ( in @ SX6 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX6 ) @ SX1 )
| ~ ( in @ ( kpair @ SX6 @ SX4 ) @ SX2 )
| SX5 )
| SX5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(911,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( binintersect @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(912,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(913,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ SX3 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(914,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ( ( binintersect @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(915,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[565,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(916,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[623,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(917,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX1: $i] :
( SX0
= ( kpair @ ( kfst @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(918,plain,
( ( ! [SX0: $i > $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)],[591,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(919,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[605,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(920,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(921,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[651,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(922,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ( breln1 @ SX0 @ ( binunion @ SX1 @ 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,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(923,plain,
( ( ! [SX0: $i,SX1: $i,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)],[482,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(924,plain,
( ( ! [SX0: $i] :
( ~ ( singleton @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( ( setunion @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(925,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[617,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(926,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(927,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ( ( binunion @ SX1 @ SX2 )
= ( binunion @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(928,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $o] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX0 )
| SX3 )
| ~ ( ~ ( in @ SX2 @ SX1 )
| SX3 )
| SX3 ) )
= $true ),
inference(unfold_def,[status(thm)],[562,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(929,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ 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)],[432,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(930,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ ( binunion @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(931,plain,
( ( ! [SX0: $i,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)],[460,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(932,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ ( binunion @ ( setminus @ SX0 @ SX1 ) @ ( setminus @ SX0 @ SX2 ) ) )
| ( in @ SX3 @ ( setminus @ SX0 @ ( binintersect @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(933,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[645,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(934,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( SX1
= ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(935,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[404,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(936,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[640,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(937,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ ( binintersect @ ( setminus @ SX0 @ SX1 ) @ ( setminus @ SX0 @ SX2 ) ) )
| ( in @ SX3 @ ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(938,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[430,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(939,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX3 @ ( setminus @ SX0 @ SX2 ) )
| ( in @ SX3 @ ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(940,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( in @ ( setminus @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(941,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(942,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[563,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(943,plain,
( ( ! [SX0: $i,SX1: $i,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)],[521,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(944,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( ( ksnd @ ( kpair @ SX2 @ SX3 ) )
= SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(945,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[403,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(946,plain,
( ( ! [SX0: $i > $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)],[622,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(947,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ SX3 )
| ~ ( subset @ SX2 @ SX4 )
| ( subset @ ( binintersect @ SX1 @ SX2 ) @ ( binintersect @ SX3 @ SX4 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(948,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[425,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(949,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( breln @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i > $o] :
( ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
| ( SX3 @ ( kpair @ SX4 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(950,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[585,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(951,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ~ SX1
| ( ( if @ SX0 @ SX1 @ SX2 @ SX3 )
= SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(952,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[654,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(953,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(954,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[588,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(955,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ SX2 )
| ~ ( subset @ SX1 @ SX3 )
| ( subset @ SX1 @ ( binintersect @ SX2 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(956,plain,
! [SV1: $i] :
( ( ~ ( in @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(957,plain,
! [SV2: $i] :
( ( ! [SY2366: $i > $i > $o] :
( breln1 @ SV2
@ ( dpsetconstr @ SV2 @ SV2
@ ^ [Xx: $i,Xy: $i] : ( SY2366 @ Xx @ Xy ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(958,plain,
! [SV3: $i] :
( ( ! [SY2369: $i,SY2370: $i > $i > $o] :
( breln @ SV3 @ SY2369
@ ( dpsetconstr @ SV3 @ SY2369
@ ^ [Xx: $i,Xy: $i] : ( SY2370 @ Xx @ Xy ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(959,plain,
! [SV4: $i] :
( ( ! [SY2373: $i,SY2374: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV4 @ SY2373
@ ^ [Xx: $i,Xy: $i] : ( SY2374 @ Xx @ Xy ) )
@ ( cartprod @ SV4 @ SY2373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(960,plain,
! [SV5: $i] :
( ( ! [SY2377: $i] :
( ( ksnd @ ( kpair @ SV5 @ SY2377 ) )
= SY2377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(961,plain,
! [SV6: $i] :
( ( ! [SY2378: $i] :
( ( kfst @ ( kpair @ SV6 @ SY2378 ) )
= SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(962,plain,
! [SV7: $i] :
( ( ( setunion @ ( setadjoin @ SV7 @ emptyset ) )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(963,plain,
! [SV8: $i] :
( ( subset @ SV8 @ ( setunion @ ( setadjoin @ SV8 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(964,plain,
! [SV9: $i] :
( ( subset @ ( setunion @ ( setadjoin @ SV9 @ emptyset ) ) @ SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(965,plain,
! [SV10: $i] :
( ( ! [SY2379: $i] : ( iskpair @ ( kpair @ SV10 @ SY2379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(966,plain,
! [SV11: $i] :
( ( ! [SY2380: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ SV11 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV11 @ ( setadjoin @ SY2380 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(967,plain,
! [SV12: $i] :
( ( ! [SY2381: $i] : ( in @ SY2381 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV12 @ ( setadjoin @ SY2381 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(968,plain,
! [SV13: $i] :
( ( ! [SY2382: $i] : ( in @ SV13 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV13 @ ( setadjoin @ SY2382 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(969,plain,
! [SV14: $i] :
( ( ! [SY2383: $i] : ( in @ SY2383 @ ( setadjoin @ SV14 @ ( setadjoin @ SY2383 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(970,plain,
! [SV15: $i] :
( ( ! [SY2384: $i] : ( subset @ ( setminus @ SV15 @ SY2384 ) @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(971,plain,
! [SV16: $i] :
( ( ! [SY2385: $i,SY2386: $i] :
( ( binintersect @ SV16 @ ( binunion @ SY2385 @ SY2386 ) )
= ( binunion @ ( binintersect @ SV16 @ SY2385 ) @ ( binintersect @ SV16 @ SY2386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(972,plain,
! [SV17: $i] :
( ( ! [SY2387: $i] : ( subset @ ( binintersect @ SV17 @ SY2387 ) @ SY2387 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(973,plain,
! [SV18: $i] :
( ( ! [SY2388: $i] : ( subset @ ( binintersect @ SV18 @ SY2388 ) @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(974,plain,
! [SV19: $i] :
( ( ! [SY2389: $i] : ( subset @ SY2389 @ ( binunion @ SV19 @ SY2389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(975,plain,
! [SV20: $i] :
( ( ! [SY2390: $i] : ( subset @ SV20 @ ( binunion @ SV20 @ SY2390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(976,plain,
! [SV21: $i] :
( ( ! [SY2391: $i] : ( in @ SY2391 @ ( setadjoin @ SV21 @ ( setadjoin @ SY2391 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(977,plain,
! [SV22: $i] :
( ( ! [SY2392: $i > $o] :
( subset
@ ( dsetconstr @ SV22
@ ^ [Xx: $i] : ( SY2392 @ Xx ) )
@ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(978,plain,
! [SV23: $i] :
( ( ! [SY2394: $i > $o] :
( in
@ ( dsetconstr @ SV23
@ ^ [Xx: $i] : ( SY2394 @ Xx ) )
@ ( powerset @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(979,plain,
! [SV24: $i] :
( ( in @ SV24 @ ( powerset @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(980,plain,
! [SV25: $i] :
( ( ! [SY2396: $i] : ( subset @ SY2396 @ ( setadjoin @ SV25 @ SY2396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(981,plain,
! [SV26: $i] :
( ( subset @ SV26 @ SV26 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(982,plain,
! [SV27: $i] :
( ( subset @ emptyset @ SV27 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(983,plain,
! [SV28: $i] :
( ( ! [SY2397: $i] : ( in @ SY2397 @ ( setadjoin @ SV28 @ ( setadjoin @ SY2397 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(984,plain,
! [SV29: $i] :
( ( ! [SY2398: $i] : ( in @ SV29 @ ( setadjoin @ SV29 @ ( setadjoin @ SY2398 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(985,plain,
! [SV30: $i] :
( ( in @ emptyset @ ( powerset @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(986,plain,
! [SV31: $i] :
( ( in @ emptyset @ ( powerset @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(987,plain,
! [SV32: $i] :
( ( ( dsetconstr @ SV32
@ ^ [Xx: $i] : $true )
= SV32 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(988,plain,
! [SV33: $i] :
( ( ! [SY2400: $i] : ( in @ SV33 @ ( setadjoin @ SV33 @ SY2400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(989,plain,
! [SV34: $i] :
( ( ~ ( in @ SV34 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(990,plain,
! [SV35: $i] :
( ( ~ ( in @ SV35 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(991,plain,
! [SV36: $i] :
( ( ! [SY2401: $i] :
( ~ ( in @ SV36 @ ( setadjoin @ SY2401 @ emptyset ) )
| ( SV36 = SY2401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(992,plain,
! [SV37: $i] :
( ( ~ ( ( SV37 != emptyset ) )
| ~ ! [SY2402: $i] :
~ ~ ( ~ ( in @ SY2402 @ SV37 )
| ~ $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(993,plain,
! [SV38: $i] :
( ( ~ ( in @ SV38 @ omega )
| ! [SY2403: $i] :
( ~ ( in @ SY2403 @ omega )
| ( ( omegaS @ SV38 )
!= ( omegaS @ SY2403 ) )
| ( SV38 = SY2403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(994,plain,
! [SV39: $i] :
( ( ! [SY2404: $i,SY2405: $i > $i] :
( ~ ! [SY2406: $i] :
( ~ ( in @ SY2406 @ SV39 )
| ( in @ ( SY2405 @ SY2406 ) @ SY2404 ) )
| ( func @ SV39 @ SY2404
@ ( dpsetconstr @ SV39 @ SY2404
@ ^ [SX3: $i,SX4: $i] :
( ( SY2405 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(995,plain,
! [SV40: $i > $o] :
( ( ~ ~ ! [SY2409: $i] :
~ ~ ( ~ ( SV40 @ SY2409 )
| ~ ! [SY2410: $i] :
( ~ ( SV40 @ SY2410 )
| ( SY2409 = SY2410 ) ) )
| ~ ! [SY2411: $i] :
~ ( SV40 @ SY2411 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(996,plain,
! [SV41: $i] :
( ( ! [SY2412: $i,SY2413: $i] :
( ~ ( in @ SY2413 @ SV41 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2412 )
| ( ( kpair @ SY2413 @ SX3 )
= ( kpair @ SY2413 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(997,plain,
! [SV42: $i > $o] :
( ( ~ ~ ! [SY2415: $i] :
~ ~ ( ~ ( SV42 @ SY2415 )
| ~ ! [SY2416: $i] :
( ~ ( SV42 @ SY2416 )
| ( SY2415 = SY2416 ) ) )
| ( SV42
@ ( descr
@ ^ [SY2417: $i] : ( SV42 @ SY2417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(998,plain,
! [SV43: $i] :
( ( ! [SY2418: $i] :
( ( SV43 != SY2418 )
| ( ( powerset @ SV43 )
= ( powerset @ SY2418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(999,plain,
! [SV44: $i] :
( ( ! [SY2419: $i > $o] :
( ~ ! [SY2420: $i] :
( ~ ( in @ SY2420 @ SV44 )
| ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SV44 )
| ~ ( SY2419 @ SY2420 )
| ~ ( SY2419 @ SY2421 )
| ( SY2420 = SY2421 ) ) )
| ~ ~ ! [SY2422: $i] :
~ ~ ( ~ ( in @ SY2422 @ SV44 )
| ~ ( SY2419 @ SY2422 ) )
| ( singleton
@ ( dsetconstr @ SV44
@ ^ [SX2: $i] : ( SY2419 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(1000,plain,
! [SV45: $i] :
( ( ! [SY2424: $i,SY2425: $i] :
( ~ ( in @ SY2425 @ ( funcSet @ SV45 @ SY2424 ) )
| ! [SY2426: $i] :
( ~ ( in @ SY2426 @ ( funcSet @ SV45 @ SY2424 ) )
| ~ ! [SY2427: $i] :
( ~ ( in @ SY2427 @ SV45 )
| ( ( ap @ SV45 @ SY2424 @ SY2425 @ SY2427 )
= ( ap @ SV45 @ SY2424 @ SY2426 @ SY2427 ) ) )
| ( SY2425 = SY2426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(1001,plain,
! [SV46: $i] :
( ( ! [SY2428: $i,SY2429: $i] :
( ~ ( in @ SY2429 @ SV46 )
| ( in @ ( setadjoin @ SY2429 @ emptyset ) @ ( powerset @ ( binunion @ SV46 @ SY2428 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(1002,plain,
! [SV47: $i] :
( ( ! [SY2430: $i,SY2431: $i] :
( ~ ( in @ SY2431 @ ( funcSet @ SV47 @ SY2430 ) )
| ! [SY2432: $i] :
( ~ ( in @ SY2432 @ SV47 )
| ( in @ ( kpair @ SY2432 @ ( ap @ SV47 @ SY2430 @ SY2431 @ SY2432 ) ) @ SY2431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(1003,plain,
! [SV48: $i] :
( ( ! [SY2433: $i,SY2434: $i,SY2435: $i] :
( ( ( setadjoin @ ( setadjoin @ SV48 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV48 @ ( setadjoin @ SY2433 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY2434 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2434 @ ( setadjoin @ SY2435 @ emptyset ) ) @ emptyset ) ) )
| ( SY2433 = SY2435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(1004,plain,
! [SV49: $i] :
( ( ! [SY2436: $i,SY2437: $i] :
( ~ ( in @ SY2437 @ ( funcSet @ SV49 @ SY2436 ) )
| ! [SY2438: $i] :
( ~ ( in @ SY2438 @ SV49 )
| ( in @ ( ap @ SV49 @ SY2436 @ SY2437 @ SY2438 ) @ SY2436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(1005,plain,
! [SV50: $i] :
( ( ! [SY2439: $i] :
( ( SV50 != SY2439 )
| ! [SY2440: $i,SY2441: $i] :
( ( SY2440 != SY2441 )
| ( ( setadjoin @ SV50 @ SY2440 )
= ( setadjoin @ SY2439 @ SY2441 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(1006,plain,
! [SV51: $i] :
( ( ! [SY2442: $i,SY2443: $i] :
( ~ ( in @ SY2443 @ ( funcSet @ SV51 @ SY2442 ) )
| ( func @ SV51 @ SY2442 @ SY2443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(1007,plain,
! [SV52: $i] :
( ( ! [SY2444: $i] :
( ~ ( in @ SY2444 @ ( powerset @ SV52 ) )
| ! [SY2445: $i] :
( ~ ( in @ SY2445 @ ( powerset @ SV52 ) )
| ! [SY2446: $i] :
( ~ ( in @ SY2446 @ ( powerset @ SV52 ) )
| ! [SY2447: $i] :
( ~ ( in @ SY2447 @ SV52 )
| ~ ( in @ SY2447 @ ( binintersect @ SY2444 @ SY2445 ) )
| ( in @ SY2447 @ ( binunion @ SY2445 @ SY2446 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(1008,plain,
! [SV53: $i] :
( ( ! [SY2448: $i] :
( ~ ( subset @ SY2448 @ SV53 )
| ( ( binintersect @ SV53 @ SY2448 )
= SY2448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(1009,plain,
! [SV54: $i] :
( ( ! [SY2449: $i,SY2450: $i > $i] :
( ~ ! [SY2451: $i] :
( ~ ( in @ SY2451 @ SV54 )
| ( in @ ( SY2450 @ SY2451 ) @ SY2449 ) )
| ( in
@ ( lam @ SV54 @ SY2449
@ ^ [SX3: $i] : ( SY2450 @ SX3 ) )
@ ( funcSet @ SV54 @ SY2449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(1010,plain,
! [SV55: $i] :
( ( ! [SY2453: $i] :
( ~ ( in @ SY2453 @ ( powerset @ SV55 ) )
| ! [SY2454: $i] :
( ~ ( in @ SY2454 @ ( powerset @ SV55 ) )
| ~ ( subset @ SY2453 @ ( setminus @ SV55 @ SY2454 ) )
| ( subset @ SY2454 @ ( setminus @ SV55 @ SY2453 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(1011,plain,
! [SV56: $i] :
( ( ! [SY2455: $i] :
( ~ ( in @ SY2455 @ ( powerset @ SV56 ) )
| ! [SY2456: $i] :
( ~ ( in @ SY2456 @ ( powerset @ SV56 ) )
| ! [SY2457: $i] :
( ~ ( in @ SY2457 @ ( powerset @ SV56 ) )
| ! [SY2458: $i] :
( ~ ( in @ SY2458 @ ( powerset @ SV56 ) )
| ( ( setminus @ SV56 @ ( binintersect @ ( binunion @ SY2455 @ SY2456 ) @ ( binunion @ SY2457 @ SY2458 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV56 @ SY2455 ) @ ( setminus @ SV56 @ SY2456 ) ) @ ( binintersect @ ( setminus @ SV56 @ SY2457 ) @ ( setminus @ SV56 @ SY2458 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(1012,plain,
! [SV57: $i] :
( ( ! [SY2459: $i] :
~ ( ~ ( ~ ( in @ SY2459 @ ( setunion @ SV57 ) )
| ~ ! [SY2460: $i] :
~ ~ ( ~ ( in @ SY2459 @ SY2460 )
| ~ ( in @ SY2460 @ SV57 ) ) )
| ~ ( ~ ~ ! [SY2461: $i] :
~ ~ ( ~ ( in @ SY2459 @ SY2461 )
| ~ ( in @ SY2461 @ SV57 ) )
| ( in @ SY2459 @ ( setunion @ SV57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(1013,plain,
! [SV58: $i > $o] :
( ( ~ ~ ! [SY2462: $i] :
~ ~ ( ~ ( SV58 @ SY2462 )
| ~ ! [SY2463: $i] :
( ~ ( SV58 @ SY2463 )
| ( SY2462 = SY2463 ) ) )
| ! [SY2464: $i,SY2465: $i] :
( ~ ( SV58 @ SY2464 )
| ~ ( SV58 @ SY2465 )
| ( SY2464 = SY2465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(1014,plain,
! [SV59: $i > $o] :
( ( ~ ~ ! [SY2466: $i] :
~ ! [SY2467: $i] :
~ ( ~ ( ~ ( SV59 @ SY2467 )
| ( SY2467 = SY2466 ) )
| ~ ( ( SY2467 != SY2466 )
| ( SV59 @ SY2467 ) ) )
| ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(1015,plain,
! [SV60: $i > $o] :
( ( ~ ~ ! [SY2470: $i] :
~ ~ ( ~ ( SV60 @ SY2470 )
| ~ ! [SY2471: $i] :
( ~ ( SV60 @ SY2471 )
| ( SY2470 = SY2471 ) ) )
| ~ ! [SY2472: $i] :
~ ~ ( ~ ( SV60 @ SY2472 )
| ~ ! [SY2473: $i] :
( ~ ( SV60 @ SY2473 )
| ( SY2472 = SY2473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(1016,plain,
! [SV61: $i] :
( ( ! [SY2474: $i > $o] :
( ~ ~ ! [SY2475: $i] :
( ~ ( in @ SY2475 @ SV61 )
| ( SY2474 @ SY2475 ) )
| ~ ! [SY2476: $i] :
~ ~ ( ~ ( in @ SY2476 @ SV61 )
| ~ ~ ( SY2474 @ SY2476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(1017,plain,
! [SV62: $i > $o] :
( ( ! [SY2477: $i] :
( ~ ( in @ SY2477 @ emptyset )
| ( SV62 @ SY2477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(1018,plain,
! [SV63: $i] :
( ( ! [SY2478: $i,SY2479: $i] :
( ~ ( func @ SV63 @ SY2478 @ SY2479 )
| ! [SY2480: $i] :
( ~ ( in @ SY2480 @ SV63 )
| ( in @ ( ap @ SV63 @ SY2478 @ SY2479 @ SY2480 ) @ SY2478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(1019,plain,
! [SV64: $i] :
( ( ! [SY2481: $i,SY2482: $i > $i] :
( ~ ! [SY2483: $i] :
( ~ ( in @ SY2483 @ SV64 )
| ( in @ ( SY2482 @ SY2483 ) @ SY2481 ) )
| ( ( lam @ SV64 @ SY2481
@ ^ [SX3: $i] : ( SY2482 @ SX3 ) )
= ( lam @ SV64 @ SY2481
@ ^ [SX3: $i] : ( SY2482 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(1020,plain,
! [SV65: $i] :
( ( ! [SY2486: $i] :
( ~ ! [SY2487: $i] :
~ ( ~ ( ~ ( in @ SY2487 @ SV65 )
| ( in @ SY2487 @ SY2486 ) )
| ~ ( ~ ( in @ SY2487 @ SY2486 )
| ( in @ SY2487 @ SV65 ) ) )
| ( SV65 = SY2486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(1021,plain,
! [SV66: $i] :
( ( ~ ( in @ SV66 @ emptyset )
| ! [SX1: $o] : SX1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(1022,plain,
! [SV67: $i] :
( ( ~ ( subset @ SV67 @ emptyset )
| ( SV67 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(1023,plain,
! [SV68: $i] :
( ( ! [SY2489: $i] :
( ~ ( in @ SY2489 @ ( powerset @ SV68 ) )
| ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( powerset @ SV68 ) )
| ~ ( subset @ SY2489 @ ( setminus @ SV68 @ SY2490 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SV68 )
| ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( setminus @ SV68 @ SY2489 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(1024,plain,
! [SV69: $i] :
( ( ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( powerset @ SV69 ) )
| ! [SY2493: $i] :
( ~ ( in @ SY2493 @ ( powerset @ SV69 ) )
| ! [SY2494: $i] :
( ~ ( in @ SY2494 @ SV69 )
| ~ ( in @ SY2494 @ ( setminus @ SV69 @ ( binintersect @ SY2492 @ SY2493 ) ) )
| ( in @ SY2494 @ ( binunion @ ( setminus @ SV69 @ SY2492 ) @ ( setminus @ SV69 @ SY2493 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(1025,plain,
! [SV70: $i] :
( ( ! [SY2495: $i] :
( ( SV70 != SY2495 )
| ( in @ SV70 @ ( setadjoin @ SY2495 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(1026,plain,
! [SV71: $i] :
( ( ! [SY2496: $i] :
( ~ ( in @ SY2496 @ ( powerset @ SV71 ) )
| ! [SY2497: $i] :
( ~ ( in @ SY2497 @ ( powerset @ SV71 ) )
| ( in @ ( binunion @ SY2496 @ SY2497 ) @ ( powerset @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(1027,plain,
! [SV72: $i] :
( ( ! [SY2498: $i,SY2499: $i] :
( ~ ( in @ SY2499 @ ( setadjoin @ SV72 @ SY2498 ) )
| ! [SY2500: $o] :
( ~ ( ( SY2499 != SV72 )
| SY2500 )
| ~ ( ~ ( in @ SY2499 @ SY2498 )
| SY2500 )
| SY2500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(1028,plain,
! [SV73: $i] :
( ( ! [SY2501: $i] :
( ~ ( breln1 @ SV73 @ SY2501 )
| ! [SY2502: $i] :
( ~ ( breln1 @ SV73 @ SY2502 )
| ( breln1 @ SV73 @ ( breln1compset @ SV73 @ SY2501 @ SY2502 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(1029,plain,
! [SV74: $i] :
( ( ! [SY2503: $i] :
( ~ ( breln1 @ SV74 @ SY2503 )
| ( SY2503
= ( breln1invset @ SV74 @ ( breln1invset @ SV74 @ SY2503 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(1030,plain,
! [SV75: $i] :
( ( ! [SY2504: $i] :
( ~ ( in @ SY2504 @ ( powerset @ SV75 ) )
| ! [SY2505: $i] :
( ~ ( in @ SY2505 @ ( powerset @ SV75 ) )
| ! [SY2506: $i] :
( ~ ( in @ SY2506 @ SV75 )
| ~ ( in @ SY2506 @ ( setminus @ SV75 @ ( binunion @ SY2504 @ SY2505 ) ) )
| ( in @ SY2506 @ ( setminus @ SV75 @ SY2505 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(1031,plain,
! [SV76: $i] :
( ( ! [SY2507: $i > $i,SY2508: $i] :
~ ( ~ ( ~ ( in @ SY2508
@ ( image1 @ SV76
@ ^ [SX3: $i] : ( SY2507 @ SX3 ) ) )
| ~ ! [SY2510: $i] :
~ ~ ( ~ ( in @ SY2510 @ SV76 )
| ( SY2508
!= ( SY2507 @ SY2510 ) ) ) )
| ~ ( ~ ~ ! [SY2511: $i] :
~ ~ ( ~ ( in @ SY2511 @ SV76 )
| ( SY2508
!= ( SY2507 @ SY2511 ) ) )
| ( in @ SY2508
@ ( image1 @ SV76
@ ^ [SX3: $i] : ( SY2507 @ SX3 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(1032,plain,
! [SV77: $i] :
( ( ! [SY2513: $i > $i,SY2514: $i] :
( ~ ~ ! [SY2515: $i] :
~ ~ ( ~ ( in @ SY2515 @ SV77 )
| ( SY2514
!= ( SY2513 @ SY2515 ) ) )
| ( in @ SY2514
@ ( image1 @ SV77
@ ^ [SX3: $i] : ( SY2513 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(1033,plain,
! [SV78: $i] :
( ( ! [SY2517: $i] :
( ~ ( breln1 @ SV78 @ SY2517 )
| ! [SY2518: $i] :
( ~ ( breln1 @ SV78 @ SY2518 )
| ! [SY2519: $i] :
( ~ ( in @ SY2519 @ SV78 )
| ! [SY2520: $i] :
( ~ ( in @ SY2520 @ SV78 )
| ~ ( in @ ( kpair @ SY2519 @ SY2520 ) @ ( breln1compset @ SV78 @ SY2517 @ SY2518 ) )
| ~ ! [SY2521: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY2521 @ SV78 )
| ~ ( in @ ( kpair @ SY2519 @ SY2521 ) @ SY2517 ) )
| ~ ( in @ ( kpair @ SY2521 @ SY2520 ) @ SY2518 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(1034,plain,
! [SV79: $i] :
( ( ! [SY2522: $i,SY2523: $i] :
( ~ ( in @ SY2523 @ ( cartprod @ SV79 @ SY2522 ) )
| ( in @ ( kfst @ SY2523 ) @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(1035,plain,
! [SV80: $i] :
( ( ! [SY2524: $i,SY2525: $i] :
~ ( ~ ( ~ ( in @ SY2525 @ ( setadjoin @ SV80 @ SY2524 ) )
| ( SY2525 = SV80 )
| ( in @ SY2525 @ SY2524 ) )
| ~ ( ~ ( ( SY2525 = SV80 )
| ( in @ SY2525 @ SY2524 ) )
| ( in @ SY2525 @ ( setadjoin @ SV80 @ SY2524 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(1036,plain,
! [SV81: $i] :
( ( ! [SY2526: $i,SY2527: $i] :
( ~ ( in @ SY2527 @ SY2526 )
| ( in @ SY2527 @ ( setadjoin @ SV81 @ SY2526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(1037,plain,
! [SV82: $i] :
( ( ! [SY2528: $i] :
( ~ ( breln1 @ SV82 @ SY2528 )
| ! [SY2529: $i] :
( ~ ( breln1 @ SV82 @ SY2529 )
| ! [SY2530: $i] :
( ~ ( in @ SY2530 @ SV82 )
| ! [SY2531: $i] :
( ~ ( in @ SY2531 @ SV82 )
| ~ ( in @ ( kpair @ SY2530 @ SY2531 ) @ ( binunion @ SY2528 @ SY2529 ) )
| ( in @ ( kpair @ SY2530 @ SY2531 ) @ SY2528 )
| ( in @ ( kpair @ SY2530 @ SY2531 ) @ SY2529 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(1038,plain,
! [SV83: $i] :
( ( ! [SY2532: $i] :
( ~ ( subset @ SY2532 @ SV83 )
| ( in @ SY2532 @ ( powerset @ SV83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(1039,plain,
! [SV84: $i] :
( ( ~ ( in @ SV84 @ omega )
| ( in @ ( setadjoin @ SV84 @ SV84 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(1040,plain,
! [SV85: $i] :
( ( ! [SY2533: $i] :
( ~ ( in @ SY2533 @ ( powerset @ SV85 ) )
| ! [SY2534: $i] :
( ~ ( in @ SY2534 @ ( powerset @ SV85 ) )
| ( ( setminus @ SV85 @ ( binintersect @ SY2533 @ SY2534 ) )
= ( binunion @ ( setminus @ SV85 @ SY2533 ) @ ( setminus @ SV85 @ SY2534 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(1041,plain,
! [SV86: $i] :
( ( ! [SY2535: $i] :
( ~ ( in @ SY2535 @ ( powerset @ SV86 ) )
| ! [SY2536: $i] :
( ~ ( in @ SY2536 @ ( powerset @ SV86 ) )
| ! [SY2537: $i] :
( ~ ( in @ SY2537 @ SV86 )
| ~ ( subset @ SY2535 @ ( setminus @ SV86 @ SY2536 ) )
| ~ ( in @ SY2537 @ SY2536 )
| ~ ( in @ SY2537 @ SY2535 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(1042,plain,
! [SV87: $i] :
( ( ! [SY2538: $i] :
( ~ ( in @ SY2538 @ ( powerset @ SV87 ) )
| ! [SY2539: $i] :
( ~ ( in @ SY2539 @ ( powerset @ SV87 ) )
| ! [SY2540: $i] :
( ~ ( in @ SY2540 @ SV87 )
| ~ ( subset @ SY2538 @ SY2539 )
| ~ ~ ( in @ SY2540 @ SY2539 )
| ~ ( in @ SY2540 @ SY2538 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(1043,plain,
! [SV88: $i] :
( ( ! [SY2541: $i] :
( ~ ( in @ SY2541 @ ( powerset @ SV88 ) )
| ! [SY2542: $i] :
( ~ ( in @ SY2542 @ ( powerset @ SV88 ) )
| ( subset @ ( setminus @ SV88 @ SY2541 ) @ ( setminus @ SV88 @ ( binintersect @ SY2541 @ SY2542 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(1044,plain,
! [SV89: $i] :
( ( ! [SY2543: $i] :
( ~ ( in @ SY2543 @ ( powerset @ SV89 ) )
| ( subset @ SY2543 @ ( setminus @ SV89 @ ( setminus @ SV89 @ SY2543 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(1045,plain,
! [SV90: $i] :
( ( ! [SY2544: $i] :
( ~ ( in @ SY2544 @ ( powerset @ SV90 ) )
| ! [SY2545: $i] :
( ~ ( in @ SY2545 @ ( powerset @ SV90 ) )
| ! [SY2546: $i] :
( ~ ( in @ SY2546 @ ( powerset @ SV90 ) )
| ! [SY2547: $i] :
( ~ ( in @ SY2547 @ SV90 )
| ~ ( in @ SY2547 @ ( binintersect @ SY2544 @ SY2545 ) )
| ( in @ SY2547 @ ( binintersect @ ( binunion @ SY2544 @ SY2546 ) @ ( binunion @ SY2545 @ SY2546 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(1046,plain,
! [SV91: $o] :
( ( ~ SV91
| ( in @ emptyset @ ( prop2set @ SV91 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[720]) ).
thf(1047,plain,
( ( ~ $true
| ( in @ emptyset @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[720]) ).
thf(1048,plain,
( ( ~ $false
| ( in @ emptyset @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[720]) ).
thf(1049,plain,
! [SV92: $i] :
( ( ! [SY2548: $i,SY2549: $i] :
( ~ ( in @ SY2549 @ SV92 )
| ~ ~ ( in @ SY2549 @ SY2548 )
| ( in @ SY2549 @ ( setminus @ SV92 @ SY2548 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(1050,plain,
! [SV93: $i] :
( ( ! [SY2550: $i] :
( ~ ( in @ SY2550 @ SV93 )
| ( in @ ( setadjoin @ SY2550 @ emptyset ) @ ( powerset @ SV93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(1051,plain,
! [SV94: $o] :
( ( ~ SV94
| ( set2prop @ ( prop2set @ SV94 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[723]) ).
thf(1052,plain,
( ( ~ $true
| ( set2prop @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[723]) ).
thf(1053,plain,
( ( ~ $false
| ( set2prop @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[723]) ).
thf(1054,plain,
! [SV95: $i] :
( ( ! [SY2551: $i,SY2552: $i] :
( ~ ( in @ SY2552 @ ( funcSet @ SV95 @ SY2551 ) )
| ! [SY2553: $i] :
( ~ ( in @ SY2553 @ SV95 )
| ( ( ap @ SV95 @ SY2551 @ SY2552 @ SY2553 )
= ( ap @ SV95 @ SY2551 @ SY2552 @ SY2553 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(1055,plain,
! [SV96: $i] :
( ( ! [SY2554: $i,SY2555: $i] :
( ~ ~ ( in @ SY2555 @ ( setminus @ SV96 @ SY2554 ) )
| ~ ( in @ SY2555 @ SV96 )
| ( in @ SY2555 @ SY2554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(1056,plain,
! [SV97: $i] :
( ( ! [SY2556: $i,SY2557: $i] :
( ~ ( in @ SY2557 @ ( cartprod @ SV97 @ SY2556 ) )
| ( iskpair @ SY2557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(1057,plain,
! [SV98: $i] :
( ( ! [SY2558: $i] :
( ~ ( in @ SY2558 @ ( powerset @ SV98 ) )
| ( in @ ( powerset @ SY2558 ) @ ( powerset @ ( powerset @ SV98 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(1058,plain,
! [SV99: $i] :
( ( ! [SY2559: $i] :
( ~ ( in @ SY2559 @ ( powerset @ SV99 ) )
| ! [SY2560: $i] :
( ~ ( in @ SY2560 @ ( powerset @ SV99 ) )
| ! [SY2561: $i] :
( ~ ( in @ SY2561 @ SV99 )
| ~ ( in @ SY2561 @ ( setminus @ SV99 @ ( binunion @ SY2559 @ SY2560 ) ) )
| ( in @ SY2561 @ ( setminus @ SV99 @ SY2559 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(1059,plain,
! [SV100: $i > $o] :
( ( ~ ~ ! [SY2562: $i] :
~ ( SV100 @ SY2562 )
| ~ ! [SY2563: $i,SY2564: $i] :
( ~ ( SV100 @ SY2563 )
| ~ ( SV100 @ SY2564 )
| ( SY2563 = SY2564 ) )
| ~ ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(1060,plain,
! [SV101: $i] :
( ( ! [SY2567: $i] :
( ( ( setadjoin @ SV101 @ emptyset )
!= ( setadjoin @ SY2567 @ emptyset ) )
| ( SV101 = SY2567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(1061,plain,
! [SV102: $i] :
( ( ! [SY2568: $i,SY2569: $i] :
( ~ ~ ( in @ SY2569 @ ( setminus @ SV102 @ SY2568 ) )
| ~ ~ ( in @ SY2569 @ SY2568 )
| ~ ( in @ SY2569 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(1062,plain,
! [SV103: $i] :
( ( ! [SY2570: $i,SY2571: $i] :
( ~ ( in @ SY2571 @ ( funcSet @ SV103 @ SY2570 ) )
| ( ( lam @ SV103 @ SY2570
@ ^ [SY2572: $i] : ( ap @ SV103 @ SY2570 @ SY2571 @ SY2572 ) )
= SY2571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(1063,plain,
! [SV104: $i] :
( ( ! [SY2573: $i > $o] :
( ~ ~ ! [SY2574: $i] :
~ ~ ( ~ ( in @ SY2574 @ SV104 )
| ~ ~ ( SY2573 @ SY2574 ) )
| ~ ! [SY2575: $i] :
( ~ ( in @ SY2575 @ SV104 )
| ( SY2573 @ SY2575 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(1064,plain,
! [SV105: $i] :
( ( ! [SY2576: $i] :
( ~ ( in @ SY2576 @ ( funcSet @ SV105 @ ( powerset @ SV105 ) ) )
| ~ ( surjective @ SV105 @ ( powerset @ SV105 ) @ SY2576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(1065,plain,
! [SV106: $i] :
( ( ~ ~ ( ~ ( in @ emptyset @ SV106 )
| ~ ! [SY2577: $i] :
( ~ ~ ( ~ ( in @ SY2577 @ omega )
| ~ ( in @ SY2577 @ SV106 ) )
| ( in @ ( setadjoin @ SY2577 @ SY2577 ) @ SV106 ) ) )
| ! [SY2578: $i] :
( ~ ( in @ SY2578 @ omega )
| ( in @ SY2578 @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(1066,plain,
! [SV107: $i] :
( ( ~ ( iskpair @ SV107 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SV107 )
@ ^ [SY2579: $i] : ( in @ ( setadjoin @ SY2579 @ emptyset ) @ SV107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(1067,plain,
! [SV108: $i] :
( ( ! [SY2580: $i,SY2581: $i] :
( ~ ( func @ SV108 @ SY2580 @ SY2581 )
| ! [SY2582: $i] :
( ~ ( in @ SY2582 @ SV108 )
| ( singleton
@ ( dsetconstr @ SY2580
@ ^ [SX4: $i] : ( in @ ( kpair @ SY2582 @ SX4 ) @ SY2581 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(1068,plain,
! [SV109: $i] :
( ( ! [SY2584: $i] :
( ~ ( in @ SY2584 @ ( powerset @ SV109 ) )
| ! [SY2585: $i] :
( ~ ( in @ SY2585 @ ( powerset @ SV109 ) )
| ~ ! [SY2586: $i] :
( ~ ( in @ SY2586 @ SV109 )
| ~ ( in @ SY2586 @ SY2584 )
| ( in @ SY2586 @ SY2585 ) )
| ( subset @ SY2584 @ SY2585 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(1069,plain,
! [SV110: $i] :
( ( ! [SY2587: $i] :
( ~ ( in @ SY2587 @ ( powerset @ SV110 ) )
| ! [SY2588: $i] :
( ~ ( in @ SY2588 @ ( powerset @ SV110 ) )
| ! [SY2589: $i] :
( ~ ( in @ SY2589 @ SV110 )
| ~ ~ ( in @ SY2589 @ SY2587 )
| ~ ( in @ SY2589 @ ( binintersect @ SY2587 @ SY2588 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(1070,plain,
! [SV111: $i] :
( ( ! [SY2590: $i,SY2591: $i] :
( ~ ( in @ SY2591 @ ( cartprod @ SV111 @ SY2590 ) )
| ( in @ ( ksnd @ SY2591 ) @ SY2590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(1071,plain,
! [SV112: $i] :
( ( ! [SY2592: $i,SY2593: $i] :
( ~ ( in @ SY2593 @ SV112 )
| ! [SY2594: $i] :
( ~ ( in @ SY2594 @ SY2592 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY2593 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2593 @ ( setadjoin @ SY2594 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV112 @ SY2592 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(1072,plain,
! [SV113: $i] :
( ( ! [SY2595: $i] :
( ~ ( in @ SY2595 @ ( powerset @ SV113 ) )
| ! [SY2596: $i] :
( ~ ( in @ SY2596 @ ( powerset @ SV113 ) )
| ! [SY2597: $i] :
( ~ ( in @ SY2597 @ SV113 )
| ~ ( in @ SY2597 @ ( setminus @ SV113 @ SY2595 ) )
| ( in @ SY2597 @ ( setminus @ SV113 @ ( binintersect @ SY2595 @ SY2596 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(1073,plain,
! [SV114: $i] :
( ( ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( powerset @ SV114 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SV114 )
| ~ ( in @ SY2599 @ SY2598 )
| ~ ( in @ SY2599 @ ( setminus @ SV114 @ SY2598 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(1074,plain,
! [SV115: $i] :
( ( ! [SY2600: $i,SY2601: $i > $i > $o,SY2602: $i,SY2603: $i] :
( ~ ( in @ ( kpair @ SY2602 @ SY2603 )
@ ( dpsetconstr @ SV115 @ SY2600
@ ^ [SX5: $i,SX6: $i] : ( SY2601 @ SX5 @ SX6 ) ) )
| ( in @ SY2602 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(1075,plain,
! [SV116: $i] :
( ( ! [SY2606: $i,SY2607: $i > $i > $o,SY2608: $i,SY2609: $i] :
( ~ ( in @ ( kpair @ SY2608 @ SY2609 )
@ ( dpsetconstr @ SV116 @ SY2606
@ ^ [SX5: $i,SX6: $i] : ( SY2607 @ SX5 @ SX6 ) ) )
| ( in @ SY2609 @ SY2606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(1076,plain,
! [SV117: $i] :
( ( ! [SY2612: $i,SY2613: $i] :
( ~ ( in @ SY2613 @ ( setminus @ SV117 @ SY2612 ) )
| ~ ( in @ SY2613 @ SY2612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(1077,plain,
! [SV118: $i] :
( ( ! [SY2614: $i > $o,SY2615: $i] :
( ~ ( in @ SY2615 @ SV118 )
| ~ ( SY2614 @ SY2615 )
| ~ ! [SY2616: $i] :
( ~ ( in @ SY2616 @ SV118 )
| ~ ( SY2614 @ SY2616 )
| ( SY2616 = SY2615 ) )
| ( ex1 @ SV118
@ ^ [SX3: $i] : ( SY2614 @ SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(1078,plain,
! [SV119: $i] :
( ( ! [SY2618: $i] :
( ( ( setminus @ SV119 @ SY2618 )
!= emptyset )
| ( subset @ SV119 @ SY2618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(1079,plain,
! [SV120: $i] :
( ( ! [SY2619: $i,SY2620: $i] :
( ~ ~ ( in @ SY2620 @ SV120 )
| ~ ~ ( in @ SY2620 @ SY2619 )
| ~ ( in @ SY2620 @ ( symdiff @ SV120 @ SY2619 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(1080,plain,
! [SV121: $i] :
( ( ! [SY2621: $i,SY2622: $i > $i] :
( ~ ! [SY2623: $i] :
( ~ ( in @ SY2623 @ SV121 )
| ( in @ ( SY2622 @ SY2623 ) @ SY2621 ) )
| ! [SY2624: $i] :
( ~ ( in @ SY2624 @ SV121 )
| ( ( ap @ SV121 @ SY2621
@ ( lam @ SV121 @ SY2621
@ ^ [SX4: $i] : ( SY2622 @ SX4 ) )
@ SY2624 )
= ( SY2622 @ SY2624 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(1081,plain,
! [SV122: $i] :
( ( ! [SY2626: $i] :
( ( SV122 != SY2626 )
| ! [SY2627: $i > $o,SY2628: $i > $o] :
( ~ ! [SY2629: $i] :
( ~ ( in @ SY2629 @ SV122 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2626 )
| ( SY2629 != SX5 )
| ~ ( ~ ( ~ ( SY2627 @ SY2629 )
| ( SY2628 @ SX5 ) )
| ~ ( ~ ( SY2628 @ SX5 )
| ( SY2627 @ SY2629 ) ) ) ) )
| ( ( dsetconstr @ SV122
@ ^ [SX4: $i] : ( SY2627 @ SX4 ) )
= ( dsetconstr @ SY2626
@ ^ [SX4: $i] : ( SY2628 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(1082,plain,
! [SV123: $i] :
( ( ! [SY2633: $i > $o] :
( ~ ( ex1 @ SV123
@ ^ [SX2: $i] : ( SY2633 @ SX2 ) )
| ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV123 )
| ! [SY2636: $i] :
( ~ ( in @ SY2636 @ SV123 )
| ~ ( SY2633 @ SY2635 )
| ~ ( SY2633 @ SY2636 )
| ( SY2635 = SY2636 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(1083,plain,
! [SV124: $i] :
( ( ! [SY2637: $i] :
( ~ ( in @ SV124 @ SY2637 )
| ~ ( in @ SY2637 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(1084,plain,
! [SV125: $i] :
( ( ! [SY2638: $i] :
( ~ ( breln1 @ SV125 @ SY2638 )
| ! [SY2639: $i] :
( ~ ( breln1 @ SV125 @ SY2639 )
| ! [SY2640: $i] :
( ~ ( in @ SY2640 @ SV125 )
| ! [SY2641: $i] :
( ~ ( in @ SY2641 @ SV125 )
| ~ ( in @ ( kpair @ SY2640 @ SY2641 ) @ SY2639 )
| ( in @ ( kpair @ SY2640 @ SY2641 ) @ ( binunion @ SY2638 @ SY2639 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(1085,plain,
! [SV126: $i] :
( ( ! [SY2642: $o,SY2643: $i] :
( ~ ( in @ SY2643 @ SV126 )
| ! [SY2644: $i] :
( ~ ( in @ SY2644 @ SV126 )
| ~ ~ SY2642
| ( in @ SY2644
@ ( dsetconstr @ SV126
@ ^ [SX4: $i] :
( ~ ( ~ SY2642
| ( SX4 != SY2643 ) )
| ~ ( ~ ~ SY2642
| ( SX4 != SY2644 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(1086,plain,
! [SV127: $i] :
( ( ! [SY2646: $i,SY2647: $i] :
( ~ ( in @ SY2647 @ ( setadjoin @ SV127 @ SY2646 ) )
| ( SY2647 = SV127 )
| ( in @ SY2647 @ SY2646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(1087,plain,
! [SV128: $i] :
( ( ! [SY2648: $i,SY2649: $i] :
( ~ ( in @ SY2649 @ SV128 )
| ~ ( in @ SY2649 @ SY2648 )
| ~ ( in @ SY2649 @ ( symdiff @ SV128 @ SY2648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(1088,plain,
! [SV129: $i] :
( ( ~ ~ ! [SY2650: $i] :
~ ( in @ SY2650 @ SV129 )
| ( SV129 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(1089,plain,
! [SV130: $i] :
( ( ! [SY2651: $i] :
~ ( ~ ( ~ ( in @ SY2651 @ ( powerset @ SV130 ) )
| ! [SY2652: $i] :
( ~ ( in @ SY2652 @ SY2651 )
| ( in @ SY2652 @ SV130 ) ) )
| ~ ( ~ ! [SY2653: $i] :
( ~ ( in @ SY2653 @ SY2651 )
| ( in @ SY2653 @ SV130 ) )
| ( in @ SY2651 @ ( powerset @ SV130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(1090,plain,
! [SV131: $i] :
( ( ! [SY2654: $i] :
( ~ ( breln1 @ SV131 @ SY2654 )
| ! [SY2655: $i] :
( ~ ( breln1 @ SV131 @ SY2655 )
| ! [SY2656: $i] :
( ~ ( in @ SY2656 @ SV131 )
| ! [SY2657: $i] :
( ~ ( in @ SY2657 @ SV131 )
| ! [SY2658: $i] :
( ~ ( in @ SY2658 @ SV131 )
| ~ ( in @ ( kpair @ SY2656 @ SY2658 ) @ SY2654 )
| ~ ( in @ ( kpair @ SY2658 @ SY2657 ) @ SY2655 )
| ( in @ ( kpair @ SY2656 @ SY2657 ) @ ( breln1compset @ SV131 @ SY2654 @ SY2655 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(1091,plain,
! [SV132: $i] :
( ( ! [SY2659: $i] :
( ~ ( in @ SY2659 @ ( powerset @ SV132 ) )
| ! [SY2660: $i] :
( ~ ( in @ SY2660 @ ( powerset @ SV132 ) )
| ( in @ ( setminus @ SV132 @ ( binunion @ SY2659 @ SY2660 ) ) @ ( powerset @ ( setminus @ SV132 @ SY2659 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(1092,plain,
! [SV133: $i] :
( ( ! [SY2661: $i,SY2662: $i] :
( ~ ( in @ ( setadjoin @ SY2662 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV133 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV133 @ ( setadjoin @ SY2661 @ emptyset ) ) @ emptyset ) ) )
| ( SV133 = SY2662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(1093,plain,
! [SV134: $i] :
( ( ! [SY2663: $i,SY2664: $i] :
( ( ( setadjoin @ SV134 @ ( setadjoin @ SY2663 @ emptyset ) )
!= ( setadjoin @ SY2664 @ emptyset ) )
| ( SV134 = SY2663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(1094,plain,
! [SV135: $i] :
( ( ! [SY2665: $i] :
( ~ ( breln1 @ SV135 @ SY2665 )
| ! [SY2666: $i] :
( ~ ( breln1 @ SV135 @ SY2666 )
| ~ ! [SY2667: $i] :
( ~ ( in @ SY2667 @ SV135 )
| ! [SY2668: $i] :
( ~ ( in @ SY2668 @ SV135 )
| ~ ( in @ ( kpair @ SY2667 @ SY2668 ) @ SY2665 )
| ( in @ ( kpair @ SY2667 @ SY2668 ) @ SY2666 ) ) )
| ( subset @ SY2665 @ SY2666 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(1095,plain,
! [SV136: $i] :
( ( ~ ( ( SV136 != emptyset ) )
| ~ ! [SY2669: $i] :
~ ~ ( ~ ( in @ SY2669 @ SV136 )
| ( ( binintersect @ SY2669 @ SV136 )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(1096,plain,
! [SV137: $i] :
( ( ! [SY2670: $i,SY2671: $i] :
( ~ ( in @ SY2671 @ ( cartprod @ SV137 @ SY2670 ) )
| ( ( kpair @ ( kfst @ SY2671 ) @ ( ksnd @ SY2671 ) )
= SY2671 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(1097,plain,
! [SV138: $i] :
( ( ! [SY2672: $i] :
( ( SV138 != SY2672 )
| ! [SY2673: $i,SY2674: $i] :
( ( SY2673 != SY2674 )
| ~ ( ~ ( ~ ( in @ SY2673 @ SV138 )
| ( in @ SY2674 @ SY2672 ) )
| ~ ( ~ ( in @ SY2674 @ SY2672 )
| ( in @ SY2673 @ SV138 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(1098,plain,
! [SV139: $i] :
( ( ! [SY2675: $i] :
( ~ ( in @ SY2675 @ ( powerset @ SV139 ) )
| ! [SY2676: $i] :
( ~ ( in @ SY2676 @ ( powerset @ SV139 ) )
| ! [SY2677: $i] :
( ~ ( in @ SY2677 @ ( powerset @ SV139 ) )
| ~ ( subset @ SY2675 @ SY2677 )
| ( subset @ ( binintersect @ SY2675 @ SY2676 ) @ SY2677 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(1099,plain,
! [SV140: $i] :
( ( ! [SY2678: $i,SY2679: $i] :
( ~ ( breln @ SV140 @ SY2678 @ SY2679 )
| ! [SY2680: $i] :
( ~ ( breln @ SV140 @ SY2678 @ SY2680 )
| ~ ! [SY2681: $i] :
( ~ ( in @ SY2681 @ SV140 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2678 )
| ~ ( in @ ( kpair @ SY2681 @ SX5 ) @ SY2679 )
| ( in @ ( kpair @ SY2681 @ SX5 ) @ SY2680 ) ) )
| ~ ! [SY2683: $i] :
( ~ ( in @ SY2683 @ SV140 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2678 )
| ~ ( in @ ( kpair @ SY2683 @ SX5 ) @ SY2680 )
| ( in @ ( kpair @ SY2683 @ SX5 ) @ SY2679 ) ) )
| ( SY2679 = SY2680 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(1100,plain,
! [SV141: $i] :
( ( ! [SY2685: $i,SY2686: $i] :
( ~ ( in @ SY2686 @ SV141 )
| ! [SY2687: $i] :
( ~ ( in @ SY2687 @ SY2685 )
| ( in @ ( kpair @ SY2686 @ SY2687 ) @ ( cartprod @ SV141 @ SY2685 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(1101,plain,
! [SV142: $i] :
( ( ! [SY2688: $i,SY2689: $i] :
( ~ ( in @ SY2689 @ SV142 )
| ! [SY2690: $i] :
( ~ ( in @ SY2690 @ SY2688 )
| ( in @ ( kpair @ SY2689 @ SY2690 ) @ ( powerset @ ( powerset @ ( binunion @ SV142 @ SY2688 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(1102,plain,
! [SV143: $i] :
( ( ! [SY2691: $i,SY2692: $i] :
( ~ ( in @ SY2692 @ ( binintersect @ SV143 @ SY2691 ) )
| ( in @ SY2692 @ SY2691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(1103,plain,
! [SV144: $i] :
( ( ! [SY2693: $i,SY2694: $i > $i] :
( ~ ! [SY2695: $i] :
( ~ ( in @ SY2695 @ SV144 )
| ( in @ ( SY2694 @ SY2695 ) @ SY2693 ) )
| ! [SY2696: $i] :
( ~ ( in @ SY2696 @ ( funcSet @ SY2693 @ SV144 ) )
| ~ ! [SY2697: $i] :
( ~ ( in @ SY2697 @ SV144 )
| ( ( ap @ SY2693 @ SV144 @ SY2696 @ ( SY2694 @ SY2697 ) )
= SY2697 ) )
| ( surjective @ SY2693 @ SV144 @ SY2696 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(1104,plain,
! [SV145: $i] :
( ( ! [SY2698: $i] :
( ~ ( in @ SY2698 @ ( powerset @ SV145 ) )
| ! [SY2699: $i] :
( ~ ( in @ SY2699 @ SV145 )
| ~ ( in @ SY2699 @ SY2698 )
| ( in @ SY2699 @ ( setminus @ SV145 @ ( setminus @ SV145 @ SY2698 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(1105,plain,
! [SV146: $i] :
( ( ! [SY2700: $i > $o] :
( ~ ! [SY2701: $i] :
( ~ ( in @ SY2701 @ SV146 )
| ! [SY2702: $i] :
( ~ ( in @ SY2702 @ SV146 )
| ~ ( SY2700 @ SY2701 )
| ~ ( SY2700 @ SY2702 )
| ( SY2701 = SY2702 ) ) )
| ~ ~ ! [SY2703: $i] :
~ ~ ( ~ ( in @ SY2703 @ SV146 )
| ~ ( SY2700 @ SY2703 ) )
| ( ex1 @ SV146
@ ^ [SX2: $i] : ( SY2700 @ SX2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(1106,plain,
! [SV147: $i] :
( ( ! [SY2705: $i] :
( ~ ( in @ SY2705 @ ( powerset @ SV147 ) )
| ! [SY2706: $i] :
( ~ ( in @ SY2706 @ ( powerset @ SV147 ) )
| ! [SY2707: $i] :
( ~ ( in @ SY2707 @ SV147 )
| ~ ( in @ SY2707 @ ( setminus @ SV147 @ SY2705 ) )
| ~ ( in @ SY2707 @ ( binintersect @ SY2705 @ SY2706 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(1107,plain,
! [SV148: $i] :
( ( ! [SY2708: $i] :
( ~ ( in @ SY2708 @ ( powerset @ SV148 ) )
| ! [SY2709: $i] :
( ~ ( in @ SY2709 @ ( powerset @ SV148 ) )
| ! [SY2710: $i] :
( ~ ( in @ SY2710 @ ( powerset @ SV148 ) )
| ! [SY2711: $i] :
( ~ ( in @ SY2711 @ SV148 )
| ~ ( in @ SY2711 @ ( binintersect @ SY2708 @ SY2709 ) )
| ( in @ SY2711 @ ( binunion @ SY2708 @ SY2710 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(1108,plain,
! [SV149: $i] :
( ( ! [SY2712: $i > $o] :
( ~ ( ex1 @ SV149
@ ^ [SX2: $i] : ( SY2712 @ SX2 ) )
| ~ ! [SY2714: $i] :
~ ~ ( ~ ( in @ SY2714 @ SV149 )
| ~ ( SY2712 @ SY2714 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(1109,plain,
! [SV150: $i] :
( ( ! [SY2715: $i] :
( ~ ( breln1 @ SV150 @ SY2715 )
| ! [SY2716: $i] :
( ~ ( breln1 @ SV150 @ SY2716 )
| ! [SY2717: $i] :
( ~ ( breln1 @ SV150 @ SY2717 )
| ( ( breln1compset @ SV150 @ ( binunion @ SY2715 @ SY2716 ) @ SY2717 )
= ( binunion @ ( breln1compset @ SV150 @ SY2715 @ SY2717 ) @ ( breln1compset @ SV150 @ SY2716 @ SY2717 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(1110,plain,
! [SV151: $i] :
( ( ! [SY2718: $i,SY2719: $i > $i > $o,SY2720: $i,SY2721: $i] :
( ~ ( in @ ( kpair @ SY2720 @ SY2721 )
@ ( dpsetconstr @ SV151 @ SY2718
@ ^ [SX5: $i,SX6: $i] : ( SY2719 @ SX5 @ SX6 ) ) )
| ( SY2719 @ SY2720 @ SY2721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(1111,plain,
! [SV152: $i > $o] :
( ( ! [SY2724: $i > $o] :
( ~ ! [SY2725: $i,SY2726: $i] :
( ( SY2725 != SY2726 )
| ~ ( ~ ( ~ ( SV152 @ SY2725 )
| ( SY2724 @ SY2726 ) )
| ~ ( ~ ( SY2724 @ SY2726 )
| ( SV152 @ SY2725 ) ) ) )
| ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY2724 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY2724 @ SX3 )
| ( SX2 = SX3 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SX2: $i] : ( SY2724 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(1112,plain,
! [SV153: $i] :
( ( ! [SY2733: $i] :
( ~ ( subset @ SV153 @ SY2733 )
| ~ ( subset @ SY2733 @ SV153 )
| ( SV153 = SY2733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(1113,plain,
! [SV154: $i] :
( ( ! [SY2734: $i,SY2735: $i] :
( ~ ( func @ SV154 @ SY2734 @ SY2735 )
| ( in @ SY2735 @ ( funcSet @ SV154 @ SY2734 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(1114,plain,
! [SV155: $i] :
( ( ! [SY2736: $o,SY2737: $i] :
( ~ ( in @ SY2737 @ SV155 )
| ! [SY2738: $i] :
( ~ ( in @ SY2738 @ SV155 )
| ~ ~ SY2736
| ( ( dsetconstr @ SV155
@ ^ [SX4: $i] :
( ~ ( ~ SY2736
| ( SX4 != SY2737 ) )
| ~ ( ~ ~ SY2736
| ( SX4 != SY2738 ) ) ) )
= ( setadjoin @ SY2738 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(1115,plain,
! [SV156: $i] :
( ( ! [SY2740: $i,SY2741: $i] :
( ~ ( in @ SY2740 @ ( powerset @ SV156 ) )
| ~ ( in @ SY2741 @ SY2740 )
| ( in @ SY2741 @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(1116,plain,
! [SV157: $i] :
( ( ! [SY2742: $i] :
( ~ ( breln1 @ SV157 @ SY2742 )
| ! [SY2743: $i] :
( ~ ( in @ SY2743 @ SV157 )
| ! [SY2744: $i] :
( ~ ( in @ SY2744 @ SV157 )
| ~ ( in @ ( kpair @ SY2743 @ SY2744 ) @ SY2742 )
| ( in @ ( kpair @ SY2744 @ SY2743 ) @ ( breln1invset @ SV157 @ SY2742 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(1117,plain,
! [SV158: $i] :
( ( ! [SY2745: $i,SY2746: $i] :
( ~ ( subset @ SV158 @ SY2745 )
| ~ ( subset @ SY2745 @ SY2746 )
| ( subset @ SV158 @ SY2746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(1118,plain,
! [SV159: $i] :
( ( ! [SY2747: $i > $o,SY2748: $i] :
( ~ ( in @ SY2748 @ SV159 )
| ~ ( SY2747 @ SY2748 )
| ( ( dsetconstr @ SV159
@ ^ [SX3: $i] : ( SY2747 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(1119,plain,
! [SV160: $i] :
( ( ! [SY2750: $i,SY2751: $i] :
( ~ ( subset @ SV160 @ SY2750 )
| ~ ( in @ SY2751 @ SV160 )
| ( in @ SY2751 @ SY2750 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(1120,plain,
! [SV161: $i] :
( ( ! [SY2752: $i] :
( ( SV161 != SY2752 )
| ( ( setadjoin @ SV161 @ ( setadjoin @ SY2752 @ emptyset ) )
= ( setadjoin @ SV161 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(1121,plain,
! [SV162: $i] :
( ( ! [SY2753: $i] :
( ~ ( in @ SY2753 @ ( powerset @ SV162 ) )
| ! [SY2754: $i] :
( ~ ( in @ SY2754 @ ( powerset @ SV162 ) )
| ( in @ ( setminus @ SV162 @ ( binunion @ SY2753 @ SY2754 ) ) @ ( powerset @ ( setminus @ SV162 @ SY2753 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(1122,plain,
! [SV163: $i] :
( ( ! [SY2755: $i] :
( ~ ( in @ SY2755 @ ( powerset @ SV163 ) )
| ! [SY2756: $i] :
( ~ ( in @ SY2756 @ ( powerset @ SV163 ) )
| ! [SY2757: $i] :
( ~ ( in @ SY2757 @ ( powerset @ SV163 ) )
| ~ ( subset @ SY2756 @ SY2757 )
| ( subset @ ( binintersect @ SY2755 @ SY2756 ) @ SY2757 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(1123,plain,
! [SV164: $i] :
( ( ! [SY2758: $i,SY2759: $i] :
( ~ ~ ( in @ SY2759 @ SV164 )
| ~ ( in @ SY2759 @ ( setminus @ SV164 @ SY2758 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(1124,plain,
! [SV165: $i] :
( ( ! [SY2760: $i] :
( ( SV165 != SY2760 )
| ( ( setunion @ SV165 )
= ( setunion @ SY2760 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(1125,plain,
! [SV166: $i] :
( ( ! [SY2761: $i,SY2762: $i] :
( ~ ( in @ SY2762 @ SY2761 )
| ~ ( in @ SY2762 @ ( setminus @ SV166 @ SY2761 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(1126,plain,
! [SV167: $i] :
( ( ! [SY2763: $i] :
( ( SV167 != SY2763 )
| ! [SY2764: $i,SY2765: $i] :
( ( SY2764 != SY2765 )
| ~ ( in @ SY2764 @ SV167 )
| ( in @ SY2765 @ SY2763 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(1127,plain,
! [SV168: $i] :
( ( ! [SY2766: $i,SY2767: $i] :
( ~ ( breln @ SV168 @ SY2766 @ SY2767 )
| ! [SY2768: $i] :
( ~ ( breln @ SV168 @ SY2766 @ SY2768 )
| ~ ! [SY2769: $i] :
( ~ ( in @ SY2769 @ SV168 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2766 )
| ~ ( in @ ( kpair @ SY2769 @ SX5 ) @ SY2767 )
| ( in @ ( kpair @ SY2769 @ SX5 ) @ SY2768 ) ) )
| ( subset @ SY2767 @ SY2768 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(1128,plain,
! [SV169: $i] :
( ( ! [SY2771: $i] :
( ~ ( breln1 @ SV169 @ SY2771 )
| ! [SY2772: $i] :
( ~ ( breln1 @ SV169 @ SY2772 )
| ! [SY2773: $i] :
( ~ ( breln1 @ SV169 @ SY2773 )
| ( ( breln1compset @ SV169 @ ( binunion @ SY2771 @ SY2772 ) @ SY2773 )
= ( binunion @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SY2773 ) @ ( breln1invset @ SV169 @ SY2772 ) ) ) @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SY2773 ) @ ( breln1invset @ SV169 @ SY2771 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(1129,plain,
! [SV170: $i] :
( ( ~ ( iskpair @ SV170 )
| ( ( kpair @ ( kfst @ SV170 ) @ ( ksnd @ SV170 ) )
= SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(1130,plain,
! [SV171: $i] :
( ( ! [SY2774: $i] :
( ~ ( in @ SY2774 @ ( powerset @ SV171 ) )
| ! [SY2775: $i] :
( ~ ( in @ SY2775 @ ( powerset @ SV171 ) )
| ! [SY2776: $i] :
( ~ ( in @ SY2776 @ ( binintersect @ SY2774 @ SY2775 ) )
| ( in @ SY2776 @ SV171 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1131,plain,
! [SV172: $i] :
( ( ! [SY2777: $i] :
( ( SV172 != SY2777 )
| ( subset @ SY2777 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(1132,plain,
! [SV173: $i] :
( ( ! [SY2778: $i] :
( ~ ( in @ SY2778 @ ( powerset @ SV173 ) )
| ! [SY2779: $i] :
( ~ ( in @ SY2779 @ ( powerset @ SV173 ) )
| ~ ( subset @ SY2778 @ ( setminus @ SV173 @ SY2779 ) )
| ( subset @ SY2779 @ ( setminus @ SV173 @ SY2778 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(1133,plain,
! [SV174: $i] :
( ( ! [SY2780: $i,SY2781: $i,SY2782: $i] :
( ( ( kpair @ SV174 @ SY2780 )
!= ( kpair @ SY2781 @ SY2782 ) )
| ( SV174 = SY2781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(1134,plain,
! [SV175: $i] :
( ( ! [SY2783: $i > $i] :
~ ! [SY2784: $i] :
~ ~ ( ~ ! [SY2785: $i] :
~ ( ~ ( ~ ( in @ SY2785 @ SY2784 )
| ~ ! [SY2786: $i] :
~ ~ ( ~ ( in @ SY2786 @ SV175 )
| ( SY2785
!= ( SY2783 @ SY2786 ) ) ) )
| ~ ( ~ ~ ! [SY2787: $i] :
~ ~ ( ~ ( in @ SY2787 @ SV175 )
| ( SY2785
!= ( SY2783 @ SY2787 ) ) )
| ( in @ SY2785 @ SY2784 ) ) )
| ~ ! [SY2788: $i] :
( ~ ! [SY2789: $i] :
~ ( ~ ( ~ ( in @ SY2789 @ SY2788 )
| ~ ! [SY2790: $i] :
~ ~ ( ~ ( in @ SY2790 @ SV175 )
| ( SY2789
!= ( SY2783 @ SY2790 ) ) ) )
| ~ ( ~ ~ ! [SY2791: $i] :
~ ~ ( ~ ( in @ SY2791 @ SV175 )
| ( SY2789
!= ( SY2783 @ SY2791 ) ) )
| ( in @ SY2789 @ SY2788 ) ) )
| ( SY2784 = SY2788 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(1135,plain,
! [SV176: $i] :
( ( ! [SY2792: $i] :
( ~ ( in @ SY2792 @ ( powerset @ SV176 ) )
| ! [SY2793: $i] :
( ~ ( in @ SY2793 @ ( powerset @ SV176 ) )
| ( in @ ( setminus @ SY2792 @ SY2793 ) @ ( powerset @ SV176 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1136,plain,
! [SV177: $i] :
( ( ! [SY2794: $i,SY2795: $i] :
( ~ ( in @ SY2795 @ ( funcSet @ SV177 @ SY2794 ) )
| ~ ( injective @ SV177 @ SY2794 @ SY2795 )
| ( in @ SY2795 @ ( injFuncSet @ SV177 @ SY2794 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(1137,plain,
! [SV178: $i] :
( ( ! [SY2796: $i] :
( ~ ( breln1 @ SV178 @ SY2796 )
| ! [SY2797: $i] :
( ~ ( breln1 @ SV178 @ SY2797 )
| ( ( breln1invset @ SV178 @ ( breln1compset @ SV178 @ SY2796 @ SY2797 ) )
= ( breln1compset @ SV178 @ ( breln1invset @ SV178 @ SY2797 ) @ ( breln1invset @ SV178 @ SY2796 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(1138,plain,
! [SV179: $i] :
( ( ! [SY2798: $i > $o,SY2799: $i] :
( ~ ( in @ SY2799
@ ( dsetconstr @ SV179
@ ^ [SX3: $i] : ( SY2798 @ SX3 ) ) )
| ( in @ SY2799 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1139,plain,
! [SV180: $i] :
( ( ! [SY2801: $i,SY2802: $i > $i > $o] :
( ~ ! [SY2803: $i] :
( ~ ( in @ SY2803 @ SV180 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SY2801 )
| ~ ( SY2802 @ SY2803 @ SX4 ) ) )
| ! [SY2805: $i] :
( ~ ( in @ SY2805 @ ( breln1Set @ SY2801 ) )
| ~ ( reflwellordering @ SY2801 @ SY2805 )
| ! [SY2806: $i] :
( ~ ( in @ SY2806 @ SV180 )
| ( singleton
@ ( dsetconstr @ SY2801
@ ^ [SX5: $i] :
~ ( ~ ( SY2802 @ SY2806 @ SX5 )
| ~ ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2801 )
| ~ ( SY2802 @ SY2806 @ SX6 )
| ( in @ ( kpair @ SX5 @ SX6 ) @ SY2805 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1140,plain,
! [SV181: $i] :
( ( ! [SY2809: $i,SY2810: $i] :
( ~ ( in @ SY2810 @ SV181 )
| ! [SY2811: $i] :
( ~ ( in @ SY2811 @ SY2809 )
| ( in @ ( setadjoin @ ( setadjoin @ SY2810 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2810 @ ( setadjoin @ SY2811 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV181 @ SY2809 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1141,plain,
! [SV182: $i] :
( ( ! [SY2812: $i,SY2813: $i > $i] :
( ~ ! [SY2814: $i] :
( ~ ( in @ SY2814 @ SV182 )
| ( in @ ( SY2813 @ SY2814 ) @ SY2812 ) )
| ! [SY2815: $i] :
( ~ ( in @ SY2815 @ SV182 )
| ( ( ap @ SV182 @ SY2812
@ ( lam @ SV182 @ SY2812
@ ^ [SX4: $i] : ( SY2813 @ SX4 ) )
@ SY2815 )
= ( SY2813 @ SY2815 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(1142,plain,
! [SV183: $i] :
( ( ! [SY2817: $i,SY2818: $i] :
( ~ ( in @ SY2818 @ SV183 )
| ~ ~ ( in @ SY2818 @ SY2817 )
| ~ ( subset @ SV183 @ SY2817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(1143,plain,
! [SV184: $i] :
( ( ! [SY2819: $i,SY2820: $i] :
( ~ ( in @ SY2820 @ SV184 )
| ~ ~ ( in @ SY2820 @ SY2819 )
| ( SV184 != SY2819 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(1144,plain,
! [SV185: $i] :
( ( ! [SY2821: $i] :
( ~ ( in @ SY2821 @ ( powerset @ SV185 ) )
| ! [SY2822: $i] :
( ~ ( in @ SY2822 @ ( powerset @ SV185 ) )
| ( in @ ( binintersect @ SY2821 @ SY2822 ) @ ( powerset @ SV185 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(1145,plain,
! [SV186: $i] :
( ( ! [SY2823: $i] :
( ~ ( in @ SY2823 @ ( powerset @ SV186 ) )
| ! [SY2824: $i] :
( ~ ( in @ SY2824 @ ( powerset @ SV186 ) )
| ! [SY2825: $i] :
( ~ ( in @ SY2825 @ SV186 )
| ~ ( in @ SY2823 @ ( powerset @ SY2824 ) )
| ~ ( in @ SY2825 @ SY2823 )
| ( in @ SY2825 @ SY2824 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1146,plain,
! [SV187: $i] :
( ( ! [SY2826: $i] :
( ( ( binintersect @ SV187 @ SY2826 )
!= SV187 )
| ( subset @ SV187 @ SY2826 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(1147,plain,
! [SV188: $i] :
( ( ! [SY2827: $i > $o,SY2828: $i] :
( ~ ( in @ SY2828 @ SV188 )
| ~ ( ~ ( ~ ( in @ SY2828
@ ( dsetconstr @ SV188
@ ^ [SX3: $i] : ( SY2827 @ SX3 ) ) )
| ( SY2827 @ SY2828 ) )
| ~ ( ~ ( SY2827 @ SY2828 )
| ( in @ SY2828
@ ( dsetconstr @ SV188
@ ^ [SX3: $i] : ( SY2827 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(1148,plain,
! [SV189: $i] :
( ( ! [SY2831: $i > $o] :
( ~ ~ ! [SY2832: $i] :
( ~ ( in @ SY2832 @ SV189 )
| ( SY2831 @ SY2832 ) )
| ~ ! [SY2833: $i] :
~ ~ ( ~ ( in @ SY2833 @ SV189 )
| ~ ~ ( SY2831 @ SY2833 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1149,plain,
! [SV190: $i] :
( ( ! [SY2834: $i] :
( ~ ( in @ SY2834 @ ( setunion @ SV190 ) )
| ! [SY2835: $o] :
( ~ ! [SY2836: $i] :
( ~ ( in @ SY2834 @ SY2836 )
| ~ ( in @ SY2836 @ SV190 )
| SY2835 )
| SY2835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1150,plain,
! [SV191: $i] :
( ( ! [SY2837: $i,SY2838: $i] :
( ~ ( in @ SY2838 @ ( funcSet @ SV191 @ SY2837 ) )
| ! [SY2839: $i] :
( ~ ( in @ SY2839 @ SV191 )
| ! [SY2840: $i] :
( ~ ( in @ SY2840 @ SY2837 )
| ~ ( in @ ( kpair @ SY2839 @ SY2840 ) @ SY2838 )
| ( ( ap @ SV191 @ SY2837 @ SY2838 @ SY2839 )
= SY2840 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1151,plain,
! [SV192: $i] :
( ( ! [SY2841: $i,SY2842: $i] :
( ~ ( subset @ SY2842 @ SV192 )
| ~ ( subset @ SY2842 @ SY2841 )
| ( subset @ SY2842 @ ( binintersect @ SV192 @ SY2841 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1152,plain,
! [SV193: $i] :
( ( ! [SY2843: $i > $i] :
~ ! [SY2844: $i] :
~ ! [SY2845: $i] :
~ ( ~ ( ~ ( in @ SY2845 @ SY2844 )
| ~ ! [SY2846: $i] :
~ ~ ( ~ ( in @ SY2846 @ SV193 )
| ( SY2845
!= ( SY2843 @ SY2846 ) ) ) )
| ~ ( ~ ~ ! [SY2847: $i] :
~ ~ ( ~ ( in @ SY2847 @ SV193 )
| ( SY2845
!= ( SY2843 @ SY2847 ) ) )
| ( in @ SY2845 @ SY2844 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1153,plain,
! [SV194: $i] :
( ( ! [SY2848: $i] :
( ~ ( in @ SY2848 @ ( powerset @ SV194 ) )
| ! [SY2849: $i] :
( ~ ( in @ SY2849 @ SV194 )
| ~ ~ ( in @ SY2849 @ ( setminus @ SV194 @ SY2848 ) )
| ( in @ SY2849 @ SY2848 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1154,plain,
! [SV195: $i] :
( ( ! [SY2850: $i,SY2851: $i] :
( ~ ( func @ SV195 @ SY2850 @ SY2851 )
| ( ( lam @ SV195 @ SY2850
@ ^ [SY2852: $i] : ( ap @ SV195 @ SY2850 @ SY2851 @ SY2852 ) )
= SY2851 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1155,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) )
| ! [SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX1 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( subset @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[825]) ).
thf(1156,plain,
! [SV196: $i > $o] :
( ( ~ ~ ! [SY2853: $i] :
~ ~ ( ~ ( SV196 @ SY2853 )
| ~ ! [SY2854: $i] :
( ~ ( SV196 @ SY2854 )
| ( SY2853 = SY2854 ) ) )
| ~ ! [SY2855: $i] :
~ ~ ( ~ ( SV196 @ SY2855 )
| ~ ! [SY2856: $i] :
( ~ ( SV196 @ SY2856 )
| ( SY2855 = SY2856 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1157,plain,
! [SV197: $i > $o] :
( ( ! [SY2857: $i > $o] :
( ~ ! [SY2858: $i,SY2859: $i] :
( ( SY2858 != SY2859 )
| ~ ( ~ ( ~ ( SV197 @ SY2858 )
| ( SY2857 @ SY2859 ) )
| ~ ( ~ ( SY2857 @ SY2859 )
| ( SV197 @ SY2858 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SY2857 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY2857 @ SX3 )
| ( SX2 = SX3 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY2857 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY2857 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1158,plain,
! [SV198: $i] :
( ( ~ ! [SY2868: $i] :
~ ( in @ SY2868 @ SV198 )
| ( SV198 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(1159,plain,
! [SV199: $i] :
( ( ! [SY2869: $i,SY2870: $i] :
( ~ ( in @ SY2870 @ ( cartprod @ SV199 @ SY2869 ) )
| ~ ! [SY2871: $i] :
~ ~ ( ~ ( in @ SY2871 @ SV199 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SY2869 )
| ( SY2870
!= ( kpair @ SY2871 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(1160,plain,
! [SV200: $i] :
( ( ! [SY2873: $i] :
( ~ ( in @ SY2873 @ ( powerset @ SV200 ) )
| ! [SY2874: $i] :
( ~ ( in @ SY2874 @ ( powerset @ SV200 ) )
| ! [SY2875: $i] :
( ~ ( in @ SY2875 @ SV200 )
| ~ ~ ( in @ SY2875 @ ( binunion @ SY2873 @ SY2874 ) )
| ~ ( in @ SY2875 @ SY2874 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1161,plain,
! [SV201: $i] :
( ( ! [SY2876: $i] :
( ( SV201 != SY2876 )
| ( subset @ SV201 @ SY2876 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(1162,plain,
! [SV202: $i] :
( ( ! [SY2877: $o,SY2878: $i] :
( ~ ( in @ SY2878 @ SV202 )
| ! [SY2879: $i] :
( ~ ( in @ SY2879 @ SV202 )
| ( in @ ( if @ SV202 @ SY2877 @ SY2878 @ SY2879 ) @ SV202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1163,plain,
! [SV203: $i] :
( ( ! [SY2880: $i,SY2881: $i] :
( ~ ( in @ SY2881 @ ( symdiff @ SV203 @ SY2880 ) )
| ! [SY2882: $o] :
( ~ ( ~ ( in @ SY2881 @ SV203 )
| ~ ~ ( in @ SY2881 @ SY2880 )
| SY2882 )
| ~ ( ~ ~ ( in @ SY2881 @ SV203 )
| ~ ( in @ SY2881 @ SY2880 )
| SY2882 )
| SY2882 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1164,plain,
! [SV204: $i] :
( ( ! [SY2883: $i,SY2884: $i > $i] :
( ~ ! [SY2885: $i] :
( ~ ( in @ SY2885 @ SV204 )
| ( in @ ( SY2884 @ SY2885 ) @ SY2883 ) )
| ( func @ SV204 @ SY2883
@ ( lam @ SV204 @ SY2883
@ ^ [SX3: $i] : ( SY2884 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1165,plain,
! [SV205: $i] :
( ( ! [SY2887: $i,SY2888: $i] :
( ~ ( subset @ SV205 @ SY2888 )
| ( subset @ SV205 @ ( setadjoin @ SY2887 @ SY2888 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1166,plain,
! [SV206: $i] :
( ( ! [SY2889: $o,SY2890: $i] :
( ~ ( in @ SY2890 @ SV206 )
| ! [SY2891: $i] :
( ~ ( in @ SY2891 @ SV206 )
| ( in @ ( if @ SV206 @ SY2889 @ SY2890 @ SY2891 ) @ ( setadjoin @ SY2890 @ ( setadjoin @ SY2891 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1167,plain,
! [SV207: $i] :
( ( ! [SY2892: $i > $o] :
( ~ ~ ~ ! [SY2893: $i] :
~ ~ ( ~ ( in @ SY2893 @ SV207 )
| ~ ( SY2892 @ SY2893 ) )
| ! [SY2894: $i] :
( ~ ( in @ SY2894 @ SV207 )
| ~ ( SY2892 @ SY2894 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1168,plain,
! [SV208: $i] :
( ( ! [SY2895: $i] :
( ~ ( in @ SY2895 @ ( powerset @ SV208 ) )
| ! [SY2896: $i] :
( ~ ( in @ SY2896 @ ( powerset @ SV208 ) )
| ! [SY2897: $o,SY2898: $i] :
( ~ ( in @ SY2898 @ SV208 )
| ~ ( in @ SY2898 @ ( binunion @ SY2895 @ SY2896 ) )
| ~ ( ~ ( in @ SY2898 @ SY2895 )
| SY2897 )
| ~ ( ~ ( in @ SY2898 @ SY2896 )
| SY2897 )
| SY2897 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(1169,plain,
! [SV209: $i] :
( ( ! [SY2899: $i,SY2900: $i] :
( ~ ( breln @ SV209 @ SY2899 @ SY2900 )
| ! [SY2901: $i > $o] :
( ~ ! [SY2902: $i] :
( ~ ( in @ SY2902 @ SV209 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2899 )
| ~ ( in @ ( kpair @ SY2902 @ SX5 ) @ SY2900 )
| ( SY2901 @ ( kpair @ SY2902 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2900 )
| ( SY2901 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1170,plain,
! [SV210: $i] :
( ( ! [SY2905: $o,SY2906: $i] :
( ~ ( in @ SY2906 @ SV210 )
| ! [SY2907: $i] :
( ~ ( in @ SY2907 @ SV210 )
| ~ SY2905
| ( in @ SY2906
@ ( dsetconstr @ SV210
@ ^ [SX4: $i] :
( ~ ( ~ SY2905
| ( SX4 != SY2906 ) )
| ~ ( ~ ~ SY2905
| ( SX4 != SY2907 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1171,plain,
! [SV211: $i] :
( ( ~ ( in @ SV211 @ omega )
| ( in @ ( setadjoin @ SV211 @ SV211 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1172,plain,
! [SV212: $i] :
( ( ! [SY2909: $i,SY2910: $i] :
( ~ ( subset @ SV212 @ SY2909 )
| ~ ~ ( in @ SY2910 @ SY2909 )
| ~ ( in @ SY2910 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1173,plain,
! [SV213: $i] :
( ( ! [SY2911: $i,SY2912: $i,SY2913: $i] :
( ( ( setadjoin @ ( setadjoin @ SV213 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV213 @ ( setadjoin @ SY2911 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY2912 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2912 @ ( setadjoin @ SY2913 @ emptyset ) ) @ emptyset ) ) )
| ( SV213 = SY2912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1174,plain,
! [SV214: $i] :
( ( ! [SY2914: $i,SY2915: $i] :
( ~ ( in @ SY2915 @ ( injFuncSet @ SV214 @ SY2914 ) )
| ( injective @ SV214 @ SY2914 @ SY2915 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1175,plain,
! [SV215: $i] :
( ( ! [SY2916: $i] :
( ~ ( in @ SY2916 @ SV215 )
| ( subset @ ( setadjoin @ SY2916 @ emptyset ) @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1176,plain,
! [SV216: $i] :
( ( ! [SY2917: $i] :
( ~ ( breln1 @ SV216 @ SY2917 )
| ! [SY2918: $i] :
( ~ ( breln1 @ SV216 @ SY2918 )
| ! [SY2919: $i] :
( ~ ( in @ SY2919 @ SV216 )
| ! [SY2920: $i] :
( ~ ( in @ SY2920 @ SV216 )
| ~ ( in @ ( kpair @ SY2919 @ SY2920 ) @ ( binunion @ SY2917 @ SY2918 ) )
| ! [SX5: $o] :
( ~ ( ~ ( in @ ( kpair @ SY2919 @ SY2920 ) @ SY2917 )
| SX5 )
| ~ ( ~ ( in @ ( kpair @ SY2919 @ SY2920 ) @ SY2918 )
| SX5 )
| SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1177,plain,
! [SV217: $i] :
( ( ! [SY2922: $i] :
( ~ ( in @ SY2922 @ ( powerset @ SV217 ) )
| ! [SY2923: $i] :
( ~ ( in @ SY2923 @ ( powerset @ SV217 ) )
| ! [SY2924: $i] :
( ~ ( in @ SY2924 @ SV217 )
| ~ ( in @ SY2924 @ ( setminus @ SV217 @ ( binunion @ SY2922 @ SY2923 ) ) )
| ( in @ SY2924 @ ( binintersect @ ( setminus @ SV217 @ SY2922 ) @ ( setminus @ SV217 @ SY2923 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1178,plain,
! [SV218: $i] :
( ( ! [SY2925: $i > $i,SY2926: $i] :
( ~ ( in @ SY2926
@ ( image1 @ SV218
@ ^ [SX3: $i] : ( SY2925 @ SX3 ) ) )
| ~ ! [SY2928: $i] :
~ ~ ( ~ ( in @ SY2928 @ SV218 )
| ( SY2926
!= ( SY2925 @ SY2928 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1179,plain,
! [SV219: $i] :
( ( ~ ( in @ SV219 @ omega )
| ( ( omegaS @ SV219 )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1180,plain,
! [SV220: $i] :
( ( ! [SY2929: $i,SY2930: $i] :
( ~ ( in @ SY2930 @ ( setadjoin @ SV220 @ ( setadjoin @ SY2929 @ emptyset ) ) )
| ( SY2930 = SV220 )
| ( SY2930 = SY2929 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1181,plain,
! [SV221: $i] :
( ( ! [SY2931: $i,SY2932: $i] :
( ~ ( in @ SY2932 @ ( surjFuncSet @ SV221 @ SY2931 ) )
| ( in @ SY2932 @ ( funcSet @ SV221 @ SY2931 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1182,plain,
! [SV222: $i] :
( ( ! [SY2933: $i] :
( ~ ( subset @ SV222 @ SY2933 )
| ( in @ SV222 @ ( powerset @ SY2933 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1183,plain,
! [SV223: $i] :
( ( ! [SY2934: $o,SY2935: $i] :
( ~ ( in @ SY2935 @ SV223 )
| ! [SY2936: $i] :
( ~ ( in @ SY2936 @ SV223 )
| ( singleton
@ ( dsetconstr @ SV223
@ ^ [SX4: $i] :
( ~ ( ~ SY2934
| ( SX4 != SY2935 ) )
| ~ ( ~ ~ SY2934
| ( SX4 != SY2936 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1184,plain,
! [SV224: $i] :
( ( ! [SY2938: $i] :
( ~ ( in @ SY2938 @ ( powerset @ SV224 ) )
| ! [SY2939: $i] :
( ~ ( in @ SY2939 @ ( powerset @ SV224 ) )
| ~ ( subset @ SY2938 @ SY2939 )
| ( subset @ ( setminus @ SV224 @ SY2939 ) @ ( setminus @ SV224 @ SY2938 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1185,plain,
! [SV225: $i] :
( ( ! [SY2940: $i,SY2941: $i,SY2942: $i] :
( ( ( kpair @ SV225 @ SY2940 )
!= ( kpair @ SY2941 @ SY2942 ) )
| ( SY2940 = SY2942 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1186,plain,
! [SV226: $i] :
( ( ~ ! [SY2943: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY2944: $i] :
( ~ ( in @ SY2944 @ SY2943 )
| ! [SY2945: $i] :
( ~ ( in @ SY2945 @ SY2944 )
| ( in @ SY2945 @ SV226 ) ) )
| ~ ! [SY2946: $i,SY2947: $i] :
( ~ ~ ( ~ ( in @ SY2946 @ SV226 )
| ~ ( in @ SY2947 @ SV226 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2943 )
| ~ ( ~ ( ~ ( in @ SY2946 @ SX4 )
| ( in @ SY2947 @ SX4 ) )
| ~ ( ~ ( in @ SY2947 @ SX4 )
| ( in @ SY2946 @ SX4 ) ) ) )
| ( SY2946 = SY2947 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY2943 )
| ~ ( in @ SX3 @ SY2943 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY2953: $i] :
( ~ ~ ( ~ ! [SY2954: $i] :
( ~ ( in @ SY2954 @ SY2953 )
| ( in @ SY2954 @ SV226 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY2953 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY2943 )
| ~ ( in @ SX4 @ SY2953 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY2953 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2943 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1187,plain,
! [SV227: $i] :
( ( ! [SY2961: $i,SY2962: $i > $i > $o,SY2963: $i] :
( ~ ( in @ SY2963 @ SV227 )
| ! [SY2964: $i] :
( ~ ( in @ SY2964 @ SY2961 )
| ~ ( in @ ( kpair @ SY2963 @ SY2964 )
@ ( dpsetconstr @ SV227 @ SY2961
@ ^ [SX5: $i,SX6: $i] : ( SY2962 @ SX5 @ SX6 ) ) )
| ( SY2962 @ SY2963 @ SY2964 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1188,plain,
! [SV228: $i] :
( ( ! [SY2967: $i,SY2968: $i] :
( ~ ( in @ SY2967 @ SY2968 )
| ~ ( in @ SY2968 @ SV228 )
| ( in @ SY2967 @ ( setunion @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1189,plain,
! [SV229: $i] :
( ( ! [SY2969: $i] :
( ~ ( in @ SY2969 @ ( powerset @ SV229 ) )
| ! [SY2970: $i] :
( ~ ( in @ SY2970 @ ( powerset @ SV229 ) )
| ! [SY2971: $i] :
( ~ ( in @ SY2971 @ SV229 )
| ~ ~ ( in @ SY2971 @ ( binunion @ SY2969 @ SY2970 ) )
| ~ ( in @ SY2971 @ SY2969 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1190,plain,
! [SV230: $i > $i > $o] :
( ( ! [SY2972: $i] :
( ~ ! [SY2973: $i] :
( ~ ( in @ SY2973 @ SY2972 )
| ~ ! [SY2974: $i] :
~ ~ ( ~ ( SV230 @ SY2973 @ SY2974 )
| ~ ! [SY2975: $i] :
( ~ ( SV230 @ SY2973 @ SY2975 )
| ( SY2974 = SY2975 ) ) ) )
| ~ ! [SY2976: $i] :
~ ! [SY2977: $i] :
~ ( ~ ( ~ ( in @ SY2977 @ SY2976 )
| ~ ! [SY2978: $i] :
~ ~ ( ~ ( in @ SY2978 @ SY2972 )
| ~ ( SV230 @ SY2978 @ SY2977 ) ) )
| ~ ( ~ ~ ! [SY2979: $i] :
~ ~ ( ~ ( in @ SY2979 @ SY2972 )
| ~ ( SV230 @ SY2979 @ SY2977 ) )
| ( in @ SY2977 @ SY2976 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1191,plain,
! [SV231: $i] :
( ( ! [SY2980: $i,SY2981: $i] :
( ~ ( func @ SV231 @ SY2980 @ SY2981 )
| ! [SY2982: $i] :
( ~ ( func @ SV231 @ SY2980 @ SY2982 )
| ~ ! [SY2983: $i] :
( ~ ( in @ SY2983 @ SV231 )
| ( ( ap @ SV231 @ SY2980 @ SY2981 @ SY2983 )
= ( ap @ SV231 @ SY2980 @ SY2982 @ SY2983 ) ) )
| ( SY2981 = SY2982 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1192,plain,
! [SV232: $i] :
( ( ! [SY2984: $o,SY2985: $i] :
( ~ ( in @ SY2985 @ SV232 )
| ! [SY2986: $i] :
( ~ ( in @ SY2986 @ SV232 )
| ~ SY2984
| ( ( if @ SV232 @ SY2984 @ SY2985 @ SY2986 )
= SY2985 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1193,plain,
! [SV233: $i] :
( ( ! [SY2987: $i] :
( ~ ( breln1 @ SV233 @ SY2987 )
| ! [SY2988: $i > $o] :
( ~ ! [SY2989: $i] :
( ~ ( in @ SY2989 @ SV233 )
| ! [SY2990: $i] :
( ~ ( in @ SY2990 @ SV233 )
| ~ ( in @ ( kpair @ SY2989 @ SY2990 ) @ SY2987 )
| ( SY2988 @ ( kpair @ SY2989 @ SY2990 ) ) ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2987 )
| ( SY2988 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1194,plain,
! [SV234: $i] :
( ( ! [SY2992: $i] :
( ~ ! [SY2993: $i] :
( ~ ( in @ SY2993 @ SY2992 )
| ( in @ SY2993 @ SV234 ) )
| ( in @ SY2992 @ ( powerset @ SV234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1195,plain,
! [SV235: $i] :
( ( ! [SY2994: $i] :
( ~ ( in @ SY2994 @ ( setunion @ SV235 ) )
| ~ ! [SY2995: $i] :
~ ~ ( ~ ( in @ SY2995 @ SV235 )
| ~ ( in @ SY2994 @ SY2995 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1196,plain,
! [SV236: $i] :
( ( ~ ( singleton @ SV236 )
| ( in @ ( setunion @ SV236 ) @ SV236 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1197,plain,
! [SV237: $i] :
( ( ! [SY2996: $i,SY2997: $i] :
( ~ ( in @ SY2997 @ ( setminus @ SV237 @ SY2996 ) )
| ( in @ SY2997 @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1198,plain,
! [SV238: $i] :
( ( ! [SY2998: $i] :
( ( SV238 != SY2998 )
| ( ( setadjoin @ ( setadjoin @ SV238 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV238 @ ( setadjoin @ SY2998 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV238 @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1199,plain,
! [SV239: $i] :
( ( ! [SY2999: $i,SY3000: $i] :
( ~ ( in @ SY3000 @ ( binunion @ SV239 @ SY2999 ) )
| ( in @ SY3000 @ SV239 )
| ( in @ SY3000 @ SY2999 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1200,plain,
! [SV240: $i] :
( ( ! [SY3001: $i,SY3002: $i] :
( ~ ( func @ SV240 @ SY3001 @ SY3002 )
| ! [SY3003: $i] :
( ~ ( in @ SY3003 @ SV240 )
| ( in @ ( kpair @ SY3003 @ ( ap @ SV240 @ SY3001 @ SY3002 @ SY3003 ) ) @ SY3002 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1201,plain,
! [SV241: $i] :
( ( ! [SY3004: $i] :
( ~ ( in @ SY3004 @ ( powerset @ SV241 ) )
| ! [SY3005: $i] :
( ~ ( in @ SY3005 @ ( powerset @ SV241 ) )
| ( in @ ( setminus @ SV241 @ SY3004 ) @ ( powerset @ ( setminus @ SV241 @ ( binintersect @ SY3004 @ SY3005 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1202,plain,
! [SV242: $i] :
( ( ~ ( ( SV242 != emptyset ) )
| ~ ! [SY3006: $i] :
~ ( in @ SY3006 @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1203,plain,
! [SV243: $i] :
( ( ! [SY3007: $i] :
( ~ ( in @ SY3007 @ ( powerset @ SV243 ) )
| ! [SY3008: $i] :
( ~ ( in @ SY3008 @ ( powerset @ SV243 ) )
| ! [SY3009: $i] :
( ~ ( in @ SY3009 @ ( powerset @ SV243 ) )
| ( in @ ( binintersect @ SY3007 @ SY3008 ) @ ( powerset @ ( binintersect @ ( binunion @ SY3007 @ SY3009 ) @ ( binunion @ SY3008 @ SY3009 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1204,plain,
! [SV244: $i] :
( ( ! [SY3010: $i] :
( ~ ( in @ SY3010 @ ( powerset @ SV244 ) )
| ! [SY3011: $i] :
( ~ ( in @ SY3011 @ SV244 )
| ~ ( in @ SY3011 @ ( setminus @ SV244 @ ( setminus @ SV244 @ SY3010 ) ) )
| ( in @ SY3011 @ SY3010 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1205,plain,
! [SV245: $i] :
( ( ! [SY3012: $i > $o] :
( ~ ~ ! [SY3013: $i] :
~ ~ ( ~ ( in @ SY3013 @ SV245 )
| ~ ( SY3012 @ SY3013 ) )
| ( ( dsetconstr @ SV245
@ ^ [SX2: $i] : ( SY3012 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1206,plain,
! [SV246: $i] :
( ( ! [SY3015: $i,SY3016: $i] :
( ~ ( func @ SV246 @ SY3015 @ SY3016 )
| ! [SY3017: $i] :
( ~ ( in @ SY3017 @ SV246 )
| ( in
@ ( setunion
@ ( dsetconstr @ SY3015
@ ^ [SX4: $i] : ( in @ ( kpair @ SY3017 @ SX4 ) @ SY3016 ) ) )
@ SY3015 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1207,plain,
! [SV247: $i] :
( ( ! [SY3019: $i] :
( ~ ( breln1 @ SV247 @ SY3019 )
| ! [SY3020: $i] :
( ~ ( in @ SY3020 @ SV247 )
| ! [SY3021: $i] :
( ~ ( in @ SY3021 @ SV247 )
| ~ ( in @ ( kpair @ SY3021 @ SY3020 ) @ ( breln1invset @ SV247 @ SY3019 ) )
| ( in @ ( kpair @ SY3020 @ SY3021 ) @ SY3019 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(1208,plain,
! [SV248: $i] :
( ( ! [SY3022: $i] :
( ( ( binintersect @ SV248 @ SY3022 )
!= SY3022 )
| ( subset @ SY3022 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1209,plain,
! [SV249: $i] :
( ( ~ ! [SY3023: $i] :
( ~ ( in @ SY3023 @ SV249 )
| ( subset @ SY3023 @ SV249 ) )
| ! [SY3024: $i] :
( ~ ( in @ SY3024 @ SV249 )
| ( subset @ SY3024 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1210,plain,
! [SV250: $i] :
( ( ! [SY3025: $i,SY3026: $i] :
( ~ ( in @ SY3026 @ ( setadjoin @ SV250 @ ( setadjoin @ SY3025 @ emptyset ) ) )
| ( SY3026 = SV250 )
| ( SY3026 = SY3025 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1211,plain,
! [SV251: $i] :
( ( ! [SY3027: $i] :
( ~ ( in @ SY3027 @ ( powerset @ SV251 ) )
| ! [SY3028: $i] :
( ~ ( in @ SY3028 @ ( powerset @ SV251 ) )
| ! [SY3029: $i] :
( ~ ( in @ SY3029 @ SV251 )
| ~ ~ ( in @ SY3029 @ SY3027 )
| ~ ~ ( in @ SY3029 @ SY3028 )
| ~ ( in @ SY3029 @ ( binunion @ SY3027 @ SY3028 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1212,plain,
! [SV252: $i] :
( ( ! [SY3030: $o,SY3031: $i] :
( ~ ( in @ SY3031 @ SV252 )
| ! [SY3032: $i] :
( ~ ( in @ SY3032 @ SV252 )
| ~ SY3030
| ( ( dsetconstr @ SV252
@ ^ [SX4: $i] :
( ~ ( ~ SY3030
| ( SX4 != SY3031 ) )
| ~ ( ~ ~ SY3030
| ( SX4 != SY3032 ) ) ) )
= ( setadjoin @ SY3031 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1213,plain,
! [SV253: $i] :
( ( ! [SY3034: $i] :
( ~ ( in @ SY3034 @ ( breln1Set @ SV253 ) )
| ( breln1 @ SV253 @ SY3034 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1214,plain,
! [SV254: $i] :
( ( ! [SY3035: $i,SY3036: $i] :
( ~ ( func @ SV254 @ SY3035 @ SY3036 )
| ! [SY3037: $i] :
( ~ ( in @ SY3037 @ SV254 )
| ( ( ap @ SV254 @ SY3035 @ SY3036 @ SY3037 )
= ( ap @ SV254 @ SY3035 @ SY3036 @ SY3037 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1215,plain,
! [SV255: $i] :
( ( ! [SY3038: $i] :
( ~ ( subset @ SV255 @ SY3038 )
| ( subset @ ( powerset @ SV255 ) @ ( powerset @ SY3038 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1216,plain,
! [SV256: $i] :
( ( ! [SY3039: $i,SY3040: $i,SY3041: $i] :
( ( ( setadjoin @ ( setadjoin @ SV256 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV256 @ ( setadjoin @ SY3039 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY3040 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3040 @ ( setadjoin @ SY3041 @ emptyset ) ) @ emptyset ) ) )
| ( SY3040 != SY3041 )
| ( SY3039 = SY3041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1217,plain,
! [SV257: $i] :
( ( ! [SY3042: $i] :
( ~ ( in @ SY3042 @ ( powerset @ SV257 ) )
| ( subset @ SY3042 @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1218,plain,
! [SV258: $o] :
( ( ! [SY3043: $i] :
( ~ ( in @ SY3043 @ ( prop2set @ SV258 ) )
| SV258 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[888]) ).
thf(1219,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $true ) )
| $true ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[888]) ).
thf(1220,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $false ) )
| $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[888]) ).
thf(1221,plain,
! [SV259: $i] :
( ( ! [SY3044: $i,SY3045: $i] :
( ~ ( func @ SV259 @ SY3044 @ SY3045 )
| ! [SY3046: $i] :
( ~ ( in @ SY3046 @ SV259 )
| ! [SY3047: $i] :
( ~ ( in @ SY3047 @ SY3044 )
| ~ ( in @ ( kpair @ SY3046 @ SY3047 ) @ SY3045 )
| ( ( ap @ SV259 @ SY3044 @ SY3045 @ SY3046 )
= SY3047 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1222,plain,
! [SV260: $i] :
( ( ! [SY3048: $i] :
( ~ ( breln1 @ SV260 @ SY3048 )
| ! [SY3049: $i] :
( ~ ( breln1 @ SV260 @ SY3049 )
| ~ ! [SY3050: $i] :
( ~ ( in @ SY3050 @ SV260 )
| ! [SY3051: $i] :
( ~ ( in @ SY3051 @ SV260 )
| ~ ( in @ ( kpair @ SY3050 @ SY3051 ) @ SY3048 )
| ( in @ ( kpair @ SY3050 @ SY3051 ) @ SY3049 ) ) )
| ~ ! [SY3052: $i] :
( ~ ( in @ SY3052 @ SV260 )
| ! [SY3053: $i] :
( ~ ( in @ SY3053 @ SV260 )
| ~ ( in @ ( kpair @ SY3052 @ SY3053 ) @ SY3049 )
| ( in @ ( kpair @ SY3052 @ SY3053 ) @ SY3048 ) ) )
| ( SY3048 = SY3049 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1223,plain,
! [SV261: $i] :
( ( ! [SY3054: $i] :
( ~ ( breln1 @ SV261 @ SY3054 )
| ( breln1 @ SV261 @ ( breln1invset @ SV261 @ SY3054 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1224,plain,
! [SV262: $i] :
( ( ! [SY3055: $i > $o,SY3056: $i] :
( ~ ( in @ SY3056
@ ( dsetconstr @ SV262
@ ^ [SX3: $i] : ( SY3055 @ SX3 ) ) )
| ( SY3055 @ SY3056 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1225,plain,
! [SV263: $i] :
( ( ! [SY3058: $i,SY3059: $i] :
( ~ ( in @ SY3059 @ SV263 )
| ~ ( in @ SY3059 @ SY3058 )
| ( in @ SY3059 @ ( binintersect @ SV263 @ SY3058 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1226,plain,
! [SV264: $i] :
( ( ! [SY3060: $i] :
( ~ ( breln1 @ SV264 @ SY3060 )
| ! [SY3061: $i] :
( ~ ( breln1 @ SV264 @ SY3061 )
| ! [SY3062: $i] :
( ~ ( in @ SY3062 @ SV264 )
| ! [SY3063: $i] :
( ~ ( in @ SY3063 @ SV264 )
| ~ ( ( in @ ( kpair @ SY3062 @ SY3063 ) @ SY3060 )
| ( in @ ( kpair @ SY3062 @ SY3063 ) @ SY3061 ) )
| ( in @ ( kpair @ SY3062 @ SY3063 ) @ ( binunion @ SY3060 @ SY3061 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1227,plain,
! [SV265: $i] :
( ( ! [SY3064: $i,SY3065: $i] :
( ~ ( in @ SY3065 @ SV265 )
| ! [SY3066: $i] :
( ~ ( in @ SY3066 @ SY3064 )
| ( subset @ ( setadjoin @ SY3065 @ ( setadjoin @ SY3066 @ emptyset ) ) @ ( binunion @ SV265 @ SY3064 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1228,plain,
! [SV266: $i] :
( ( ! [SY3067: $i] :
( ~ ( in @ SY3067 @ ( powerset @ SV266 ) )
| ! [SY3068: $i] :
( ~ ( in @ SY3068 @ ( powerset @ SV266 ) )
| ( in @ ( setminus @ SV266 @ SY3067 ) @ ( powerset @ ( setminus @ SV266 @ ( binintersect @ SY3067 @ SY3068 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1229,plain,
! [SV267: $i] :
( ( ! [SY3069: $i,SY3070: $i] :
( ~ ( in @ SY3070 @ ( injFuncSet @ SV267 @ SY3069 ) )
| ( in @ SY3070 @ ( funcSet @ SV267 @ SY3069 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1230,plain,
! [SV268: $i] :
( ( ! [SY3071: $i,SY3072: $i] :
( ~ ( in @ SY3072 @ ( surjFuncSet @ SV268 @ SY3071 ) )
| ( surjective @ SV268 @ SY3071 @ SY3072 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1231,plain,
! [SV269: $i] :
( ( ~ ( in @ SV269 @ omega )
| ( in @ ( omegaS @ SV269 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1232,plain,
! [SV270: $i] :
( ( ! [SY3073: $i] :
( ~ ( in @ SY3073 @ ( powerset @ SV270 ) )
| ! [SY3074: $i] :
( ~ ( in @ SY3074 @ ( powerset @ SV270 ) )
| ( ( setminus @ SV270 @ ( binunion @ SY3073 @ SY3074 ) )
= ( binintersect @ ( setminus @ SV270 @ SY3073 ) @ ( setminus @ SV270 @ SY3074 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1233,plain,
! [SV271: $i] :
( ( ! [SY3075: $i] :
( ~ ( breln1 @ SV271 @ SY3075 )
| ! [SY3076: $i > $o] :
( ~ ! [SY3077: $i] :
( ~ ( in @ SY3077 @ SV271 )
| ! [SY3078: $i] :
( ~ ( in @ SY3078 @ SV271 )
| ~ ( in @ ( kpair @ SY3077 @ SY3078 ) @ SY3075 )
| ( SY3076 @ ( kpair @ SY3077 @ SY3078 ) ) ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3075 )
| ( SY3076 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1234,plain,
! [SV272: $i] :
( ( ! [SY3080: $i,SY3081: $i] :
( ~ ( in @ SY3081 @ SV272 )
| ~ ~ ( in @ SY3081 @ SY3080 )
| ( in @ SY3081 @ ( symdiff @ SV272 @ SY3080 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1235,plain,
! [SV273: $i] :
( ( ! [SY3082: $i,SY3083: $i] :
( ~ ( in @ SY3083 @ SV273 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3082 )
| ( ( kfst @ ( kpair @ SY3083 @ SX3 ) )
= SY3083 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1236,plain,
! [SV274: $i] :
( ( ! [SY3085: $i] :
( ~ ( in @ SY3085 @ ( powerset @ SV274 ) )
| ! [SY3086: $i] :
( ~ ( in @ SY3086 @ ( powerset @ SV274 ) )
| ~ ( subset @ ( setminus @ SV274 @ SY3086 ) @ ( setminus @ SV274 @ SY3085 ) )
| ( subset @ SY3085 @ SY3086 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1237,plain,
! [SV275: $i] :
( ( ! [SY3087: $i > $o] :
( ~ ! [SY3088: $i] :
( ~ ( in @ SY3088 @ SV275 )
| ~ ( SY3087 @ SY3088 ) )
| ~ ~ ! [SY3089: $i] :
~ ~ ( ~ ( in @ SY3089 @ SV275 )
| ~ ( SY3087 @ SY3089 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1238,plain,
! [SV276: $i] :
( ( ! [SY3090: $i] :
( ~ ( subset @ SV276 @ SY3090 )
| ( ( setminus @ SV276 @ SY3090 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1239,plain,
! [SV277: $i] :
( ( ! [SY3091: $i] :
( ~ ( in @ SY3091 @ ( powerset @ SV277 ) )
| ! [SY3092: $i] :
( ~ ( in @ SY3092 @ ( powerset @ SV277 ) )
| ! [SY3093: $i] :
( ~ ( in @ SY3093 @ SV277 )
| ~ ( in @ SY3093 @ ( setminus @ SV277 @ ( binunion @ SY3091 @ SY3092 ) ) )
| ( in @ SY3093 @ ( setminus @ SV277 @ SY3091 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1240,plain,
! [SV278: $i] :
( ( ! [SY3094: $i] :
( ~ ! [SY3095: $i] :
( ~ ( in @ SY3095 @ SV278 )
| ( in @ SY3095 @ SY3094 ) )
| ~ ! [SY3096: $i] :
( ~ ( in @ SY3096 @ SY3094 )
| ( in @ SY3096 @ SV278 ) )
| ( SV278 = SY3094 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1241,plain,
! [SV279: $i] :
( ( ! [SY3097: $i,SY3098: $i] :
( ~ ( in @ SY3098 @ ( binintersect @ SV279 @ SY3097 ) )
| ( in @ SY3098 @ SV279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1242,plain,
! [SV280: $i] :
( ( ! [SY3099: $i] :
( ~ ( breln1 @ SV280 @ SY3099 )
| ! [SY3100: $i] :
( ~ ( breln1 @ SV280 @ SY3100 )
| ! [SY3101: $i] :
( ~ ( in @ SY3101 @ SV280 )
| ! [SY3102: $i] :
( ~ ( in @ SY3102 @ SV280 )
| ~ ( in @ ( kpair @ SY3101 @ SY3102 ) @ ( breln1compset @ SV280 @ SY3099 @ SY3100 ) )
| ! [SY3103: $o] :
( ~ ! [SY3104: $i] :
( ~ ( in @ SY3104 @ SV280 )
| ~ ( in @ ( kpair @ SY3101 @ SY3104 ) @ SY3099 )
| ~ ( in @ ( kpair @ SY3104 @ SY3102 ) @ SY3100 )
| SY3103 )
| SY3103 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1243,plain,
! [SV281: $i] :
( ( ! [SY3105: $i] :
( ~ ( subset @ SV281 @ SY3105 )
| ( ( binintersect @ SV281 @ SY3105 )
= SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1244,plain,
! [SV282: $i] :
( ( ! [SY3106: $i,SY3107: $i] :
( ~ ~ ( in @ SY3107 @ SV282 )
| ~ ( in @ SY3107 @ SY3106 )
| ( in @ SY3107 @ ( symdiff @ SV282 @ SY3106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1245,plain,
! [SV283: $i] :
( ( ! [SY3108: $i,SY3109: $i,SY3110: $i] :
( ~ ( in @ ( kpair @ SY3109 @ SY3110 ) @ ( cartprod @ SV283 @ SY3108 ) )
| ( in @ SY3110 @ SY3108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1246,plain,
! [SV284: $i] :
( ( ! [SY3111: $i] :
( ~ ~ ~ ! [SY3112: $i] :
~ ~ ( ~ ( in @ SY3112 @ SV284 )
| ~ ( in @ SY3112 @ SY3111 ) )
| ( ( binintersect @ SV284 @ SY3111 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1247,plain,
! [SV285: $i] :
( ( ! [SY3113: $i,SY3114: $i] :
( ~ ( in @ SY3114 @ SV285 )
| ( in @ SY3114 @ ( binunion @ SV285 @ SY3113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1248,plain,
! [SV286: $i] :
( ( ! [SY3115: $i] :
( ~ ( in @ SY3115 @ SV286 )
| ( in @ SY3115 @ ( powerset @ ( setunion @ SV286 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1249,plain,
! [SV287: $i] :
( ( ~ ( iskpair @ SV287 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SV287 )
@ ^ [SY3116: $i] :
( SV287
= ( kpair @ ( kfst @ SV287 ) @ SY3116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1250,plain,
! [SV288: $i > $o] :
( ( ~ ~ ! [SY3117: $i] :
~ ~ ( ~ ( SV288 @ SY3117 )
| ~ ! [SY3118: $i] :
( ~ ( SV288 @ SY3118 )
| ( SY3117 = SY3118 ) ) )
| ! [SY3119: $i,SY3120: $i] :
( ~ ( SV288 @ SY3119 )
| ~ ( SV288 @ SY3120 )
| ( SY3119 = SY3120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1251,plain,
! [SV289: $i] :
( ( ! [SY3121: $i > $o] :
( ~ ~ ~ ! [SY3122: $i] :
~ ~ ( ~ ( in @ SY3122 @ SV289 )
| ~ ( SY3121 @ SY3122 ) )
| ! [SY3123: $i] :
( ~ ( in @ SY3123 @ SV289 )
| ~ ( SY3121 @ SY3123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1252,plain,
! [SV290: $i] :
( ( ! [SY3124: $i] :
( ~ ( in @ SY3124 @ ( powerset @ SV290 ) )
| ( subset @ ( setminus @ SV290 @ ( setminus @ SV290 @ SY3124 ) ) @ SY3124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1253,plain,
! [SV291: $i] :
( ( ! [SY3125: $i > $o,SY3126: $i] :
( ~ ( in @ SY3126 @ SV291 )
| ~ ( SY3125 @ SY3126 )
| ( in @ SY3126
@ ( dsetconstr @ SV291
@ ^ [SX3: $i] : ( SY3125 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1254,plain,
! [SV292: $i] :
( ( ! [SY3128: $i] :
( ~ ( breln1 @ SV292 @ SY3128 )
| ! [SY3129: $i] :
( ~ ( breln1 @ SV292 @ SY3129 )
| ( breln1 @ SV292 @ ( binunion @ SY3128 @ SY3129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1255,plain,
! [SV293: $i] :
( ( ! [SY3130: $i,SY3131: $i > $i > $o,SY3132: $i] :
( ~ ( in @ SY3132 @ SV293 )
| ! [SY3133: $i] :
( ~ ( in @ SY3133 @ SY3130 )
| ~ ( SY3131 @ SY3132 @ SY3133 )
| ( in @ ( kpair @ SY3132 @ SY3133 )
@ ( dpsetconstr @ SV293 @ SY3130
@ ^ [SX5: $i,SX6: $i] : ( SY3131 @ SX5 @ SX6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1256,plain,
! [SV294: $i] :
( ( ~ ( singleton @ SV294 )
| ! [SY3136: $i] :
( ~ ( in @ SY3136 @ SV294 )
| ( ( setunion @ SV294 )
= SY3136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1257,plain,
! [SV295: $i] :
( ( ! [SY3137: $i] :
( ~ ( in @ SV295 @ ( setadjoin @ SY3137 @ emptyset ) )
| ( in @ SY3137 @ ( setadjoin @ SV295 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1258,plain,
! [SV296: $i] :
( ( ! [SY3138: $i] :
( ~ ~ ( subset @ SV296 @ SY3138 )
| ( SV296 != SY3138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1259,plain,
! [SV297: $i] :
( ( ! [SY3139: $i] :
( ~ ( breln1 @ SV297 @ SY3139 )
| ! [SY3140: $i] :
( ~ ( breln1 @ SV297 @ SY3140 )
| ( ( binunion @ SY3139 @ SY3140 )
= ( binunion @ SY3140 @ SY3139 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1260,plain,
! [SV298: $i] :
( ( ! [SY3141: $i,SY3142: $i,SY3143: $o] :
( ~ ( in @ SY3142 @ ( binunion @ SV298 @ SY3141 ) )
| ~ ( ~ ( in @ SY3142 @ SV298 )
| SY3143 )
| ~ ( ~ ( in @ SY3142 @ SY3141 )
| SY3143 )
| SY3143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1261,plain,
! [SV299: $i] :
( ( ! [SY3144: $i] :
( ~ ( in @ SY3144 @ ( powerset @ SV299 ) )
| ! [SY3145: $i] :
( ~ ( in @ SY3145 @ ( powerset @ SV299 ) )
| ~ ! [SY3146: $i] :
( ~ ( in @ SY3146 @ SV299 )
| ~ ( in @ SY3146 @ SY3144 )
| ( in @ SY3146 @ SY3145 ) )
| ~ ! [SY3147: $i] :
( ~ ( in @ SY3147 @ SV299 )
| ~ ( in @ SY3147 @ SY3145 )
| ( in @ SY3147 @ SY3144 ) )
| ( SY3144 = SY3145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1262,plain,
! [SV300: $i] :
( ( ! [SY3148: $i] :
( ~ ( breln1 @ SV300 @ SY3148 )
| ! [SY3149: $i] :
( ~ ( breln1 @ SV300 @ SY3149 )
| ! [SY3150: $i] :
( ~ ( in @ SY3150 @ SV300 )
| ! [SY3151: $i] :
( ~ ( in @ SY3151 @ SV300 )
| ~ ( in @ ( kpair @ SY3150 @ SY3151 ) @ SY3148 )
| ( in @ ( kpair @ SY3150 @ SY3151 ) @ ( binunion @ SY3148 @ SY3149 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1263,plain,
! [SV301: $i] :
( ( ! [SY3152: $i,SY3153: $i] :
( ~ ( func @ SV301 @ SY3152 @ SY3153 )
| ! [SY3154: $i] :
( ~ ( func @ SV301 @ SY3152 @ SY3154 )
| ~ ! [SY3155: $i] :
( ~ ( in @ SY3155 @ SV301 )
| ( ( ap @ SV301 @ SY3152 @ SY3153 @ SY3155 )
= ( ap @ SV301 @ SY3152 @ SY3154 @ SY3155 ) ) )
| ! [SY3156: $i] :
( ~ ( in @ SY3156 @ SV301 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY3152 )
| ~ ( in @ ( kpair @ SY3156 @ SX5 ) @ SY3154 )
| ( in @ ( kpair @ SY3156 @ SX5 ) @ SY3153 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1264,plain,
! [SV302: $i] :
( ( ! [SY3158: $i] :
( ~ ( in @ SY3158 @ ( powerset @ SV302 ) )
| ! [SY3159: $i] :
( ~ ( in @ SY3159 @ ( powerset @ SV302 ) )
| ! [SY3160: $i] :
( ~ ( in @ SY3160 @ SV302 )
| ~ ( in @ SY3160 @ ( binunion @ ( setminus @ SV302 @ SY3158 ) @ ( setminus @ SV302 @ SY3159 ) ) )
| ( in @ SY3160 @ ( setminus @ SV302 @ ( binintersect @ SY3158 @ SY3159 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1265,plain,
! [SV303: $i] :
( ( ~ ( in @ SV303 @ emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1266,plain,
! [SV304: $i] :
( ( ! [SY3161: $i] :
( ~ ( in @ SY3161 @ ( powerset @ SV304 ) )
| ( SY3161
= ( setminus @ SV304 @ ( setminus @ SV304 @ SY3161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1267,plain,
! [SV305: $i] :
( ( ! [SY3162: $i] :
( ~ ( in @ SY3162 @ ( powerset @ SV305 ) )
| ! [SY3163: $i] :
( ~ ( in @ SY3163 @ ( powerset @ SV305 ) )
| ! [SY3164: $i] :
( ~ ( in @ SY3164 @ ( powerset @ SV305 ) )
| ( in @ ( binintersect @ SY3162 @ SY3163 ) @ ( powerset @ ( binintersect @ ( binunion @ SY3162 @ SY3164 ) @ ( binunion @ SY3163 @ SY3164 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1268,plain,
! [SV306: $i] :
( ( ~ ! [SY3165: $i] :
~ ( in @ SY3165 @ SV306 )
| ( SV306 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1269,plain,
! [SV307: $i] :
( ( ! [SY3166: $i] :
( ~ ( in @ SY3166 @ ( powerset @ SV307 ) )
| ! [SY3167: $i] :
( ~ ( in @ SY3167 @ ( powerset @ SV307 ) )
| ! [SY3168: $i] :
( ~ ( in @ SY3168 @ SV307 )
| ~ ( in @ SY3168 @ ( binintersect @ ( setminus @ SV307 @ SY3166 ) @ ( setminus @ SV307 @ SY3167 ) ) )
| ( in @ SY3168 @ ( setminus @ SV307 @ ( binunion @ SY3166 @ SY3167 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1270,plain,
! [SV308: $i] :
( ( ! [SY3169: $i] :
( ~ ( in @ SY3169 @ ( powerset @ SV308 ) )
| ! [SY3170: $i] :
( ~ ( in @ SY3170 @ ( powerset @ SV308 ) )
| ~ ! [SY3171: $i] :
( ~ ( in @ SY3171 @ SV308 )
| ~ ( in @ SY3171 @ SY3169 )
| ( in @ SY3171 @ SY3170 ) )
| ( in @ SY3169 @ ( powerset @ SY3170 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1271,plain,
! [SV309: $i] :
( ( ! [SY3172: $i] :
( ~ ( in @ SY3172 @ ( powerset @ SV309 ) )
| ! [SY3173: $i] :
( ~ ( in @ SY3173 @ ( powerset @ SV309 ) )
| ! [SY3174: $i] :
( ~ ( in @ SY3174 @ SV309 )
| ~ ( in @ SY3174 @ ( setminus @ SV309 @ SY3172 ) )
| ~ ( in @ SY3174 @ ( setminus @ SV309 @ SY3173 ) )
| ( in @ SY3174 @ ( setminus @ SV309 @ ( binunion @ SY3172 @ SY3173 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1272,plain,
! [SV310: $i] :
( ( ! [SY3175: $i] :
( ~ ( in @ SY3175 @ ( powerset @ SV310 ) )
| ( in @ ( setminus @ SV310 @ SY3175 ) @ ( powerset @ SV310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1273,plain,
! [SV311: $i] :
( ( ! [SY3176: $i] :
( ~ ( ( SV311 != SY3176 ) )
| ~ ( in @ SY3176 @ ( setadjoin @ SV311 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1274,plain,
! [SV312: $i] :
( ( ! [SY3177: $i,SY3178: $i] :
( ~ ( in @ SY3178 @ SY3177 )
| ( in @ SY3178 @ ( binunion @ SV312 @ SY3177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1275,plain,
! [SV313: $i] :
( ( ! [SY3179: $i,SY3180: $i] :
( ~ ( in @ SY3180 @ SV313 )
| ! [SY3181: $i] :
( ~ ( in @ SY3181 @ SY3179 )
| ( in @ ( setadjoin @ SY3180 @ ( setadjoin @ SY3181 @ emptyset ) ) @ ( powerset @ ( binunion @ SV313 @ SY3179 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1276,plain,
! [SV314: $i] :
( ( ! [SY3182: $i,SY3183: $i] :
( ~ ( in @ SY3183 @ SV314 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3182 )
| ( ( ksnd @ ( kpair @ SY3183 @ SX3 ) )
= SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1277,plain,
! [SV315: $i] :
( ( ! [SY3185: $i] :
( ~ ( in @ SY3185 @ ( powerset @ SV315 ) )
| ! [SY3186: $i] :
( ~ ( in @ SY3186 @ ( powerset @ SV315 ) )
| ! [SY3187: $i] :
( ~ ( in @ SY3187 @ SV315 )
| ~ ( in @ SY3187 @ ( setminus @ SV315 @ ( binunion @ SY3185 @ SY3186 ) ) )
| ~ ( in @ SY3187 @ SY3185 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1278,plain,
! [SV316: $i > $o] :
( ( ~ ~ ! [SY3188: $i] :
~ ~ ( ~ ( SV316 @ SY3188 )
| ~ ! [SY3189: $i] :
( ~ ( SV316 @ SY3189 )
| ( SY3188 = SY3189 ) ) )
| ~ ! [SY3190: $i] :
~ ! [SY3191: $i] :
~ ( ~ ( ~ ( SV316 @ SY3191 )
| ( SY3191 = SY3190 ) )
| ~ ( ( SY3191 != SY3190 )
| ( SV316 @ SY3191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1279,plain,
! [SV317: $i] :
( ( ! [SY3192: $i] :
( ~ ( in @ SY3192 @ ( powerset @ SV317 ) )
| ! [SY3193: $i] :
( ~ ( in @ SY3193 @ ( powerset @ SV317 ) )
| ! [SY3194: $i] :
( ~ ( in @ SY3194 @ ( powerset @ SV317 ) )
| ! [SY3195: $i] :
( ~ ( in @ SY3195 @ ( powerset @ SV317 ) )
| ~ ( subset @ SY3192 @ SY3194 )
| ~ ( subset @ SY3193 @ SY3195 )
| ( subset @ ( binintersect @ SY3192 @ SY3193 ) @ ( binintersect @ SY3194 @ SY3195 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1280,plain,
! [SV318: $i] :
( ( ! [SY3196: $i] :
( ~ ( in @ SY3196 @ ( powerset @ SV318 ) )
| ! [SY3197: $i] :
( ~ ( in @ SY3197 @ ( powerset @ SV318 ) )
| ! [SY3198: $i] :
( ~ ( in @ SY3198 @ SV318 )
| ~ ~ ( in @ SY3198 @ SY3197 )
| ~ ( in @ SY3198 @ ( binintersect @ SY3196 @ SY3197 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1281,plain,
! [SV319: $i] :
( ( ! [SY3199: $i,SY3200: $i] :
( ~ ( breln @ SV319 @ SY3199 @ SY3200 )
| ! [SY3201: $i > $o] :
( ~ ! [SY3202: $i] :
( ~ ( in @ SY3202 @ SV319 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY3199 )
| ~ ( in @ ( kpair @ SY3202 @ SX5 ) @ SY3200 )
| ( SY3201 @ ( kpair @ SY3202 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3200 )
| ( SY3201 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1282,plain,
! [SV320: $i] :
( ( ! [SY3205: $i] :
( ~ ! [SY3206: $i] :
( ~ ( in @ SY3206 @ SV320 )
| ( in @ SY3206 @ SY3205 ) )
| ( subset @ SV320 @ SY3205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1283,plain,
! [SV321: $i] :
( ( ! [SY3207: $o,SY3208: $i] :
( ~ ( in @ SY3208 @ SV321 )
| ! [SY3209: $i] :
( ~ ( in @ SY3209 @ SV321 )
| ~ ~ SY3207
| ( ( if @ SV321 @ SY3207 @ SY3208 @ SY3209 )
= SY3209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1284,plain,
! [SV322: $i] :
( ( ~ ~ ! [SY3210: $i] :
~ ( in @ SY3210 @ SV322 )
| ~ ! [SY3211: $i] :
~ ~ ( ~ ( in @ SY3211 @ SV322 )
| ~ ~ ~ ! [SY3212: $i] :
~ ~ ( ~ ( in @ SY3212 @ SY3211 )
| ~ ( in @ SY3212 @ SV322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1285,plain,
! [SV323: $i] :
( ( ! [SY3213: $i,SY3214: $i,SY3215: $i] :
( ~ ( in @ ( kpair @ SY3214 @ SY3215 ) @ ( cartprod @ SV323 @ SY3213 ) )
| ( in @ SY3214 @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1286,plain,
! [SV324: $i] :
( ( ! [SY3216: $i] :
( ~ ! [SY3217: $i] :
( ~ ( in @ SY3217 @ SV324 )
| ( in @ SY3217 @ SY3216 ) )
| ( subset @ SV324 @ SY3216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1287,plain,
! [SV325: $i] :
( ( ! [SY3218: $i] :
( ~ ( in @ SY3218 @ ( powerset @ SV325 ) )
| ! [SY3219: $i] :
( ~ ( in @ SY3219 @ ( powerset @ SV325 ) )
| ! [SY3220: $i] :
( ~ ( in @ SY3220 @ ( powerset @ SV325 ) )
| ~ ( subset @ SY3218 @ SY3219 )
| ~ ( subset @ SY3218 @ SY3220 )
| ( subset @ SY3218 @ ( binintersect @ SY3219 @ SY3220 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1288,plain,
! [SV1: $i] :
( ( in @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(1289,plain,
! [SV326: $i > $i > $o,SV2: $i] :
( ( breln1 @ SV2
@ ( dpsetconstr @ SV2 @ SV2
@ ^ [SY3221: $i,SY3222: $i] : ( SV326 @ SY3221 @ SY3222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1290,plain,
! [SV327: $i,SV3: $i] :
( ( ! [SY3223: $i > $i > $o] :
( breln @ SV3 @ SV327
@ ( dpsetconstr @ SV3 @ SV327
@ ^ [Xx: $i,Xy: $i] : ( SY3223 @ Xx @ Xy ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1291,plain,
! [SV328: $i,SV4: $i] :
( ( ! [SY3226: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV4 @ SV328
@ ^ [Xx: $i,Xy: $i] : ( SY3226 @ Xx @ Xy ) )
@ ( cartprod @ SV4 @ SV328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1292,plain,
! [SV329: $i,SV5: $i] :
( ( ( ksnd @ ( kpair @ SV5 @ SV329 ) )
= SV329 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1293,plain,
! [SV330: $i,SV6: $i] :
( ( ( kfst @ ( kpair @ SV6 @ SV330 ) )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1294,plain,
! [SV331: $i,SV10: $i] :
( ( iskpair @ ( kpair @ SV10 @ SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1295,plain,
! [SV332: $i,SV11: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ SV11 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV11 @ ( setadjoin @ SV332 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1296,plain,
! [SV12: $i,SV333: $i] :
( ( in @ SV333 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV12 @ ( setadjoin @ SV333 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1297,plain,
! [SV334: $i,SV13: $i] :
( ( in @ SV13 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV13 @ ( setadjoin @ SV334 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1298,plain,
! [SV14: $i,SV335: $i] :
( ( in @ SV335 @ ( setadjoin @ SV14 @ ( setadjoin @ SV335 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1299,plain,
! [SV336: $i,SV15: $i] :
( ( subset @ ( setminus @ SV15 @ SV336 ) @ SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1300,plain,
! [SV337: $i,SV16: $i] :
( ( ! [SY3229: $i] :
( ( binintersect @ SV16 @ ( binunion @ SV337 @ SY3229 ) )
= ( binunion @ ( binintersect @ SV16 @ SV337 ) @ ( binintersect @ SV16 @ SY3229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1301,plain,
! [SV338: $i,SV17: $i] :
( ( subset @ ( binintersect @ SV17 @ SV338 ) @ SV338 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1302,plain,
! [SV339: $i,SV18: $i] :
( ( subset @ ( binintersect @ SV18 @ SV339 ) @ SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1303,plain,
! [SV19: $i,SV340: $i] :
( ( subset @ SV340 @ ( binunion @ SV19 @ SV340 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1304,plain,
! [SV341: $i,SV20: $i] :
( ( subset @ SV20 @ ( binunion @ SV20 @ SV341 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1305,plain,
! [SV21: $i,SV342: $i] :
( ( in @ SV342 @ ( setadjoin @ SV21 @ ( setadjoin @ SV342 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1306,plain,
! [SV343: $i > $o,SV22: $i] :
( ( subset
@ ( dsetconstr @ SV22
@ ^ [SY3230: $i] : ( SV343 @ SY3230 ) )
@ SV22 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1307,plain,
! [SV344: $i > $o,SV23: $i] :
( ( in
@ ( dsetconstr @ SV23
@ ^ [SY3231: $i] : ( SV344 @ SY3231 ) )
@ ( powerset @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1308,plain,
! [SV25: $i,SV345: $i] :
( ( subset @ SV345 @ ( setadjoin @ SV25 @ SV345 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1309,plain,
! [SV28: $i,SV346: $i] :
( ( in @ SV346 @ ( setadjoin @ SV28 @ ( setadjoin @ SV346 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1310,plain,
! [SV347: $i,SV29: $i] :
( ( in @ SV29 @ ( setadjoin @ SV29 @ ( setadjoin @ SV347 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1311,plain,
! [SV348: $i,SV33: $i] :
( ( in @ SV33 @ ( setadjoin @ SV33 @ SV348 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1312,plain,
! [SV34: $i] :
( ( in @ SV34 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1313,plain,
! [SV35: $i] :
( ( in @ SV35 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1314,plain,
! [SV349: $i,SV36: $i] :
( ( ~ ( in @ SV36 @ ( setadjoin @ SV349 @ emptyset ) )
| ( SV36 = SV349 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1315,plain,
! [SV37: $i] :
( ( ( ~ ( ( SV37 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY2402: $i] :
~ ~ ( ~ ( in @ SY2402 @ SV37 )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[992]) ).
thf(1316,plain,
! [SV38: $i] :
( ( ( ~ ( in @ SV38 @ omega ) )
= $true )
| ( ( ! [SY2403: $i] :
( ~ ( in @ SY2403 @ omega )
| ( ( omegaS @ SV38 )
!= ( omegaS @ SY2403 ) )
| ( SV38 = SY2403 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1317,plain,
! [SV350: $i,SV39: $i] :
( ( ! [SY3232: $i > $i] :
( ~ ! [SY3233: $i] :
( ~ ( in @ SY3233 @ SV39 )
| ( in @ ( SY3232 @ SY3233 ) @ SV350 ) )
| ( func @ SV39 @ SV350
@ ( dpsetconstr @ SV39 @ SV350
@ ^ [SX3: $i,SX4: $i] :
( ( SY3232 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1318,plain,
! [SV40: $i > $o] :
( ( ( ~ ~ ! [SY2409: $i] :
~ ~ ( ~ ( SV40 @ SY2409 )
| ~ ! [SY2410: $i] :
( ~ ( SV40 @ SY2410 )
| ( SY2409 = SY2410 ) ) ) )
= $true )
| ( ( ~ ! [SY2411: $i] :
~ ( SV40 @ SY2411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[995]) ).
thf(1319,plain,
! [SV351: $i,SV41: $i] :
( ( ! [SY3236: $i] :
( ~ ( in @ SY3236 @ SV41 )
| ! [SY3237: $i] :
( ~ ( in @ SY3237 @ SV351 )
| ( ( kpair @ SY3236 @ SY3237 )
= ( kpair @ SY3236 @ SY3237 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1320,plain,
! [SV42: $i > $o] :
( ( ( ~ ~ ! [SY2415: $i] :
~ ~ ( ~ ( SV42 @ SY2415 )
| ~ ! [SY2416: $i] :
( ~ ( SV42 @ SY2416 )
| ( SY2415 = SY2416 ) ) ) )
= $true )
| ( ( SV42
@ ( descr
@ ^ [SY2417: $i] : ( SV42 @ SY2417 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1321,plain,
! [SV352: $i,SV43: $i] :
( ( ( SV43 != SV352 )
| ( ( powerset @ SV43 )
= ( powerset @ SV352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1322,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ~ ! [SY3238: $i] :
( ~ ( in @ SY3238 @ SV44 )
| ! [SY3239: $i] :
( ~ ( in @ SY3239 @ SV44 )
| ~ ( SV353 @ SY3238 )
| ~ ( SV353 @ SY3239 )
| ( SY3238 = SY3239 ) ) )
| ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) )
| ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1323,plain,
! [SV354: $i,SV45: $i] :
( ( ! [SY3242: $i] :
( ~ ( in @ SY3242 @ ( funcSet @ SV45 @ SV354 ) )
| ! [SY3243: $i] :
( ~ ( in @ SY3243 @ ( funcSet @ SV45 @ SV354 ) )
| ~ ! [SY3244: $i] :
( ~ ( in @ SY3244 @ SV45 )
| ( ( ap @ SV45 @ SV354 @ SY3242 @ SY3244 )
= ( ap @ SV45 @ SV354 @ SY3243 @ SY3244 ) ) )
| ( SY3242 = SY3243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1324,plain,
! [SV355: $i,SV46: $i] :
( ( ! [SY3245: $i] :
( ~ ( in @ SY3245 @ SV46 )
| ( in @ ( setadjoin @ SY3245 @ emptyset ) @ ( powerset @ ( binunion @ SV46 @ SV355 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1325,plain,
! [SV356: $i,SV47: $i] :
( ( ! [SY3246: $i] :
( ~ ( in @ SY3246 @ ( funcSet @ SV47 @ SV356 ) )
| ! [SY3247: $i] :
( ~ ( in @ SY3247 @ SV47 )
| ( in @ ( kpair @ SY3247 @ ( ap @ SV47 @ SV356 @ SY3246 @ SY3247 ) ) @ SY3246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1326,plain,
! [SV357: $i,SV48: $i] :
( ( ! [SY3248: $i,SY3249: $i] :
( ( ( setadjoin @ ( setadjoin @ SV48 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV48 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY3248 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3248 @ ( setadjoin @ SY3249 @ emptyset ) ) @ emptyset ) ) )
| ( SV357 = SY3249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1327,plain,
! [SV358: $i,SV49: $i] :
( ( ! [SY3250: $i] :
( ~ ( in @ SY3250 @ ( funcSet @ SV49 @ SV358 ) )
| ! [SY3251: $i] :
( ~ ( in @ SY3251 @ SV49 )
| ( in @ ( ap @ SV49 @ SV358 @ SY3250 @ SY3251 ) @ SV358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1328,plain,
! [SV359: $i,SV50: $i] :
( ( ( SV50 != SV359 )
| ! [SY3252: $i,SY3253: $i] :
( ( SY3252 != SY3253 )
| ( ( setadjoin @ SV50 @ SY3252 )
= ( setadjoin @ SV359 @ SY3253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1329,plain,
! [SV360: $i,SV51: $i] :
( ( ! [SY3254: $i] :
( ~ ( in @ SY3254 @ ( funcSet @ SV51 @ SV360 ) )
| ( func @ SV51 @ SV360 @ SY3254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1330,plain,
! [SV52: $i,SV361: $i] :
( ( ~ ( in @ SV361 @ ( powerset @ SV52 ) )
| ! [SY3255: $i] :
( ~ ( in @ SY3255 @ ( powerset @ SV52 ) )
| ! [SY3256: $i] :
( ~ ( in @ SY3256 @ ( powerset @ SV52 ) )
| ! [SY3257: $i] :
( ~ ( in @ SY3257 @ SV52 )
| ~ ( in @ SY3257 @ ( binintersect @ SV361 @ SY3255 ) )
| ( in @ SY3257 @ ( binunion @ SY3255 @ SY3256 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1331,plain,
! [SV53: $i,SV362: $i] :
( ( ~ ( subset @ SV362 @ SV53 )
| ( ( binintersect @ SV53 @ SV362 )
= SV362 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1332,plain,
! [SV363: $i,SV54: $i] :
( ( ! [SY3258: $i > $i] :
( ~ ! [SY3259: $i] :
( ~ ( in @ SY3259 @ SV54 )
| ( in @ ( SY3258 @ SY3259 ) @ SV363 ) )
| ( in
@ ( lam @ SV54 @ SV363
@ ^ [SX3: $i] : ( SY3258 @ SX3 ) )
@ ( funcSet @ SV54 @ SV363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1333,plain,
! [SV55: $i,SV364: $i] :
( ( ~ ( in @ SV364 @ ( powerset @ SV55 ) )
| ! [SY3261: $i] :
( ~ ( in @ SY3261 @ ( powerset @ SV55 ) )
| ~ ( subset @ SV364 @ ( setminus @ SV55 @ SY3261 ) )
| ( subset @ SY3261 @ ( setminus @ SV55 @ SV364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1334,plain,
! [SV56: $i,SV365: $i] :
( ( ~ ( in @ SV365 @ ( powerset @ SV56 ) )
| ! [SY3262: $i] :
( ~ ( in @ SY3262 @ ( powerset @ SV56 ) )
| ! [SY3263: $i] :
( ~ ( in @ SY3263 @ ( powerset @ SV56 ) )
| ! [SY3264: $i] :
( ~ ( in @ SY3264 @ ( powerset @ SV56 ) )
| ( ( setminus @ SV56 @ ( binintersect @ ( binunion @ SV365 @ SY3262 ) @ ( binunion @ SY3263 @ SY3264 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV56 @ SV365 ) @ ( setminus @ SV56 @ SY3262 ) ) @ ( binintersect @ ( setminus @ SV56 @ SY3263 ) @ ( setminus @ SV56 @ SY3264 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1335,plain,
! [SV57: $i,SV366: $i] :
( ( ~ ( ~ ( ~ ( in @ SV366 @ ( setunion @ SV57 ) )
| ~ ! [SY3265: $i] :
~ ~ ( ~ ( in @ SV366 @ SY3265 )
| ~ ( in @ SY3265 @ SV57 ) ) )
| ~ ( ~ ~ ! [SY3266: $i] :
~ ~ ( ~ ( in @ SV366 @ SY3266 )
| ~ ( in @ SY3266 @ SV57 ) )
| ( in @ SV366 @ ( setunion @ SV57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1336,plain,
! [SV58: $i > $o] :
( ( ( ~ ~ ! [SY2462: $i] :
~ ~ ( ~ ( SV58 @ SY2462 )
| ~ ! [SY2463: $i] :
( ~ ( SV58 @ SY2463 )
| ( SY2462 = SY2463 ) ) ) )
= $true )
| ( ( ! [SY2464: $i,SY2465: $i] :
( ~ ( SV58 @ SY2464 )
| ~ ( SV58 @ SY2465 )
| ( SY2464 = SY2465 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1337,plain,
! [SV59: $i > $o] :
( ( ( ~ ~ ! [SY2466: $i] :
~ ! [SY2467: $i] :
~ ( ~ ( ~ ( SV59 @ SY2467 )
| ( SY2467 = SY2466 ) )
| ~ ( ( SY2467 != SY2466 )
| ( SV59 @ SY2467 ) ) ) )
= $true )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1338,plain,
! [SV60: $i > $o] :
( ( ( ~ ~ ! [SY2470: $i] :
~ ~ ( ~ ( SV60 @ SY2470 )
| ~ ! [SY2471: $i] :
( ~ ( SV60 @ SY2471 )
| ( SY2470 = SY2471 ) ) ) )
= $true )
| ( ( ~ ! [SY2472: $i] :
~ ~ ( ~ ( SV60 @ SY2472 )
| ~ ! [SY2473: $i] :
( ~ ( SV60 @ SY2473 )
| ( SY2472 = SY2473 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1339,plain,
! [SV367: $i > $o,SV61: $i] :
( ( ~ ~ ! [SY3267: $i] :
( ~ ( in @ SY3267 @ SV61 )
| ( SV367 @ SY3267 ) )
| ~ ! [SY3268: $i] :
~ ~ ( ~ ( in @ SY3268 @ SV61 )
| ~ ~ ( SV367 @ SY3268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1340,plain,
! [SV62: $i > $o,SV368: $i] :
( ( ~ ( in @ SV368 @ emptyset )
| ( SV62 @ SV368 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1341,plain,
! [SV369: $i,SV63: $i] :
( ( ! [SY3269: $i] :
( ~ ( func @ SV63 @ SV369 @ SY3269 )
| ! [SY3270: $i] :
( ~ ( in @ SY3270 @ SV63 )
| ( in @ ( ap @ SV63 @ SV369 @ SY3269 @ SY3270 ) @ SV369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1342,plain,
! [SV370: $i,SV64: $i] :
( ( ! [SY3271: $i > $i] :
( ~ ! [SY3272: $i] :
( ~ ( in @ SY3272 @ SV64 )
| ( in @ ( SY3271 @ SY3272 ) @ SV370 ) )
| ( ( lam @ SV64 @ SV370
@ ^ [SX3: $i] : ( SY3271 @ SX3 ) )
= ( lam @ SV64 @ SV370
@ ^ [SX3: $i] : ( SY3271 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1343,plain,
! [SV371: $i,SV65: $i] :
( ( ~ ! [SY3275: $i] :
~ ( ~ ( ~ ( in @ SY3275 @ SV65 )
| ( in @ SY3275 @ SV371 ) )
| ~ ( ~ ( in @ SY3275 @ SV371 )
| ( in @ SY3275 @ SV65 ) ) )
| ( SV65 = SV371 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1344,plain,
! [SV66: $i] :
( ( ( ~ ( in @ SV66 @ emptyset ) )
= $true )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1021]) ).
thf(1345,plain,
! [SV67: $i] :
( ( ( ~ ( subset @ SV67 @ emptyset ) )
= $true )
| ( ( SV67 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1022]) ).
thf(1346,plain,
! [SV68: $i,SV372: $i] :
( ( ~ ( in @ SV372 @ ( powerset @ SV68 ) )
| ! [SY3276: $i] :
( ~ ( in @ SY3276 @ ( powerset @ SV68 ) )
| ~ ( subset @ SV372 @ ( setminus @ SV68 @ SY3276 ) )
| ! [SY3277: $i] :
( ~ ( in @ SY3277 @ SV68 )
| ~ ( in @ SY3277 @ SY3276 )
| ( in @ SY3277 @ ( setminus @ SV68 @ SV372 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1347,plain,
! [SV69: $i,SV373: $i] :
( ( ~ ( in @ SV373 @ ( powerset @ SV69 ) )
| ! [SY3278: $i] :
( ~ ( in @ SY3278 @ ( powerset @ SV69 ) )
| ! [SY3279: $i] :
( ~ ( in @ SY3279 @ SV69 )
| ~ ( in @ SY3279 @ ( setminus @ SV69 @ ( binintersect @ SV373 @ SY3278 ) ) )
| ( in @ SY3279 @ ( binunion @ ( setminus @ SV69 @ SV373 ) @ ( setminus @ SV69 @ SY3278 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1348,plain,
! [SV374: $i,SV70: $i] :
( ( ( SV70 != SV374 )
| ( in @ SV70 @ ( setadjoin @ SV374 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1349,plain,
! [SV71: $i,SV375: $i] :
( ( ~ ( in @ SV375 @ ( powerset @ SV71 ) )
| ! [SY3280: $i] :
( ~ ( in @ SY3280 @ ( powerset @ SV71 ) )
| ( in @ ( binunion @ SV375 @ SY3280 ) @ ( powerset @ SV71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1350,plain,
! [SV376: $i,SV72: $i] :
( ( ! [SY3281: $i] :
( ~ ( in @ SY3281 @ ( setadjoin @ SV72 @ SV376 ) )
| ! [SY3282: $o] :
( ~ ( ( SY3281 != SV72 )
| SY3282 )
| ~ ( ~ ( in @ SY3281 @ SV376 )
| SY3282 )
| SY3282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1351,plain,
! [SV377: $i,SV73: $i] :
( ( ~ ( breln1 @ SV73 @ SV377 )
| ! [SY3283: $i] :
( ~ ( breln1 @ SV73 @ SY3283 )
| ( breln1 @ SV73 @ ( breln1compset @ SV73 @ SV377 @ SY3283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1352,plain,
! [SV378: $i,SV74: $i] :
( ( ~ ( breln1 @ SV74 @ SV378 )
| ( SV378
= ( breln1invset @ SV74 @ ( breln1invset @ SV74 @ SV378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1353,plain,
! [SV75: $i,SV379: $i] :
( ( ~ ( in @ SV379 @ ( powerset @ SV75 ) )
| ! [SY3284: $i] :
( ~ ( in @ SY3284 @ ( powerset @ SV75 ) )
| ! [SY3285: $i] :
( ~ ( in @ SY3285 @ SV75 )
| ~ ( in @ SY3285 @ ( setminus @ SV75 @ ( binunion @ SV379 @ SY3284 ) ) )
| ( in @ SY3285 @ ( setminus @ SV75 @ SY3284 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1354,plain,
! [SV380: $i > $i,SV76: $i] :
( ( ! [SY3286: $i] :
~ ( ~ ( ~ ( in @ SY3286
@ ( image1 @ SV76
@ ^ [SY3287: $i] : ( SV380 @ SY3287 ) ) )
| ~ ! [SY3288: $i] :
~ ~ ( ~ ( in @ SY3288 @ SV76 )
| ( SY3286
!= ( SV380 @ SY3288 ) ) ) )
| ~ ( ~ ~ ! [SY3289: $i] :
~ ~ ( ~ ( in @ SY3289 @ SV76 )
| ( SY3286
!= ( SV380 @ SY3289 ) ) )
| ( in @ SY3286
@ ( image1 @ SV76
@ ^ [SY3290: $i] : ( SV380 @ SY3290 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1355,plain,
! [SV381: $i > $i,SV77: $i] :
( ( ! [SY3291: $i] :
( ~ ~ ! [SY3292: $i] :
~ ~ ( ~ ( in @ SY3292 @ SV77 )
| ( SY3291
!= ( SV381 @ SY3292 ) ) )
| ( in @ SY3291
@ ( image1 @ SV77
@ ^ [SY3293: $i] : ( SV381 @ SY3293 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1356,plain,
! [SV382: $i,SV78: $i] :
( ( ~ ( breln1 @ SV78 @ SV382 )
| ! [SY3294: $i] :
( ~ ( breln1 @ SV78 @ SY3294 )
| ! [SY3295: $i] :
( ~ ( in @ SY3295 @ SV78 )
| ! [SY3296: $i] :
( ~ ( in @ SY3296 @ SV78 )
| ~ ( in @ ( kpair @ SY3295 @ SY3296 ) @ ( breln1compset @ SV78 @ SV382 @ SY3294 ) )
| ~ ! [SY3297: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3297 @ SV78 )
| ~ ( in @ ( kpair @ SY3295 @ SY3297 ) @ SV382 ) )
| ~ ( in @ ( kpair @ SY3297 @ SY3296 ) @ SY3294 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1357,plain,
! [SV383: $i,SV79: $i] :
( ( ! [SY3298: $i] :
( ~ ( in @ SY3298 @ ( cartprod @ SV79 @ SV383 ) )
| ( in @ ( kfst @ SY3298 ) @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1358,plain,
! [SV384: $i,SV80: $i] :
( ( ! [SY3299: $i] :
~ ( ~ ( ~ ( in @ SY3299 @ ( setadjoin @ SV80 @ SV384 ) )
| ( SY3299 = SV80 )
| ( in @ SY3299 @ SV384 ) )
| ~ ( ~ ( ( SY3299 = SV80 )
| ( in @ SY3299 @ SV384 ) )
| ( in @ SY3299 @ ( setadjoin @ SV80 @ SV384 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1359,plain,
! [SV81: $i,SV385: $i] :
( ( ! [SY3300: $i] :
( ~ ( in @ SY3300 @ SV385 )
| ( in @ SY3300 @ ( setadjoin @ SV81 @ SV385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1360,plain,
! [SV386: $i,SV82: $i] :
( ( ~ ( breln1 @ SV82 @ SV386 )
| ! [SY3301: $i] :
( ~ ( breln1 @ SV82 @ SY3301 )
| ! [SY3302: $i] :
( ~ ( in @ SY3302 @ SV82 )
| ! [SY3303: $i] :
( ~ ( in @ SY3303 @ SV82 )
| ~ ( in @ ( kpair @ SY3302 @ SY3303 ) @ ( binunion @ SV386 @ SY3301 ) )
| ( in @ ( kpair @ SY3302 @ SY3303 ) @ SV386 )
| ( in @ ( kpair @ SY3302 @ SY3303 ) @ SY3301 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1361,plain,
! [SV83: $i,SV387: $i] :
( ( ~ ( subset @ SV387 @ SV83 )
| ( in @ SV387 @ ( powerset @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1362,plain,
! [SV84: $i] :
( ( ( ~ ( in @ SV84 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV84 @ SV84 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1039]) ).
thf(1363,plain,
! [SV85: $i,SV388: $i] :
( ( ~ ( in @ SV388 @ ( powerset @ SV85 ) )
| ! [SY3304: $i] :
( ~ ( in @ SY3304 @ ( powerset @ SV85 ) )
| ( ( setminus @ SV85 @ ( binintersect @ SV388 @ SY3304 ) )
= ( binunion @ ( setminus @ SV85 @ SV388 ) @ ( setminus @ SV85 @ SY3304 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1364,plain,
! [SV86: $i,SV389: $i] :
( ( ~ ( in @ SV389 @ ( powerset @ SV86 ) )
| ! [SY3305: $i] :
( ~ ( in @ SY3305 @ ( powerset @ SV86 ) )
| ! [SY3306: $i] :
( ~ ( in @ SY3306 @ SV86 )
| ~ ( subset @ SV389 @ ( setminus @ SV86 @ SY3305 ) )
| ~ ( in @ SY3306 @ SY3305 )
| ~ ( in @ SY3306 @ SV389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1365,plain,
! [SV87: $i,SV390: $i] :
( ( ~ ( in @ SV390 @ ( powerset @ SV87 ) )
| ! [SY3307: $i] :
( ~ ( in @ SY3307 @ ( powerset @ SV87 ) )
| ! [SY3308: $i] :
( ~ ( in @ SY3308 @ SV87 )
| ~ ( subset @ SV390 @ SY3307 )
| ~ ~ ( in @ SY3308 @ SY3307 )
| ~ ( in @ SY3308 @ SV390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1366,plain,
! [SV88: $i,SV391: $i] :
( ( ~ ( in @ SV391 @ ( powerset @ SV88 ) )
| ! [SY3309: $i] :
( ~ ( in @ SY3309 @ ( powerset @ SV88 ) )
| ( subset @ ( setminus @ SV88 @ SV391 ) @ ( setminus @ SV88 @ ( binintersect @ SV391 @ SY3309 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1367,plain,
! [SV89: $i,SV392: $i] :
( ( ~ ( in @ SV392 @ ( powerset @ SV89 ) )
| ( subset @ SV392 @ ( setminus @ SV89 @ ( setminus @ SV89 @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1368,plain,
! [SV90: $i,SV393: $i] :
( ( ~ ( in @ SV393 @ ( powerset @ SV90 ) )
| ! [SY3310: $i] :
( ~ ( in @ SY3310 @ ( powerset @ SV90 ) )
| ! [SY3311: $i] :
( ~ ( in @ SY3311 @ ( powerset @ SV90 ) )
| ! [SY3312: $i] :
( ~ ( in @ SY3312 @ SV90 )
| ~ ( in @ SY3312 @ ( binintersect @ SV393 @ SY3310 ) )
| ( in @ SY3312 @ ( binintersect @ ( binunion @ SV393 @ SY3311 ) @ ( binunion @ SY3310 @ SY3311 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1369,plain,
! [SV91: $o] :
( ( ( ~ SV91 ) = $true )
| ( ( in @ emptyset @ ( prop2set @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1046]) ).
thf(1370,plain,
( ( ( ~ $true ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1047]) ).
thf(1371,plain,
( ( ( ~ $false ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1372,plain,
! [SV394: $i,SV92: $i] :
( ( ! [SY3313: $i] :
( ~ ( in @ SY3313 @ SV92 )
| ~ ~ ( in @ SY3313 @ SV394 )
| ( in @ SY3313 @ ( setminus @ SV92 @ SV394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1373,plain,
! [SV93: $i,SV395: $i] :
( ( ~ ( in @ SV395 @ SV93 )
| ( in @ ( setadjoin @ SV395 @ emptyset ) @ ( powerset @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1374,plain,
! [SV94: $o] :
( ( ( ~ SV94 ) = $true )
| ( ( set2prop @ ( prop2set @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1375,plain,
( ( ( ~ $true ) = $true )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1052]) ).
thf(1376,plain,
( ( ( ~ $false ) = $true )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1377,plain,
! [SV396: $i,SV95: $i] :
( ( ! [SY3314: $i] :
( ~ ( in @ SY3314 @ ( funcSet @ SV95 @ SV396 ) )
| ! [SY3315: $i] :
( ~ ( in @ SY3315 @ SV95 )
| ( ( ap @ SV95 @ SV396 @ SY3314 @ SY3315 )
= ( ap @ SV95 @ SV396 @ SY3314 @ SY3315 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1378,plain,
! [SV397: $i,SV96: $i] :
( ( ! [SY3316: $i] :
( ~ ~ ( in @ SY3316 @ ( setminus @ SV96 @ SV397 ) )
| ~ ( in @ SY3316 @ SV96 )
| ( in @ SY3316 @ SV397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1379,plain,
! [SV398: $i,SV97: $i] :
( ( ! [SY3317: $i] :
( ~ ( in @ SY3317 @ ( cartprod @ SV97 @ SV398 ) )
| ( iskpair @ SY3317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1380,plain,
! [SV98: $i,SV399: $i] :
( ( ~ ( in @ SV399 @ ( powerset @ SV98 ) )
| ( in @ ( powerset @ SV399 ) @ ( powerset @ ( powerset @ SV98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1381,plain,
! [SV99: $i,SV400: $i] :
( ( ~ ( in @ SV400 @ ( powerset @ SV99 ) )
| ! [SY3318: $i] :
( ~ ( in @ SY3318 @ ( powerset @ SV99 ) )
| ! [SY3319: $i] :
( ~ ( in @ SY3319 @ SV99 )
| ~ ( in @ SY3319 @ ( setminus @ SV99 @ ( binunion @ SV400 @ SY3318 ) ) )
| ( in @ SY3319 @ ( setminus @ SV99 @ SV400 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1382,plain,
! [SV100: $i > $o] :
( ( ( ~ ~ ! [SY2562: $i] :
~ ( SV100 @ SY2562 ) )
= $true )
| ( ( ~ ! [SY2563: $i,SY2564: $i] :
( ~ ( SV100 @ SY2563 )
| ~ ( SV100 @ SY2564 )
| ( SY2563 = SY2564 ) )
| ~ ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1383,plain,
! [SV401: $i,SV101: $i] :
( ( ( ( setadjoin @ SV101 @ emptyset )
!= ( setadjoin @ SV401 @ emptyset ) )
| ( SV101 = SV401 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1384,plain,
! [SV402: $i,SV102: $i] :
( ( ! [SY3320: $i] :
( ~ ~ ( in @ SY3320 @ ( setminus @ SV102 @ SV402 ) )
| ~ ~ ( in @ SY3320 @ SV402 )
| ~ ( in @ SY3320 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1385,plain,
! [SV403: $i,SV103: $i] :
( ( ! [SY3321: $i] :
( ~ ( in @ SY3321 @ ( funcSet @ SV103 @ SV403 ) )
| ( ( lam @ SV103 @ SV403
@ ^ [SY3322: $i] : ( ap @ SV103 @ SV403 @ SY3321 @ SY3322 ) )
= SY3321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1386,plain,
! [SV404: $i > $o,SV104: $i] :
( ( ~ ~ ! [SY3323: $i] :
~ ~ ( ~ ( in @ SY3323 @ SV104 )
| ~ ~ ( SV404 @ SY3323 ) )
| ~ ! [SY3324: $i] :
( ~ ( in @ SY3324 @ SV104 )
| ( SV404 @ SY3324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1387,plain,
! [SV105: $i,SV405: $i] :
( ( ~ ( in @ SV405 @ ( funcSet @ SV105 @ ( powerset @ SV105 ) ) )
| ~ ( surjective @ SV105 @ ( powerset @ SV105 ) @ SV405 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1388,plain,
! [SV106: $i] :
( ( ( ~ ~ ( ~ ( in @ emptyset @ SV106 )
| ~ ! [SY2577: $i] :
( ~ ~ ( ~ ( in @ SY2577 @ omega )
| ~ ( in @ SY2577 @ SV106 ) )
| ( in @ ( setadjoin @ SY2577 @ SY2577 ) @ SV106 ) ) ) )
= $true )
| ( ( ! [SY2578: $i] :
( ~ ( in @ SY2578 @ omega )
| ( in @ SY2578 @ SV106 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1389,plain,
! [SV107: $i] :
( ( ( ~ ( iskpair @ SV107 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV107 )
@ ^ [SY2579: $i] : ( in @ ( setadjoin @ SY2579 @ emptyset ) @ SV107 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1390,plain,
! [SV406: $i,SV108: $i] :
( ( ! [SY3325: $i] :
( ~ ( func @ SV108 @ SV406 @ SY3325 )
| ! [SY3326: $i] :
( ~ ( in @ SY3326 @ SV108 )
| ( singleton
@ ( dsetconstr @ SV406
@ ^ [SX4: $i] : ( in @ ( kpair @ SY3326 @ SX4 ) @ SY3325 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1391,plain,
! [SV109: $i,SV407: $i] :
( ( ~ ( in @ SV407 @ ( powerset @ SV109 ) )
| ! [SY3328: $i] :
( ~ ( in @ SY3328 @ ( powerset @ SV109 ) )
| ~ ! [SY3329: $i] :
( ~ ( in @ SY3329 @ SV109 )
| ~ ( in @ SY3329 @ SV407 )
| ( in @ SY3329 @ SY3328 ) )
| ( subset @ SV407 @ SY3328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1392,plain,
! [SV110: $i,SV408: $i] :
( ( ~ ( in @ SV408 @ ( powerset @ SV110 ) )
| ! [SY3330: $i] :
( ~ ( in @ SY3330 @ ( powerset @ SV110 ) )
| ! [SY3331: $i] :
( ~ ( in @ SY3331 @ SV110 )
| ~ ~ ( in @ SY3331 @ SV408 )
| ~ ( in @ SY3331 @ ( binintersect @ SV408 @ SY3330 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1393,plain,
! [SV409: $i,SV111: $i] :
( ( ! [SY3332: $i] :
( ~ ( in @ SY3332 @ ( cartprod @ SV111 @ SV409 ) )
| ( in @ ( ksnd @ SY3332 ) @ SV409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1394,plain,
! [SV410: $i,SV112: $i] :
( ( ! [SY3333: $i] :
( ~ ( in @ SY3333 @ SV112 )
| ! [SY3334: $i] :
( ~ ( in @ SY3334 @ SV410 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY3333 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3333 @ ( setadjoin @ SY3334 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV112 @ SV410 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1395,plain,
! [SV113: $i,SV411: $i] :
( ( ~ ( in @ SV411 @ ( powerset @ SV113 ) )
| ! [SY3335: $i] :
( ~ ( in @ SY3335 @ ( powerset @ SV113 ) )
| ! [SY3336: $i] :
( ~ ( in @ SY3336 @ SV113 )
| ~ ( in @ SY3336 @ ( setminus @ SV113 @ SV411 ) )
| ( in @ SY3336 @ ( setminus @ SV113 @ ( binintersect @ SV411 @ SY3335 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1396,plain,
! [SV114: $i,SV412: $i] :
( ( ~ ( in @ SV412 @ ( powerset @ SV114 ) )
| ! [SY3337: $i] :
( ~ ( in @ SY3337 @ SV114 )
| ~ ( in @ SY3337 @ SV412 )
| ~ ( in @ SY3337 @ ( setminus @ SV114 @ SV412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1397,plain,
! [SV413: $i,SV115: $i] :
( ( ! [SY3338: $i > $i > $o,SY3339: $i,SY3340: $i] :
( ~ ( in @ ( kpair @ SY3339 @ SY3340 )
@ ( dpsetconstr @ SV115 @ SV413
@ ^ [SX5: $i,SX6: $i] : ( SY3338 @ SX5 @ SX6 ) ) )
| ( in @ SY3339 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1398,plain,
! [SV414: $i,SV116: $i] :
( ( ! [SY3343: $i > $i > $o,SY3344: $i,SY3345: $i] :
( ~ ( in @ ( kpair @ SY3344 @ SY3345 )
@ ( dpsetconstr @ SV116 @ SV414
@ ^ [SX5: $i,SX6: $i] : ( SY3343 @ SX5 @ SX6 ) ) )
| ( in @ SY3345 @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1399,plain,
! [SV415: $i,SV117: $i] :
( ( ! [SY3348: $i] :
( ~ ( in @ SY3348 @ ( setminus @ SV117 @ SV415 ) )
| ~ ( in @ SY3348 @ SV415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1400,plain,
! [SV416: $i > $o,SV118: $i] :
( ( ! [SY3349: $i] :
( ~ ( in @ SY3349 @ SV118 )
| ~ ( SV416 @ SY3349 )
| ~ ! [SY3350: $i] :
( ~ ( in @ SY3350 @ SV118 )
| ~ ( SV416 @ SY3350 )
| ( SY3350 = SY3349 ) )
| ( ex1 @ SV118
@ ^ [SY3351: $i] : ( SV416 @ SY3351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1401,plain,
! [SV417: $i,SV119: $i] :
( ( ( ( setminus @ SV119 @ SV417 )
!= emptyset )
| ( subset @ SV119 @ SV417 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1402,plain,
! [SV418: $i,SV120: $i] :
( ( ! [SY3352: $i] :
( ~ ~ ( in @ SY3352 @ SV120 )
| ~ ~ ( in @ SY3352 @ SV418 )
| ~ ( in @ SY3352 @ ( symdiff @ SV120 @ SV418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1403,plain,
! [SV419: $i,SV121: $i] :
( ( ! [SY3353: $i > $i] :
( ~ ! [SY3354: $i] :
( ~ ( in @ SY3354 @ SV121 )
| ( in @ ( SY3353 @ SY3354 ) @ SV419 ) )
| ! [SY3355: $i] :
( ~ ( in @ SY3355 @ SV121 )
| ( ( ap @ SV121 @ SV419
@ ( lam @ SV121 @ SV419
@ ^ [SX4: $i] : ( SY3353 @ SX4 ) )
@ SY3355 )
= ( SY3353 @ SY3355 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1404,plain,
! [SV420: $i,SV122: $i] :
( ( ( SV122 != SV420 )
| ! [SY3357: $i > $o,SY3358: $i > $o] :
( ~ ! [SY3359: $i] :
( ~ ( in @ SY3359 @ SV122 )
| ! [SY3360: $i] :
( ~ ( in @ SY3360 @ SV420 )
| ( SY3359 != SY3360 )
| ~ ( ~ ( ~ ( SY3357 @ SY3359 )
| ( SY3358 @ SY3360 ) )
| ~ ( ~ ( SY3358 @ SY3360 )
| ( SY3357 @ SY3359 ) ) ) ) )
| ( ( dsetconstr @ SV122
@ ^ [SX4: $i] : ( SY3357 @ SX4 ) )
= ( dsetconstr @ SV420
@ ^ [SX4: $i] : ( SY3358 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1405,plain,
! [SV421: $i > $o,SV123: $i] :
( ( ~ ( ex1 @ SV123
@ ^ [SY3363: $i] : ( SV421 @ SY3363 ) )
| ! [SY3364: $i] :
( ~ ( in @ SY3364 @ SV123 )
| ! [SY3365: $i] :
( ~ ( in @ SY3365 @ SV123 )
| ~ ( SV421 @ SY3364 )
| ~ ( SV421 @ SY3365 )
| ( SY3364 = SY3365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1406,plain,
! [SV422: $i,SV124: $i] :
( ( ~ ( in @ SV124 @ SV422 )
| ~ ( in @ SV422 @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1407,plain,
! [SV423: $i,SV125: $i] :
( ( ~ ( breln1 @ SV125 @ SV423 )
| ! [SY3366: $i] :
( ~ ( breln1 @ SV125 @ SY3366 )
| ! [SY3367: $i] :
( ~ ( in @ SY3367 @ SV125 )
| ! [SY3368: $i] :
( ~ ( in @ SY3368 @ SV125 )
| ~ ( in @ ( kpair @ SY3367 @ SY3368 ) @ SY3366 )
| ( in @ ( kpair @ SY3367 @ SY3368 ) @ ( binunion @ SV423 @ SY3366 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1408,plain,
! [SV424: $o,SV126: $i] :
( ( ! [SY3369: $i] :
( ~ ( in @ SY3369 @ SV126 )
| ! [SY3370: $i] :
( ~ ( in @ SY3370 @ SV126 )
| ~ ~ SV424
| ( in @ SY3370
@ ( dsetconstr @ SV126
@ ^ [SY3371: $i] :
( ~ ( ~ SV424
| ( SY3371 != SY3369 ) )
| ~ ( ~ ~ SV424
| ( SY3371 != SY3370 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1085]) ).
thf(1409,plain,
! [SV126: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV126 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV126 )
| ~ ~ $true
| ( in @ SX1
@ ( dsetconstr @ SV126
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1085]) ).
thf(1410,plain,
! [SV126: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV126 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV126 )
| ~ ~ $false
| ( in @ SX1
@ ( dsetconstr @ SV126
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1085]) ).
thf(1411,plain,
! [SV425: $i,SV127: $i] :
( ( ! [SY3372: $i] :
( ~ ( in @ SY3372 @ ( setadjoin @ SV127 @ SV425 ) )
| ( SY3372 = SV127 )
| ( in @ SY3372 @ SV425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1412,plain,
! [SV426: $i,SV128: $i] :
( ( ! [SY3373: $i] :
( ~ ( in @ SY3373 @ SV128 )
| ~ ( in @ SY3373 @ SV426 )
| ~ ( in @ SY3373 @ ( symdiff @ SV128 @ SV426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1413,plain,
! [SV129: $i] :
( ( ( ~ ~ ! [SY2650: $i] :
~ ( in @ SY2650 @ SV129 ) )
= $true )
| ( ( SV129 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1414,plain,
! [SV130: $i,SV427: $i] :
( ( ~ ( ~ ( ~ ( in @ SV427 @ ( powerset @ SV130 ) )
| ! [SY3374: $i] :
( ~ ( in @ SY3374 @ SV427 )
| ( in @ SY3374 @ SV130 ) ) )
| ~ ( ~ ! [SY3375: $i] :
( ~ ( in @ SY3375 @ SV427 )
| ( in @ SY3375 @ SV130 ) )
| ( in @ SV427 @ ( powerset @ SV130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1415,plain,
! [SV428: $i,SV131: $i] :
( ( ~ ( breln1 @ SV131 @ SV428 )
| ! [SY3376: $i] :
( ~ ( breln1 @ SV131 @ SY3376 )
| ! [SY3377: $i] :
( ~ ( in @ SY3377 @ SV131 )
| ! [SY3378: $i] :
( ~ ( in @ SY3378 @ SV131 )
| ! [SY3379: $i] :
( ~ ( in @ SY3379 @ SV131 )
| ~ ( in @ ( kpair @ SY3377 @ SY3379 ) @ SV428 )
| ~ ( in @ ( kpair @ SY3379 @ SY3378 ) @ SY3376 )
| ( in @ ( kpair @ SY3377 @ SY3378 ) @ ( breln1compset @ SV131 @ SV428 @ SY3376 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1416,plain,
! [SV132: $i,SV429: $i] :
( ( ~ ( in @ SV429 @ ( powerset @ SV132 ) )
| ! [SY3380: $i] :
( ~ ( in @ SY3380 @ ( powerset @ SV132 ) )
| ( in @ ( setminus @ SV132 @ ( binunion @ SV429 @ SY3380 ) ) @ ( powerset @ ( setminus @ SV132 @ SV429 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1417,plain,
! [SV430: $i,SV133: $i] :
( ( ! [SY3381: $i] :
( ~ ( in @ ( setadjoin @ SY3381 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV133 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV133 @ ( setadjoin @ SV430 @ emptyset ) ) @ emptyset ) ) )
| ( SV133 = SY3381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1418,plain,
! [SV431: $i,SV134: $i] :
( ( ! [SY3382: $i] :
( ( ( setadjoin @ SV134 @ ( setadjoin @ SV431 @ emptyset ) )
!= ( setadjoin @ SY3382 @ emptyset ) )
| ( SV134 = SV431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1419,plain,
! [SV432: $i,SV135: $i] :
( ( ~ ( breln1 @ SV135 @ SV432 )
| ! [SY3383: $i] :
( ~ ( breln1 @ SV135 @ SY3383 )
| ~ ! [SY3384: $i] :
( ~ ( in @ SY3384 @ SV135 )
| ! [SY3385: $i] :
( ~ ( in @ SY3385 @ SV135 )
| ~ ( in @ ( kpair @ SY3384 @ SY3385 ) @ SV432 )
| ( in @ ( kpair @ SY3384 @ SY3385 ) @ SY3383 ) ) )
| ( subset @ SV432 @ SY3383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1420,plain,
! [SV136: $i] :
( ( ( ~ ( ( SV136 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY2669: $i] :
~ ~ ( ~ ( in @ SY2669 @ SV136 )
| ( ( binintersect @ SY2669 @ SV136 )
!= emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1095]) ).
thf(1421,plain,
! [SV433: $i,SV137: $i] :
( ( ! [SY3386: $i] :
( ~ ( in @ SY3386 @ ( cartprod @ SV137 @ SV433 ) )
| ( ( kpair @ ( kfst @ SY3386 ) @ ( ksnd @ SY3386 ) )
= SY3386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1422,plain,
! [SV434: $i,SV138: $i] :
( ( ( SV138 != SV434 )
| ! [SY3387: $i,SY3388: $i] :
( ( SY3387 != SY3388 )
| ~ ( ~ ( ~ ( in @ SY3387 @ SV138 )
| ( in @ SY3388 @ SV434 ) )
| ~ ( ~ ( in @ SY3388 @ SV434 )
| ( in @ SY3387 @ SV138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1423,plain,
! [SV139: $i,SV435: $i] :
( ( ~ ( in @ SV435 @ ( powerset @ SV139 ) )
| ! [SY3389: $i] :
( ~ ( in @ SY3389 @ ( powerset @ SV139 ) )
| ! [SY3390: $i] :
( ~ ( in @ SY3390 @ ( powerset @ SV139 ) )
| ~ ( subset @ SV435 @ SY3390 )
| ( subset @ ( binintersect @ SV435 @ SY3389 ) @ SY3390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1424,plain,
! [SV436: $i,SV140: $i] :
( ( ! [SY3391: $i] :
( ~ ( breln @ SV140 @ SV436 @ SY3391 )
| ! [SY3392: $i] :
( ~ ( breln @ SV140 @ SV436 @ SY3392 )
| ~ ! [SY3393: $i] :
( ~ ( in @ SY3393 @ SV140 )
| ! [SY3394: $i] :
( ~ ( in @ SY3394 @ SV436 )
| ~ ( in @ ( kpair @ SY3393 @ SY3394 ) @ SY3391 )
| ( in @ ( kpair @ SY3393 @ SY3394 ) @ SY3392 ) ) )
| ~ ! [SY3395: $i] :
( ~ ( in @ SY3395 @ SV140 )
| ! [SY3396: $i] :
( ~ ( in @ SY3396 @ SV436 )
| ~ ( in @ ( kpair @ SY3395 @ SY3396 ) @ SY3392 )
| ( in @ ( kpair @ SY3395 @ SY3396 ) @ SY3391 ) ) )
| ( SY3391 = SY3392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1425,plain,
! [SV437: $i,SV141: $i] :
( ( ! [SY3397: $i] :
( ~ ( in @ SY3397 @ SV141 )
| ! [SY3398: $i] :
( ~ ( in @ SY3398 @ SV437 )
| ( in @ ( kpair @ SY3397 @ SY3398 ) @ ( cartprod @ SV141 @ SV437 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1426,plain,
! [SV438: $i,SV142: $i] :
( ( ! [SY3399: $i] :
( ~ ( in @ SY3399 @ SV142 )
| ! [SY3400: $i] :
( ~ ( in @ SY3400 @ SV438 )
| ( in @ ( kpair @ SY3399 @ SY3400 ) @ ( powerset @ ( powerset @ ( binunion @ SV142 @ SV438 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1427,plain,
! [SV439: $i,SV143: $i] :
( ( ! [SY3401: $i] :
( ~ ( in @ SY3401 @ ( binintersect @ SV143 @ SV439 ) )
| ( in @ SY3401 @ SV439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1428,plain,
! [SV440: $i,SV144: $i] :
( ( ! [SY3402: $i > $i] :
( ~ ! [SY3403: $i] :
( ~ ( in @ SY3403 @ SV144 )
| ( in @ ( SY3402 @ SY3403 ) @ SV440 ) )
| ! [SY3404: $i] :
( ~ ( in @ SY3404 @ ( funcSet @ SV440 @ SV144 ) )
| ~ ! [SY3405: $i] :
( ~ ( in @ SY3405 @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SY3404 @ ( SY3402 @ SY3405 ) )
= SY3405 ) )
| ( surjective @ SV440 @ SV144 @ SY3404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1429,plain,
! [SV145: $i,SV441: $i] :
( ( ~ ( in @ SV441 @ ( powerset @ SV145 ) )
| ! [SY3406: $i] :
( ~ ( in @ SY3406 @ SV145 )
| ~ ( in @ SY3406 @ SV441 )
| ( in @ SY3406 @ ( setminus @ SV145 @ ( setminus @ SV145 @ SV441 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1430,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ~ ! [SY3407: $i] :
( ~ ( in @ SY3407 @ SV146 )
| ! [SY3408: $i] :
( ~ ( in @ SY3408 @ SV146 )
| ~ ( SV442 @ SY3407 )
| ~ ( SV442 @ SY3408 )
| ( SY3407 = SY3408 ) ) )
| ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) )
| ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1431,plain,
! [SV147: $i,SV443: $i] :
( ( ~ ( in @ SV443 @ ( powerset @ SV147 ) )
| ! [SY3411: $i] :
( ~ ( in @ SY3411 @ ( powerset @ SV147 ) )
| ! [SY3412: $i] :
( ~ ( in @ SY3412 @ SV147 )
| ~ ( in @ SY3412 @ ( setminus @ SV147 @ SV443 ) )
| ~ ( in @ SY3412 @ ( binintersect @ SV443 @ SY3411 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1432,plain,
! [SV148: $i,SV444: $i] :
( ( ~ ( in @ SV444 @ ( powerset @ SV148 ) )
| ! [SY3413: $i] :
( ~ ( in @ SY3413 @ ( powerset @ SV148 ) )
| ! [SY3414: $i] :
( ~ ( in @ SY3414 @ ( powerset @ SV148 ) )
| ! [SY3415: $i] :
( ~ ( in @ SY3415 @ SV148 )
| ~ ( in @ SY3415 @ ( binintersect @ SV444 @ SY3413 ) )
| ( in @ SY3415 @ ( binunion @ SV444 @ SY3414 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1433,plain,
! [SV445: $i > $o,SV149: $i] :
( ( ~ ( ex1 @ SV149
@ ^ [SY3416: $i] : ( SV445 @ SY3416 ) )
| ~ ! [SY3417: $i] :
~ ~ ( ~ ( in @ SY3417 @ SV149 )
| ~ ( SV445 @ SY3417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1434,plain,
! [SV446: $i,SV150: $i] :
( ( ~ ( breln1 @ SV150 @ SV446 )
| ! [SY3418: $i] :
( ~ ( breln1 @ SV150 @ SY3418 )
| ! [SY3419: $i] :
( ~ ( breln1 @ SV150 @ SY3419 )
| ( ( breln1compset @ SV150 @ ( binunion @ SV446 @ SY3418 ) @ SY3419 )
= ( binunion @ ( breln1compset @ SV150 @ SV446 @ SY3419 ) @ ( breln1compset @ SV150 @ SY3418 @ SY3419 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1435,plain,
! [SV447: $i,SV151: $i] :
( ( ! [SY3420: $i > $i > $o,SY3421: $i,SY3422: $i] :
( ~ ( in @ ( kpair @ SY3421 @ SY3422 )
@ ( dpsetconstr @ SV151 @ SV447
@ ^ [SX5: $i,SX6: $i] : ( SY3420 @ SX5 @ SX6 ) ) )
| ( SY3420 @ SY3421 @ SY3422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1436,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ~ ! [SY3425: $i,SY3426: $i] :
( ( SY3425 != SY3426 )
| ~ ( ~ ( ~ ( SV152 @ SY3425 )
| ( SV448 @ SY3426 ) )
| ~ ( ~ ( SV448 @ SY3426 )
| ( SV152 @ SY3425 ) ) ) )
| ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1437,plain,
! [SV449: $i,SV153: $i] :
( ( ~ ( subset @ SV153 @ SV449 )
| ~ ( subset @ SV449 @ SV153 )
| ( SV153 = SV449 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1438,plain,
! [SV450: $i,SV154: $i] :
( ( ! [SY3433: $i] :
( ~ ( func @ SV154 @ SV450 @ SY3433 )
| ( in @ SY3433 @ ( funcSet @ SV154 @ SV450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1439,plain,
! [SV451: $o,SV155: $i] :
( ( ! [SY3434: $i] :
( ~ ( in @ SY3434 @ SV155 )
| ! [SY3435: $i] :
( ~ ( in @ SY3435 @ SV155 )
| ~ ~ SV451
| ( ( dsetconstr @ SV155
@ ^ [SY3436: $i] :
( ~ ( ~ SV451
| ( SY3436 != SY3434 ) )
| ~ ( ~ ~ SV451
| ( SY3436 != SY3435 ) ) ) )
= ( setadjoin @ SY3435 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1114]) ).
thf(1440,plain,
! [SV155: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV155 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV155 )
| ~ ~ $true
| ( ( dsetconstr @ SV155
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX1 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1114]) ).
thf(1441,plain,
! [SV155: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV155 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV155 )
| ~ ~ $false
| ( ( dsetconstr @ SV155
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX1 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1114]) ).
thf(1442,plain,
! [SV156: $i,SV452: $i] :
( ( ! [SY3437: $i] :
( ~ ( in @ SV452 @ ( powerset @ SV156 ) )
| ~ ( in @ SY3437 @ SV452 )
| ( in @ SY3437 @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1443,plain,
! [SV453: $i,SV157: $i] :
( ( ~ ( breln1 @ SV157 @ SV453 )
| ! [SY3438: $i] :
( ~ ( in @ SY3438 @ SV157 )
| ! [SY3439: $i] :
( ~ ( in @ SY3439 @ SV157 )
| ~ ( in @ ( kpair @ SY3438 @ SY3439 ) @ SV453 )
| ( in @ ( kpair @ SY3439 @ SY3438 ) @ ( breln1invset @ SV157 @ SV453 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1444,plain,
! [SV454: $i,SV158: $i] :
( ( ! [SY3440: $i] :
( ~ ( subset @ SV158 @ SV454 )
| ~ ( subset @ SV454 @ SY3440 )
| ( subset @ SV158 @ SY3440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1445,plain,
! [SV455: $i > $o,SV159: $i] :
( ( ! [SY3441: $i] :
( ~ ( in @ SY3441 @ SV159 )
| ~ ( SV455 @ SY3441 )
| ( ( dsetconstr @ SV159
@ ^ [SY3442: $i] : ( SV455 @ SY3442 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1446,plain,
! [SV456: $i,SV160: $i] :
( ( ! [SY3443: $i] :
( ~ ( subset @ SV160 @ SV456 )
| ~ ( in @ SY3443 @ SV160 )
| ( in @ SY3443 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1447,plain,
! [SV457: $i,SV161: $i] :
( ( ( SV161 != SV457 )
| ( ( setadjoin @ SV161 @ ( setadjoin @ SV457 @ emptyset ) )
= ( setadjoin @ SV161 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1448,plain,
! [SV162: $i,SV458: $i] :
( ( ~ ( in @ SV458 @ ( powerset @ SV162 ) )
| ! [SY3444: $i] :
( ~ ( in @ SY3444 @ ( powerset @ SV162 ) )
| ( in @ ( setminus @ SV162 @ ( binunion @ SV458 @ SY3444 ) ) @ ( powerset @ ( setminus @ SV162 @ SV458 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1449,plain,
! [SV163: $i,SV459: $i] :
( ( ~ ( in @ SV459 @ ( powerset @ SV163 ) )
| ! [SY3445: $i] :
( ~ ( in @ SY3445 @ ( powerset @ SV163 ) )
| ! [SY3446: $i] :
( ~ ( in @ SY3446 @ ( powerset @ SV163 ) )
| ~ ( subset @ SY3445 @ SY3446 )
| ( subset @ ( binintersect @ SV459 @ SY3445 ) @ SY3446 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1450,plain,
! [SV460: $i,SV164: $i] :
( ( ! [SY3447: $i] :
( ~ ~ ( in @ SY3447 @ SV164 )
| ~ ( in @ SY3447 @ ( setminus @ SV164 @ SV460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1451,plain,
! [SV461: $i,SV165: $i] :
( ( ( SV165 != SV461 )
| ( ( setunion @ SV165 )
= ( setunion @ SV461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1452,plain,
! [SV166: $i,SV462: $i] :
( ( ! [SY3448: $i] :
( ~ ( in @ SY3448 @ SV462 )
| ~ ( in @ SY3448 @ ( setminus @ SV166 @ SV462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1453,plain,
! [SV463: $i,SV167: $i] :
( ( ( SV167 != SV463 )
| ! [SY3449: $i,SY3450: $i] :
( ( SY3449 != SY3450 )
| ~ ( in @ SY3449 @ SV167 )
| ( in @ SY3450 @ SV463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1454,plain,
! [SV464: $i,SV168: $i] :
( ( ! [SY3451: $i] :
( ~ ( breln @ SV168 @ SV464 @ SY3451 )
| ! [SY3452: $i] :
( ~ ( breln @ SV168 @ SV464 @ SY3452 )
| ~ ! [SY3453: $i] :
( ~ ( in @ SY3453 @ SV168 )
| ! [SY3454: $i] :
( ~ ( in @ SY3454 @ SV464 )
| ~ ( in @ ( kpair @ SY3453 @ SY3454 ) @ SY3451 )
| ( in @ ( kpair @ SY3453 @ SY3454 ) @ SY3452 ) ) )
| ( subset @ SY3451 @ SY3452 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1455,plain,
! [SV465: $i,SV169: $i] :
( ( ~ ( breln1 @ SV169 @ SV465 )
| ! [SY3455: $i] :
( ~ ( breln1 @ SV169 @ SY3455 )
| ! [SY3456: $i] :
( ~ ( breln1 @ SV169 @ SY3456 )
| ( ( breln1compset @ SV169 @ ( binunion @ SV465 @ SY3455 ) @ SY3456 )
= ( binunion @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SY3456 ) @ ( breln1invset @ SV169 @ SY3455 ) ) ) @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SY3456 ) @ ( breln1invset @ SV169 @ SV465 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1456,plain,
! [SV170: $i] :
( ( ( ~ ( iskpair @ SV170 ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV170 ) @ ( ksnd @ SV170 ) )
= SV170 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1457,plain,
! [SV171: $i,SV466: $i] :
( ( ~ ( in @ SV466 @ ( powerset @ SV171 ) )
| ! [SY3457: $i] :
( ~ ( in @ SY3457 @ ( powerset @ SV171 ) )
| ! [SY3458: $i] :
( ~ ( in @ SY3458 @ ( binintersect @ SV466 @ SY3457 ) )
| ( in @ SY3458 @ SV171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1458,plain,
! [SV467: $i,SV172: $i] :
( ( ( SV172 != SV467 )
| ( subset @ SV467 @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1459,plain,
! [SV173: $i,SV468: $i] :
( ( ~ ( in @ SV468 @ ( powerset @ SV173 ) )
| ! [SY3459: $i] :
( ~ ( in @ SY3459 @ ( powerset @ SV173 ) )
| ~ ( subset @ SV468 @ ( setminus @ SV173 @ SY3459 ) )
| ( subset @ SY3459 @ ( setminus @ SV173 @ SV468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1460,plain,
! [SV469: $i,SV174: $i] :
( ( ! [SY3460: $i,SY3461: $i] :
( ( ( kpair @ SV174 @ SV469 )
!= ( kpair @ SY3460 @ SY3461 ) )
| ( SV174 = SY3460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1461,plain,
! [SV470: $i > $i,SV175: $i] :
( ( ~ ! [SY3462: $i] :
~ ~ ( ~ ! [SY3463: $i] :
~ ( ~ ( ~ ( in @ SY3463 @ SY3462 )
| ~ ! [SY3464: $i] :
~ ~ ( ~ ( in @ SY3464 @ SV175 )
| ( SY3463
!= ( SV470 @ SY3464 ) ) ) )
| ~ ( ~ ~ ! [SY3465: $i] :
~ ~ ( ~ ( in @ SY3465 @ SV175 )
| ( SY3463
!= ( SV470 @ SY3465 ) ) )
| ( in @ SY3463 @ SY3462 ) ) )
| ~ ! [SY3466: $i] :
( ~ ! [SY3467: $i] :
~ ( ~ ( ~ ( in @ SY3467 @ SY3466 )
| ~ ! [SY3468: $i] :
~ ~ ( ~ ( in @ SY3468 @ SV175 )
| ( SY3467
!= ( SV470 @ SY3468 ) ) ) )
| ~ ( ~ ~ ! [SY3469: $i] :
~ ~ ( ~ ( in @ SY3469 @ SV175 )
| ( SY3467
!= ( SV470 @ SY3469 ) ) )
| ( in @ SY3467 @ SY3466 ) ) )
| ( SY3462 = SY3466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1462,plain,
! [SV176: $i,SV471: $i] :
( ( ~ ( in @ SV471 @ ( powerset @ SV176 ) )
| ! [SY3470: $i] :
( ~ ( in @ SY3470 @ ( powerset @ SV176 ) )
| ( in @ ( setminus @ SV471 @ SY3470 ) @ ( powerset @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1463,plain,
! [SV472: $i,SV177: $i] :
( ( ! [SY3471: $i] :
( ~ ( in @ SY3471 @ ( funcSet @ SV177 @ SV472 ) )
| ~ ( injective @ SV177 @ SV472 @ SY3471 )
| ( in @ SY3471 @ ( injFuncSet @ SV177 @ SV472 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1464,plain,
! [SV473: $i,SV178: $i] :
( ( ~ ( breln1 @ SV178 @ SV473 )
| ! [SY3472: $i] :
( ~ ( breln1 @ SV178 @ SY3472 )
| ( ( breln1invset @ SV178 @ ( breln1compset @ SV178 @ SV473 @ SY3472 ) )
= ( breln1compset @ SV178 @ ( breln1invset @ SV178 @ SY3472 ) @ ( breln1invset @ SV178 @ SV473 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1465,plain,
! [SV474: $i > $o,SV179: $i] :
( ( ! [SY3473: $i] :
( ~ ( in @ SY3473
@ ( dsetconstr @ SV179
@ ^ [SY3474: $i] : ( SV474 @ SY3474 ) ) )
| ( in @ SY3473 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1466,plain,
! [SV475: $i,SV180: $i] :
( ( ! [SY3475: $i > $i > $o] :
( ~ ! [SY3476: $i] :
( ~ ( in @ SY3476 @ SV180 )
| ~ ! [SY3477: $i] :
~ ~ ( ~ ( in @ SY3477 @ SV475 )
| ~ ( SY3475 @ SY3476 @ SY3477 ) ) )
| ! [SY3478: $i] :
( ~ ( in @ SY3478 @ ( breln1Set @ SV475 ) )
| ~ ( reflwellordering @ SV475 @ SY3478 )
| ! [SY3479: $i] :
( ~ ( in @ SY3479 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY3480: $i] :
~ ( ~ ( SY3475 @ SY3479 @ SY3480 )
| ~ ! [SY3481: $i] :
( ~ ( in @ SY3481 @ SV475 )
| ~ ( SY3475 @ SY3479 @ SY3481 )
| ( in @ ( kpair @ SY3480 @ SY3481 ) @ SY3478 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1467,plain,
! [SV476: $i,SV181: $i] :
( ( ! [SY3482: $i] :
( ~ ( in @ SY3482 @ SV181 )
| ! [SY3483: $i] :
( ~ ( in @ SY3483 @ SV476 )
| ( in @ ( setadjoin @ ( setadjoin @ SY3482 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3482 @ ( setadjoin @ SY3483 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV181 @ SV476 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1468,plain,
! [SV477: $i,SV182: $i] :
( ( ! [SY3484: $i > $i] :
( ~ ! [SY3485: $i] :
( ~ ( in @ SY3485 @ SV182 )
| ( in @ ( SY3484 @ SY3485 ) @ SV477 ) )
| ! [SY3486: $i] :
( ~ ( in @ SY3486 @ SV182 )
| ( ( ap @ SV182 @ SV477
@ ( lam @ SV182 @ SV477
@ ^ [SX4: $i] : ( SY3484 @ SX4 ) )
@ SY3486 )
= ( SY3484 @ SY3486 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1469,plain,
! [SV478: $i,SV183: $i] :
( ( ! [SY3488: $i] :
( ~ ( in @ SY3488 @ SV183 )
| ~ ~ ( in @ SY3488 @ SV478 )
| ~ ( subset @ SV183 @ SV478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1470,plain,
! [SV479: $i,SV184: $i] :
( ( ! [SY3489: $i] :
( ~ ( in @ SY3489 @ SV184 )
| ~ ~ ( in @ SY3489 @ SV479 )
| ( SV184 != SV479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1471,plain,
! [SV185: $i,SV480: $i] :
( ( ~ ( in @ SV480 @ ( powerset @ SV185 ) )
| ! [SY3490: $i] :
( ~ ( in @ SY3490 @ ( powerset @ SV185 ) )
| ( in @ ( binintersect @ SV480 @ SY3490 ) @ ( powerset @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1472,plain,
! [SV186: $i,SV481: $i] :
( ( ~ ( in @ SV481 @ ( powerset @ SV186 ) )
| ! [SY3491: $i] :
( ~ ( in @ SY3491 @ ( powerset @ SV186 ) )
| ! [SY3492: $i] :
( ~ ( in @ SY3492 @ SV186 )
| ~ ( in @ SV481 @ ( powerset @ SY3491 ) )
| ~ ( in @ SY3492 @ SV481 )
| ( in @ SY3492 @ SY3491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1473,plain,
! [SV482: $i,SV187: $i] :
( ( ( ( binintersect @ SV187 @ SV482 )
!= SV187 )
| ( subset @ SV187 @ SV482 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1474,plain,
! [SV483: $i > $o,SV188: $i] :
( ( ! [SY3493: $i] :
( ~ ( in @ SY3493 @ SV188 )
| ~ ( ~ ( ~ ( in @ SY3493
@ ( dsetconstr @ SV188
@ ^ [SY3494: $i] : ( SV483 @ SY3494 ) ) )
| ( SV483 @ SY3493 ) )
| ~ ( ~ ( SV483 @ SY3493 )
| ( in @ SY3493
@ ( dsetconstr @ SV188
@ ^ [SY3495: $i] : ( SV483 @ SY3495 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1475,plain,
! [SV484: $i > $o,SV189: $i] :
( ( ~ ~ ! [SY3496: $i] :
( ~ ( in @ SY3496 @ SV189 )
| ( SV484 @ SY3496 ) )
| ~ ! [SY3497: $i] :
~ ~ ( ~ ( in @ SY3497 @ SV189 )
| ~ ~ ( SV484 @ SY3497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1476,plain,
! [SV190: $i,SV485: $i] :
( ( ~ ( in @ SV485 @ ( setunion @ SV190 ) )
| ! [SY3498: $o] :
( ~ ! [SY3499: $i] :
( ~ ( in @ SV485 @ SY3499 )
| ~ ( in @ SY3499 @ SV190 )
| SY3498 )
| SY3498 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1477,plain,
! [SV486: $i,SV191: $i] :
( ( ! [SY3500: $i] :
( ~ ( in @ SY3500 @ ( funcSet @ SV191 @ SV486 ) )
| ! [SY3501: $i] :
( ~ ( in @ SY3501 @ SV191 )
| ! [SY3502: $i] :
( ~ ( in @ SY3502 @ SV486 )
| ~ ( in @ ( kpair @ SY3501 @ SY3502 ) @ SY3500 )
| ( ( ap @ SV191 @ SV486 @ SY3500 @ SY3501 )
= SY3502 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1478,plain,
! [SV487: $i,SV192: $i] :
( ( ! [SY3503: $i] :
( ~ ( subset @ SY3503 @ SV192 )
| ~ ( subset @ SY3503 @ SV487 )
| ( subset @ SY3503 @ ( binintersect @ SV192 @ SV487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1479,plain,
! [SV488: $i > $i,SV193: $i] :
( ( ~ ! [SY3504: $i] :
~ ! [SY3505: $i] :
~ ( ~ ( ~ ( in @ SY3505 @ SY3504 )
| ~ ! [SY3506: $i] :
~ ~ ( ~ ( in @ SY3506 @ SV193 )
| ( SY3505
!= ( SV488 @ SY3506 ) ) ) )
| ~ ( ~ ~ ! [SY3507: $i] :
~ ~ ( ~ ( in @ SY3507 @ SV193 )
| ( SY3505
!= ( SV488 @ SY3507 ) ) )
| ( in @ SY3505 @ SY3504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1480,plain,
! [SV194: $i,SV489: $i] :
( ( ~ ( in @ SV489 @ ( powerset @ SV194 ) )
| ! [SY3508: $i] :
( ~ ( in @ SY3508 @ SV194 )
| ~ ~ ( in @ SY3508 @ ( setminus @ SV194 @ SV489 ) )
| ( in @ SY3508 @ SV489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1481,plain,
! [SV490: $i,SV195: $i] :
( ( ! [SY3509: $i] :
( ~ ( func @ SV195 @ SV490 @ SY3509 )
| ( ( lam @ SV195 @ SV490
@ ^ [SY3510: $i] : ( ap @ SV195 @ SV490 @ SY3509 @ SY3510 ) )
= SY3509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1482,plain,
( ( ~ ! [SY3511: $i] :
( ~ ( in @ SY3511 @ sK1_SX0 )
| ( subset @ SY3511 @ sK1_SX0 ) )
| ! [SY3512: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY3512 )
| ( subset @ SX2 @ SY3512 ) )
| ! [SY3514: $i] :
( ~ ( in @ SY3514 @ ( binintersect @ sK1_SX0 @ SY3512 ) )
| ( subset @ SY3514 @ ( binintersect @ sK1_SX0 @ SY3512 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1155]) ).
thf(1483,plain,
! [SV196: $i > $o] :
( ( ( ~ ~ ! [SY2853: $i] :
~ ~ ( ~ ( SV196 @ SY2853 )
| ~ ! [SY2854: $i] :
( ~ ( SV196 @ SY2854 )
| ( SY2853 = SY2854 ) ) ) )
= $true )
| ( ( ~ ! [SY2855: $i] :
~ ~ ( ~ ( SV196 @ SY2855 )
| ~ ! [SY2856: $i] :
( ~ ( SV196 @ SY2856 )
| ( SY2855 = SY2856 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1156]) ).
thf(1484,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ~ ! [SY3515: $i,SY3516: $i] :
( ( SY3515 != SY3516 )
| ~ ( ~ ( ~ ( SV197 @ SY3515 )
| ( SV491 @ SY3516 ) )
| ~ ( ~ ( SV491 @ SY3516 )
| ( SV197 @ SY3515 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1485,plain,
! [SV198: $i] :
( ( ( ~ ! [SY2868: $i] :
~ ( in @ SY2868 @ SV198 ) )
= $true )
| ( ( SV198 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1486,plain,
! [SV492: $i,SV199: $i] :
( ( ! [SY3525: $i] :
( ~ ( in @ SY3525 @ ( cartprod @ SV199 @ SV492 ) )
| ~ ! [SY3526: $i] :
~ ~ ( ~ ( in @ SY3526 @ SV199 )
| ~ ~ ! [SY3527: $i] :
~ ~ ( ~ ( in @ SY3527 @ SV492 )
| ( SY3525
!= ( kpair @ SY3526 @ SY3527 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1487,plain,
! [SV200: $i,SV493: $i] :
( ( ~ ( in @ SV493 @ ( powerset @ SV200 ) )
| ! [SY3528: $i] :
( ~ ( in @ SY3528 @ ( powerset @ SV200 ) )
| ! [SY3529: $i] :
( ~ ( in @ SY3529 @ SV200 )
| ~ ~ ( in @ SY3529 @ ( binunion @ SV493 @ SY3528 ) )
| ~ ( in @ SY3529 @ SY3528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1488,plain,
! [SV494: $i,SV201: $i] :
( ( ( SV201 != SV494 )
| ( subset @ SV201 @ SV494 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1489,plain,
! [SV495: $o,SV202: $i] :
( ( ! [SY3530: $i] :
( ~ ( in @ SY3530 @ SV202 )
| ! [SY3531: $i] :
( ~ ( in @ SY3531 @ SV202 )
| ( in @ ( if @ SV202 @ SV495 @ SY3530 @ SY3531 ) @ SV202 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1162]) ).
thf(1490,plain,
! [SV202: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV202 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV202 )
| ( in @ ( if @ SV202 @ $true @ SX0 @ SX1 ) @ SV202 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1162]) ).
thf(1491,plain,
! [SV202: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV202 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV202 )
| ( in @ ( if @ SV202 @ $false @ SX0 @ SX1 ) @ SV202 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1162]) ).
thf(1492,plain,
! [SV496: $i,SV203: $i] :
( ( ! [SY3532: $i] :
( ~ ( in @ SY3532 @ ( symdiff @ SV203 @ SV496 ) )
| ! [SY3533: $o] :
( ~ ( ~ ( in @ SY3532 @ SV203 )
| ~ ~ ( in @ SY3532 @ SV496 )
| SY3533 )
| ~ ( ~ ~ ( in @ SY3532 @ SV203 )
| ~ ( in @ SY3532 @ SV496 )
| SY3533 )
| SY3533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1493,plain,
! [SV497: $i,SV204: $i] :
( ( ! [SY3534: $i > $i] :
( ~ ! [SY3535: $i] :
( ~ ( in @ SY3535 @ SV204 )
| ( in @ ( SY3534 @ SY3535 ) @ SV497 ) )
| ( func @ SV204 @ SV497
@ ( lam @ SV204 @ SV497
@ ^ [SX3: $i] : ( SY3534 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1494,plain,
! [SV498: $i,SV205: $i] :
( ( ! [SY3537: $i] :
( ~ ( subset @ SV205 @ SY3537 )
| ( subset @ SV205 @ ( setadjoin @ SV498 @ SY3537 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1495,plain,
! [SV499: $o,SV206: $i] :
( ( ! [SY3538: $i] :
( ~ ( in @ SY3538 @ SV206 )
| ! [SY3539: $i] :
( ~ ( in @ SY3539 @ SV206 )
| ( in @ ( if @ SV206 @ SV499 @ SY3538 @ SY3539 ) @ ( setadjoin @ SY3538 @ ( setadjoin @ SY3539 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1166]) ).
thf(1496,plain,
! [SV206: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV206 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV206 )
| ( in @ ( if @ SV206 @ $true @ SX0 @ SX1 ) @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1166]) ).
thf(1497,plain,
! [SV206: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV206 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV206 )
| ( in @ ( if @ SV206 @ $false @ SX0 @ SX1 ) @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1166]) ).
thf(1498,plain,
! [SV500: $i > $o,SV207: $i] :
( ( ~ ~ ~ ! [SY3540: $i] :
~ ~ ( ~ ( in @ SY3540 @ SV207 )
| ~ ( SV500 @ SY3540 ) )
| ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SV207 )
| ~ ( SV500 @ SY3541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1499,plain,
! [SV208: $i,SV501: $i] :
( ( ~ ( in @ SV501 @ ( powerset @ SV208 ) )
| ! [SY3542: $i] :
( ~ ( in @ SY3542 @ ( powerset @ SV208 ) )
| ! [SY3543: $o,SY3544: $i] :
( ~ ( in @ SY3544 @ SV208 )
| ~ ( in @ SY3544 @ ( binunion @ SV501 @ SY3542 ) )
| ~ ( ~ ( in @ SY3544 @ SV501 )
| SY3543 )
| ~ ( ~ ( in @ SY3544 @ SY3542 )
| SY3543 )
| SY3543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1500,plain,
! [SV502: $i,SV209: $i] :
( ( ! [SY3545: $i] :
( ~ ( breln @ SV209 @ SV502 @ SY3545 )
| ! [SY3546: $i > $o] :
( ~ ! [SY3547: $i] :
( ~ ( in @ SY3547 @ SV209 )
| ! [SY3548: $i] :
( ~ ( in @ SY3548 @ SV502 )
| ~ ( in @ ( kpair @ SY3547 @ SY3548 ) @ SY3545 )
| ( SY3546 @ ( kpair @ SY3547 @ SY3548 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3545 )
| ( SY3546 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1501,plain,
! [SV503: $o,SV210: $i] :
( ( ! [SY3550: $i] :
( ~ ( in @ SY3550 @ SV210 )
| ! [SY3551: $i] :
( ~ ( in @ SY3551 @ SV210 )
| ~ SV503
| ( in @ SY3550
@ ( dsetconstr @ SV210
@ ^ [SY3552: $i] :
( ~ ( ~ SV503
| ( SY3552 != SY3550 ) )
| ~ ( ~ ~ SV503
| ( SY3552 != SY3551 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1170]) ).
thf(1502,plain,
! [SV210: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV210 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV210 )
| ~ $true
| ( in @ SX0
@ ( dsetconstr @ SV210
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1170]) ).
thf(1503,plain,
! [SV210: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV210 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV210 )
| ~ $false
| ( in @ SX0
@ ( dsetconstr @ SV210
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1170]) ).
thf(1504,plain,
! [SV211: $i] :
( ( ( ~ ( in @ SV211 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV211 @ SV211 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1505,plain,
! [SV504: $i,SV212: $i] :
( ( ! [SY3553: $i] :
( ~ ( subset @ SV212 @ SV504 )
| ~ ~ ( in @ SY3553 @ SV504 )
| ~ ( in @ SY3553 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1506,plain,
! [SV505: $i,SV213: $i] :
( ( ! [SY3554: $i,SY3555: $i] :
( ( ( setadjoin @ ( setadjoin @ SV213 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV213 @ ( setadjoin @ SV505 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY3554 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3554 @ ( setadjoin @ SY3555 @ emptyset ) ) @ emptyset ) ) )
| ( SV213 = SY3554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1507,plain,
! [SV506: $i,SV214: $i] :
( ( ! [SY3556: $i] :
( ~ ( in @ SY3556 @ ( injFuncSet @ SV214 @ SV506 ) )
| ( injective @ SV214 @ SV506 @ SY3556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1508,plain,
! [SV215: $i,SV507: $i] :
( ( ~ ( in @ SV507 @ SV215 )
| ( subset @ ( setadjoin @ SV507 @ emptyset ) @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1509,plain,
! [SV508: $i,SV216: $i] :
( ( ~ ( breln1 @ SV216 @ SV508 )
| ! [SY3557: $i] :
( ~ ( breln1 @ SV216 @ SY3557 )
| ! [SY3558: $i] :
( ~ ( in @ SY3558 @ SV216 )
| ! [SY3559: $i] :
( ~ ( in @ SY3559 @ SV216 )
| ~ ( in @ ( kpair @ SY3558 @ SY3559 ) @ ( binunion @ SV508 @ SY3557 ) )
| ! [SY3560: $o] :
( ~ ( ~ ( in @ ( kpair @ SY3558 @ SY3559 ) @ SV508 )
| SY3560 )
| ~ ( ~ ( in @ ( kpair @ SY3558 @ SY3559 ) @ SY3557 )
| SY3560 )
| SY3560 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1510,plain,
! [SV217: $i,SV509: $i] :
( ( ~ ( in @ SV509 @ ( powerset @ SV217 ) )
| ! [SY3561: $i] :
( ~ ( in @ SY3561 @ ( powerset @ SV217 ) )
| ! [SY3562: $i] :
( ~ ( in @ SY3562 @ SV217 )
| ~ ( in @ SY3562 @ ( setminus @ SV217 @ ( binunion @ SV509 @ SY3561 ) ) )
| ( in @ SY3562 @ ( binintersect @ ( setminus @ SV217 @ SV509 ) @ ( setminus @ SV217 @ SY3561 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1511,plain,
! [SV510: $i > $i,SV218: $i] :
( ( ! [SY3563: $i] :
( ~ ( in @ SY3563
@ ( image1 @ SV218
@ ^ [SY3564: $i] : ( SV510 @ SY3564 ) ) )
| ~ ! [SY3565: $i] :
~ ~ ( ~ ( in @ SY3565 @ SV218 )
| ( SY3563
!= ( SV510 @ SY3565 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1512,plain,
! [SV219: $i] :
( ( ( ~ ( in @ SV219 @ omega ) )
= $true )
| ( ( ( omegaS @ SV219 )
!= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1179]) ).
thf(1513,plain,
! [SV511: $i,SV220: $i] :
( ( ! [SY3566: $i] :
( ~ ( in @ SY3566 @ ( setadjoin @ SV220 @ ( setadjoin @ SV511 @ emptyset ) ) )
| ( SY3566 = SV220 )
| ( SY3566 = SV511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1514,plain,
! [SV512: $i,SV221: $i] :
( ( ! [SY3567: $i] :
( ~ ( in @ SY3567 @ ( surjFuncSet @ SV221 @ SV512 ) )
| ( in @ SY3567 @ ( funcSet @ SV221 @ SV512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1515,plain,
! [SV513: $i,SV222: $i] :
( ( ~ ( subset @ SV222 @ SV513 )
| ( in @ SV222 @ ( powerset @ SV513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1516,plain,
! [SV514: $o,SV223: $i] :
( ( ! [SY3568: $i] :
( ~ ( in @ SY3568 @ SV223 )
| ! [SY3569: $i] :
( ~ ( in @ SY3569 @ SV223 )
| ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY3570: $i] :
( ~ ( ~ SV514
| ( SY3570 != SY3568 ) )
| ~ ( ~ ~ SV514
| ( SY3570 != SY3569 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1183]) ).
thf(1517,plain,
! [SV223: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV223 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV223 )
| ( singleton
@ ( dsetconstr @ SV223
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1183]) ).
thf(1518,plain,
! [SV223: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV223 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV223 )
| ( singleton
@ ( dsetconstr @ SV223
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1183]) ).
thf(1519,plain,
! [SV224: $i,SV515: $i] :
( ( ~ ( in @ SV515 @ ( powerset @ SV224 ) )
| ! [SY3571: $i] :
( ~ ( in @ SY3571 @ ( powerset @ SV224 ) )
| ~ ( subset @ SV515 @ SY3571 )
| ( subset @ ( setminus @ SV224 @ SY3571 ) @ ( setminus @ SV224 @ SV515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1520,plain,
! [SV516: $i,SV225: $i] :
( ( ! [SY3572: $i,SY3573: $i] :
( ( ( kpair @ SV225 @ SV516 )
!= ( kpair @ SY3572 @ SY3573 ) )
| ( SV516 = SY3573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1521,plain,
! [SV226: $i] :
( ( ! [SY2943: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY2944: $i] :
( ~ ( in @ SY2944 @ SY2943 )
| ! [SY2945: $i] :
( ~ ( in @ SY2945 @ SY2944 )
| ( in @ SY2945 @ SV226 ) ) )
| ~ ! [SY2946: $i,SY2947: $i] :
( ~ ~ ( ~ ( in @ SY2946 @ SV226 )
| ~ ( in @ SY2947 @ SV226 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2943 )
| ~ ( ~ ( ~ ( in @ SY2946 @ SX4 )
| ( in @ SY2947 @ SX4 ) )
| ~ ( ~ ( in @ SY2947 @ SX4 )
| ( in @ SY2946 @ SX4 ) ) ) )
| ( SY2946 = SY2947 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY2943 )
| ~ ( in @ SX3 @ SY2943 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY2953: $i] :
( ~ ~ ( ~ ! [SY2954: $i] :
( ~ ( in @ SY2954 @ SY2953 )
| ( in @ SY2954 @ SV226 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY2953 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY2943 )
| ~ ( in @ SX4 @ SY2953 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY2953 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2943 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1522,plain,
! [SV517: $i,SV227: $i] :
( ( ! [SY3574: $i > $i > $o,SY3575: $i] :
( ~ ( in @ SY3575 @ SV227 )
| ! [SY3576: $i] :
( ~ ( in @ SY3576 @ SV517 )
| ~ ( in @ ( kpair @ SY3575 @ SY3576 )
@ ( dpsetconstr @ SV227 @ SV517
@ ^ [SX5: $i,SX6: $i] : ( SY3574 @ SX5 @ SX6 ) ) )
| ( SY3574 @ SY3575 @ SY3576 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1523,plain,
! [SV228: $i,SV518: $i] :
( ( ! [SY3579: $i] :
( ~ ( in @ SV518 @ SY3579 )
| ~ ( in @ SY3579 @ SV228 )
| ( in @ SV518 @ ( setunion @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1524,plain,
! [SV229: $i,SV519: $i] :
( ( ~ ( in @ SV519 @ ( powerset @ SV229 ) )
| ! [SY3580: $i] :
( ~ ( in @ SY3580 @ ( powerset @ SV229 ) )
| ! [SY3581: $i] :
( ~ ( in @ SY3581 @ SV229 )
| ~ ~ ( in @ SY3581 @ ( binunion @ SV519 @ SY3580 ) )
| ~ ( in @ SY3581 @ SV519 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1525,plain,
! [SV230: $i > $i > $o,SV520: $i] :
( ( ~ ! [SY3582: $i] :
( ~ ( in @ SY3582 @ SV520 )
| ~ ! [SY2974: $i] :
~ ~ ( ~ ( SV230 @ SY3582 @ SY2974 )
| ~ ! [SY2975: $i] :
( ~ ( SV230 @ SY3582 @ SY2975 )
| ( SY2974 = SY2975 ) ) ) )
| ~ ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1526,plain,
! [SV521: $i,SV231: $i] :
( ( ! [SY3589: $i] :
( ~ ( func @ SV231 @ SV521 @ SY3589 )
| ! [SY3590: $i] :
( ~ ( func @ SV231 @ SV521 @ SY3590 )
| ~ ! [SY3591: $i] :
( ~ ( in @ SY3591 @ SV231 )
| ( ( ap @ SV231 @ SV521 @ SY3589 @ SY3591 )
= ( ap @ SV231 @ SV521 @ SY3590 @ SY3591 ) ) )
| ( SY3589 = SY3590 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1527,plain,
! [SV522: $o,SV232: $i] :
( ( ! [SY3592: $i] :
( ~ ( in @ SY3592 @ SV232 )
| ! [SY3593: $i] :
( ~ ( in @ SY3593 @ SV232 )
| ~ SV522
| ( ( if @ SV232 @ SV522 @ SY3592 @ SY3593 )
= SY3592 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1192]) ).
thf(1528,plain,
! [SV232: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV232 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV232 )
| ~ $true
| ( ( if @ SV232 @ $true @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1192]) ).
thf(1529,plain,
! [SV232: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV232 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV232 )
| ~ $false
| ( ( if @ SV232 @ $false @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1192]) ).
thf(1530,plain,
! [SV523: $i,SV233: $i] :
( ( ~ ( breln1 @ SV233 @ SV523 )
| ! [SY3594: $i > $o] :
( ~ ! [SY3595: $i] :
( ~ ( in @ SY3595 @ SV233 )
| ! [SY3596: $i] :
( ~ ( in @ SY3596 @ SV233 )
| ~ ( in @ ( kpair @ SY3595 @ SY3596 ) @ SV523 )
| ( SY3594 @ ( kpair @ SY3595 @ SY3596 ) ) ) )
| ! [SY3597: $i] :
( ~ ( in @ SY3597 @ SV523 )
| ( SY3594 @ SY3597 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1531,plain,
! [SV234: $i,SV524: $i] :
( ( ~ ! [SY3598: $i] :
( ~ ( in @ SY3598 @ SV524 )
| ( in @ SY3598 @ SV234 ) )
| ( in @ SV524 @ ( powerset @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1532,plain,
! [SV235: $i,SV525: $i] :
( ( ~ ( in @ SV525 @ ( setunion @ SV235 ) )
| ~ ! [SY3599: $i] :
~ ~ ( ~ ( in @ SY3599 @ SV235 )
| ~ ( in @ SV525 @ SY3599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1533,plain,
! [SV236: $i] :
( ( ( ~ ( singleton @ SV236 ) )
= $true )
| ( ( in @ ( setunion @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1534,plain,
! [SV526: $i,SV237: $i] :
( ( ! [SY3600: $i] :
( ~ ( in @ SY3600 @ ( setminus @ SV237 @ SV526 ) )
| ( in @ SY3600 @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1535,plain,
! [SV527: $i,SV238: $i] :
( ( ( SV238 != SV527 )
| ( ( setadjoin @ ( setadjoin @ SV238 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV238 @ ( setadjoin @ SV527 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV238 @ emptyset ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1536,plain,
! [SV528: $i,SV239: $i] :
( ( ! [SY3601: $i] :
( ~ ( in @ SY3601 @ ( binunion @ SV239 @ SV528 ) )
| ( in @ SY3601 @ SV239 )
| ( in @ SY3601 @ SV528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1537,plain,
! [SV529: $i,SV240: $i] :
( ( ! [SY3602: $i] :
( ~ ( func @ SV240 @ SV529 @ SY3602 )
| ! [SY3603: $i] :
( ~ ( in @ SY3603 @ SV240 )
| ( in @ ( kpair @ SY3603 @ ( ap @ SV240 @ SV529 @ SY3602 @ SY3603 ) ) @ SY3602 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1538,plain,
! [SV241: $i,SV530: $i] :
( ( ~ ( in @ SV530 @ ( powerset @ SV241 ) )
| ! [SY3604: $i] :
( ~ ( in @ SY3604 @ ( powerset @ SV241 ) )
| ( in @ ( setminus @ SV241 @ SV530 ) @ ( powerset @ ( setminus @ SV241 @ ( binintersect @ SV530 @ SY3604 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1539,plain,
! [SV242: $i] :
( ( ( ~ ( ( SV242 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY3006: $i] :
~ ( in @ SY3006 @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1540,plain,
! [SV243: $i,SV531: $i] :
( ( ~ ( in @ SV531 @ ( powerset @ SV243 ) )
| ! [SY3605: $i] :
( ~ ( in @ SY3605 @ ( powerset @ SV243 ) )
| ! [SY3606: $i] :
( ~ ( in @ SY3606 @ ( powerset @ SV243 ) )
| ( in @ ( binintersect @ SV531 @ SY3605 ) @ ( powerset @ ( binintersect @ ( binunion @ SV531 @ SY3606 ) @ ( binunion @ SY3605 @ SY3606 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1541,plain,
! [SV244: $i,SV532: $i] :
( ( ~ ( in @ SV532 @ ( powerset @ SV244 ) )
| ! [SY3607: $i] :
( ~ ( in @ SY3607 @ SV244 )
| ~ ( in @ SY3607 @ ( setminus @ SV244 @ ( setminus @ SV244 @ SV532 ) ) )
| ( in @ SY3607 @ SV532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1542,plain,
! [SV533: $i > $o,SV245: $i] :
( ( ~ ~ ! [SY3608: $i] :
~ ~ ( ~ ( in @ SY3608 @ SV245 )
| ~ ( SV533 @ SY3608 ) )
| ( ( dsetconstr @ SV245
@ ^ [SY3609: $i] : ( SV533 @ SY3609 ) )
!= emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1543,plain,
! [SV534: $i,SV246: $i] :
( ( ! [SY3610: $i] :
( ~ ( func @ SV246 @ SV534 @ SY3610 )
| ! [SY3611: $i] :
( ~ ( in @ SY3611 @ SV246 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV534
@ ^ [SX4: $i] : ( in @ ( kpair @ SY3611 @ SX4 ) @ SY3610 ) ) )
@ SV534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1544,plain,
! [SV535: $i,SV247: $i] :
( ( ~ ( breln1 @ SV247 @ SV535 )
| ! [SY3613: $i] :
( ~ ( in @ SY3613 @ SV247 )
| ! [SY3614: $i] :
( ~ ( in @ SY3614 @ SV247 )
| ~ ( in @ ( kpair @ SY3614 @ SY3613 ) @ ( breln1invset @ SV247 @ SV535 ) )
| ( in @ ( kpair @ SY3613 @ SY3614 ) @ SV535 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1545,plain,
! [SV536: $i,SV248: $i] :
( ( ( ( binintersect @ SV248 @ SV536 )
!= SV536 )
| ( subset @ SV536 @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1546,plain,
! [SV249: $i] :
( ( ( ~ ! [SY3023: $i] :
( ~ ( in @ SY3023 @ SV249 )
| ( subset @ SY3023 @ SV249 ) ) )
= $true )
| ( ( ! [SY3024: $i] :
( ~ ( in @ SY3024 @ SV249 )
| ( subset @ SY3024 @ SV249 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1547,plain,
! [SV537: $i,SV250: $i] :
( ( ! [SY3615: $i] :
( ~ ( in @ SY3615 @ ( setadjoin @ SV250 @ ( setadjoin @ SV537 @ emptyset ) ) )
| ( SY3615 = SV250 )
| ( SY3615 = SV537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1548,plain,
! [SV251: $i,SV538: $i] :
( ( ~ ( in @ SV538 @ ( powerset @ SV251 ) )
| ! [SY3616: $i] :
( ~ ( in @ SY3616 @ ( powerset @ SV251 ) )
| ! [SY3617: $i] :
( ~ ( in @ SY3617 @ SV251 )
| ~ ~ ( in @ SY3617 @ SV538 )
| ~ ~ ( in @ SY3617 @ SY3616 )
| ~ ( in @ SY3617 @ ( binunion @ SV538 @ SY3616 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1549,plain,
! [SV539: $o,SV252: $i] :
( ( ! [SY3618: $i] :
( ~ ( in @ SY3618 @ SV252 )
| ! [SY3619: $i] :
( ~ ( in @ SY3619 @ SV252 )
| ~ SV539
| ( ( dsetconstr @ SV252
@ ^ [SY3620: $i] :
( ~ ( ~ SV539
| ( SY3620 != SY3618 ) )
| ~ ( ~ ~ SV539
| ( SY3620 != SY3619 ) ) ) )
= ( setadjoin @ SY3618 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1212]) ).
thf(1550,plain,
! [SV252: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV252 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV252 )
| ~ $true
| ( ( dsetconstr @ SV252
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1212]) ).
thf(1551,plain,
! [SV252: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV252 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV252 )
| ~ $false
| ( ( dsetconstr @ SV252
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1212]) ).
thf(1552,plain,
! [SV253: $i,SV540: $i] :
( ( ~ ( in @ SV540 @ ( breln1Set @ SV253 ) )
| ( breln1 @ SV253 @ SV540 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1553,plain,
! [SV541: $i,SV254: $i] :
( ( ! [SY3621: $i] :
( ~ ( func @ SV254 @ SV541 @ SY3621 )
| ! [SY3622: $i] :
( ~ ( in @ SY3622 @ SV254 )
| ( ( ap @ SV254 @ SV541 @ SY3621 @ SY3622 )
= ( ap @ SV254 @ SV541 @ SY3621 @ SY3622 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1554,plain,
! [SV542: $i,SV255: $i] :
( ( ~ ( subset @ SV255 @ SV542 )
| ( subset @ ( powerset @ SV255 ) @ ( powerset @ SV542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1555,plain,
! [SV543: $i,SV256: $i] :
( ( ! [SY3623: $i,SY3624: $i] :
( ( ( setadjoin @ ( setadjoin @ SV256 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV256 @ ( setadjoin @ SV543 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY3623 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3623 @ ( setadjoin @ SY3624 @ emptyset ) ) @ emptyset ) ) )
| ( SY3623 != SY3624 )
| ( SV543 = SY3624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1556,plain,
! [SV257: $i,SV544: $i] :
( ( ~ ( in @ SV544 @ ( powerset @ SV257 ) )
| ( subset @ SV544 @ SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1557,plain,
! [SV258: $o,SV545: $i] :
( ( ~ ( in @ SV545 @ ( prop2set @ SV258 ) )
| SV258 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1558,plain,
! [SV546: $i] :
( ( ~ ( in @ SV546 @ ( prop2set @ $true ) )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1559,plain,
! [SV547: $i] :
( ( ~ ( in @ SV547 @ ( prop2set @ $false ) )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1560,plain,
! [SV548: $i,SV259: $i] :
( ( ! [SY3625: $i] :
( ~ ( func @ SV259 @ SV548 @ SY3625 )
| ! [SY3626: $i] :
( ~ ( in @ SY3626 @ SV259 )
| ! [SY3627: $i] :
( ~ ( in @ SY3627 @ SV548 )
| ~ ( in @ ( kpair @ SY3626 @ SY3627 ) @ SY3625 )
| ( ( ap @ SV259 @ SV548 @ SY3625 @ SY3626 )
= SY3627 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1561,plain,
! [SV549: $i,SV260: $i] :
( ( ~ ( breln1 @ SV260 @ SV549 )
| ! [SY3628: $i] :
( ~ ( breln1 @ SV260 @ SY3628 )
| ~ ! [SY3629: $i] :
( ~ ( in @ SY3629 @ SV260 )
| ! [SY3630: $i] :
( ~ ( in @ SY3630 @ SV260 )
| ~ ( in @ ( kpair @ SY3629 @ SY3630 ) @ SV549 )
| ( in @ ( kpair @ SY3629 @ SY3630 ) @ SY3628 ) ) )
| ~ ! [SY3631: $i] :
( ~ ( in @ SY3631 @ SV260 )
| ! [SY3632: $i] :
( ~ ( in @ SY3632 @ SV260 )
| ~ ( in @ ( kpair @ SY3631 @ SY3632 ) @ SY3628 )
| ( in @ ( kpair @ SY3631 @ SY3632 ) @ SV549 ) ) )
| ( SV549 = SY3628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1562,plain,
! [SV550: $i,SV261: $i] :
( ( ~ ( breln1 @ SV261 @ SV550 )
| ( breln1 @ SV261 @ ( breln1invset @ SV261 @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1563,plain,
! [SV551: $i > $o,SV262: $i] :
( ( ! [SY3633: $i] :
( ~ ( in @ SY3633
@ ( dsetconstr @ SV262
@ ^ [SY3634: $i] : ( SV551 @ SY3634 ) ) )
| ( SV551 @ SY3633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1564,plain,
! [SV552: $i,SV263: $i] :
( ( ! [SY3635: $i] :
( ~ ( in @ SY3635 @ SV263 )
| ~ ( in @ SY3635 @ SV552 )
| ( in @ SY3635 @ ( binintersect @ SV263 @ SV552 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1565,plain,
! [SV553: $i,SV264: $i] :
( ( ~ ( breln1 @ SV264 @ SV553 )
| ! [SY3636: $i] :
( ~ ( breln1 @ SV264 @ SY3636 )
| ! [SY3637: $i] :
( ~ ( in @ SY3637 @ SV264 )
| ! [SY3638: $i] :
( ~ ( in @ SY3638 @ SV264 )
| ~ ( ( in @ ( kpair @ SY3637 @ SY3638 ) @ SV553 )
| ( in @ ( kpair @ SY3637 @ SY3638 ) @ SY3636 ) )
| ( in @ ( kpair @ SY3637 @ SY3638 ) @ ( binunion @ SV553 @ SY3636 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1566,plain,
! [SV554: $i,SV265: $i] :
( ( ! [SY3639: $i] :
( ~ ( in @ SY3639 @ SV265 )
| ! [SY3640: $i] :
( ~ ( in @ SY3640 @ SV554 )
| ( subset @ ( setadjoin @ SY3639 @ ( setadjoin @ SY3640 @ emptyset ) ) @ ( binunion @ SV265 @ SV554 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1567,plain,
! [SV266: $i,SV555: $i] :
( ( ~ ( in @ SV555 @ ( powerset @ SV266 ) )
| ! [SY3641: $i] :
( ~ ( in @ SY3641 @ ( powerset @ SV266 ) )
| ( in @ ( setminus @ SV266 @ SV555 ) @ ( powerset @ ( setminus @ SV266 @ ( binintersect @ SV555 @ SY3641 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1568,plain,
! [SV556: $i,SV267: $i] :
( ( ! [SY3642: $i] :
( ~ ( in @ SY3642 @ ( injFuncSet @ SV267 @ SV556 ) )
| ( in @ SY3642 @ ( funcSet @ SV267 @ SV556 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1569,plain,
! [SV557: $i,SV268: $i] :
( ( ! [SY3643: $i] :
( ~ ( in @ SY3643 @ ( surjFuncSet @ SV268 @ SV557 ) )
| ( surjective @ SV268 @ SV557 @ SY3643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1570,plain,
! [SV269: $i] :
( ( ( ~ ( in @ SV269 @ omega ) )
= $true )
| ( ( in @ ( omegaS @ SV269 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1231]) ).
thf(1571,plain,
! [SV270: $i,SV558: $i] :
( ( ~ ( in @ SV558 @ ( powerset @ SV270 ) )
| ! [SY3644: $i] :
( ~ ( in @ SY3644 @ ( powerset @ SV270 ) )
| ( ( setminus @ SV270 @ ( binunion @ SV558 @ SY3644 ) )
= ( binintersect @ ( setminus @ SV270 @ SV558 ) @ ( setminus @ SV270 @ SY3644 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1572,plain,
! [SV559: $i,SV271: $i] :
( ( ~ ( breln1 @ SV271 @ SV559 )
| ! [SY3645: $i > $o] :
( ~ ! [SY3646: $i] :
( ~ ( in @ SY3646 @ SV271 )
| ! [SY3647: $i] :
( ~ ( in @ SY3647 @ SV271 )
| ~ ( in @ ( kpair @ SY3646 @ SY3647 ) @ SV559 )
| ( SY3645 @ ( kpair @ SY3646 @ SY3647 ) ) ) )
| ! [SY3648: $i] :
( ~ ( in @ SY3648 @ SV559 )
| ( SY3645 @ SY3648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1573,plain,
! [SV560: $i,SV272: $i] :
( ( ! [SY3649: $i] :
( ~ ( in @ SY3649 @ SV272 )
| ~ ~ ( in @ SY3649 @ SV560 )
| ( in @ SY3649 @ ( symdiff @ SV272 @ SV560 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1574,plain,
! [SV561: $i,SV273: $i] :
( ( ! [SY3650: $i] :
( ~ ( in @ SY3650 @ SV273 )
| ! [SY3651: $i] :
( ~ ( in @ SY3651 @ SV561 )
| ( ( kfst @ ( kpair @ SY3650 @ SY3651 ) )
= SY3650 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1575,plain,
! [SV274: $i,SV562: $i] :
( ( ~ ( in @ SV562 @ ( powerset @ SV274 ) )
| ! [SY3652: $i] :
( ~ ( in @ SY3652 @ ( powerset @ SV274 ) )
| ~ ( subset @ ( setminus @ SV274 @ SY3652 ) @ ( setminus @ SV274 @ SV562 ) )
| ( subset @ SV562 @ SY3652 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1576,plain,
! [SV563: $i > $o,SV275: $i] :
( ( ~ ! [SY3653: $i] :
( ~ ( in @ SY3653 @ SV275 )
| ~ ( SV563 @ SY3653 ) )
| ~ ~ ! [SY3654: $i] :
~ ~ ( ~ ( in @ SY3654 @ SV275 )
| ~ ( SV563 @ SY3654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1577,plain,
! [SV564: $i,SV276: $i] :
( ( ~ ( subset @ SV276 @ SV564 )
| ( ( setminus @ SV276 @ SV564 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1578,plain,
! [SV277: $i,SV565: $i] :
( ( ~ ( in @ SV565 @ ( powerset @ SV277 ) )
| ! [SY3655: $i] :
( ~ ( in @ SY3655 @ ( powerset @ SV277 ) )
| ! [SY3656: $i] :
( ~ ( in @ SY3656 @ SV277 )
| ~ ( in @ SY3656 @ ( setminus @ SV277 @ ( binunion @ SV565 @ SY3655 ) ) )
| ( in @ SY3656 @ ( setminus @ SV277 @ SV565 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1579,plain,
! [SV566: $i,SV278: $i] :
( ( ~ ! [SY3657: $i] :
( ~ ( in @ SY3657 @ SV278 )
| ( in @ SY3657 @ SV566 ) )
| ~ ! [SY3658: $i] :
( ~ ( in @ SY3658 @ SV566 )
| ( in @ SY3658 @ SV278 ) )
| ( SV278 = SV566 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1580,plain,
! [SV567: $i,SV279: $i] :
( ( ! [SY3659: $i] :
( ~ ( in @ SY3659 @ ( binintersect @ SV279 @ SV567 ) )
| ( in @ SY3659 @ SV279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1581,plain,
! [SV568: $i,SV280: $i] :
( ( ~ ( breln1 @ SV280 @ SV568 )
| ! [SY3660: $i] :
( ~ ( breln1 @ SV280 @ SY3660 )
| ! [SY3661: $i] :
( ~ ( in @ SY3661 @ SV280 )
| ! [SY3662: $i] :
( ~ ( in @ SY3662 @ SV280 )
| ~ ( in @ ( kpair @ SY3661 @ SY3662 ) @ ( breln1compset @ SV280 @ SV568 @ SY3660 ) )
| ! [SY3663: $o] :
( ~ ! [SY3664: $i] :
( ~ ( in @ SY3664 @ SV280 )
| ~ ( in @ ( kpair @ SY3661 @ SY3664 ) @ SV568 )
| ~ ( in @ ( kpair @ SY3664 @ SY3662 ) @ SY3660 )
| SY3663 )
| SY3663 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1582,plain,
! [SV569: $i,SV281: $i] :
( ( ~ ( subset @ SV281 @ SV569 )
| ( ( binintersect @ SV281 @ SV569 )
= SV281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1583,plain,
! [SV570: $i,SV282: $i] :
( ( ! [SY3665: $i] :
( ~ ~ ( in @ SY3665 @ SV282 )
| ~ ( in @ SY3665 @ SV570 )
| ( in @ SY3665 @ ( symdiff @ SV282 @ SV570 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1584,plain,
! [SV571: $i,SV283: $i] :
( ( ! [SY3666: $i,SY3667: $i] :
( ~ ( in @ ( kpair @ SY3666 @ SY3667 ) @ ( cartprod @ SV283 @ SV571 ) )
| ( in @ SY3667 @ SV571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1585,plain,
! [SV572: $i,SV284: $i] :
( ( ~ ~ ~ ! [SY3668: $i] :
~ ~ ( ~ ( in @ SY3668 @ SV284 )
| ~ ( in @ SY3668 @ SV572 ) )
| ( ( binintersect @ SV284 @ SV572 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1586,plain,
! [SV573: $i,SV285: $i] :
( ( ! [SY3669: $i] :
( ~ ( in @ SY3669 @ SV285 )
| ( in @ SY3669 @ ( binunion @ SV285 @ SV573 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1587,plain,
! [SV286: $i,SV574: $i] :
( ( ~ ( in @ SV574 @ SV286 )
| ( in @ SV574 @ ( powerset @ ( setunion @ SV286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1588,plain,
! [SV287: $i] :
( ( ( ~ ( iskpair @ SV287 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV287 )
@ ^ [SY3116: $i] :
( SV287
= ( kpair @ ( kfst @ SV287 ) @ SY3116 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1589,plain,
! [SV288: $i > $o] :
( ( ( ~ ~ ! [SY3117: $i] :
~ ~ ( ~ ( SV288 @ SY3117 )
| ~ ! [SY3118: $i] :
( ~ ( SV288 @ SY3118 )
| ( SY3117 = SY3118 ) ) ) )
= $true )
| ( ( ! [SY3119: $i,SY3120: $i] :
( ~ ( SV288 @ SY3119 )
| ~ ( SV288 @ SY3120 )
| ( SY3119 = SY3120 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1250]) ).
thf(1590,plain,
! [SV575: $i > $o,SV289: $i] :
( ( ~ ~ ~ ! [SY3670: $i] :
~ ~ ( ~ ( in @ SY3670 @ SV289 )
| ~ ( SV575 @ SY3670 ) )
| ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV289 )
| ~ ( SV575 @ SY3671 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1591,plain,
! [SV290: $i,SV576: $i] :
( ( ~ ( in @ SV576 @ ( powerset @ SV290 ) )
| ( subset @ ( setminus @ SV290 @ ( setminus @ SV290 @ SV576 ) ) @ SV576 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1592,plain,
! [SV577: $i > $o,SV291: $i] :
( ( ! [SY3672: $i] :
( ~ ( in @ SY3672 @ SV291 )
| ~ ( SV577 @ SY3672 )
| ( in @ SY3672
@ ( dsetconstr @ SV291
@ ^ [SY3673: $i] : ( SV577 @ SY3673 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1593,plain,
! [SV578: $i,SV292: $i] :
( ( ~ ( breln1 @ SV292 @ SV578 )
| ! [SY3674: $i] :
( ~ ( breln1 @ SV292 @ SY3674 )
| ( breln1 @ SV292 @ ( binunion @ SV578 @ SY3674 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1594,plain,
! [SV579: $i,SV293: $i] :
( ( ! [SY3675: $i > $i > $o,SY3676: $i] :
( ~ ( in @ SY3676 @ SV293 )
| ! [SY3677: $i] :
( ~ ( in @ SY3677 @ SV579 )
| ~ ( SY3675 @ SY3676 @ SY3677 )
| ( in @ ( kpair @ SY3676 @ SY3677 )
@ ( dpsetconstr @ SV293 @ SV579
@ ^ [SX5: $i,SX6: $i] : ( SY3675 @ SX5 @ SX6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1595,plain,
! [SV294: $i] :
( ( ( ~ ( singleton @ SV294 ) )
= $true )
| ( ( ! [SY3136: $i] :
( ~ ( in @ SY3136 @ SV294 )
| ( ( setunion @ SV294 )
= SY3136 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1256]) ).
thf(1596,plain,
! [SV580: $i,SV295: $i] :
( ( ~ ( in @ SV295 @ ( setadjoin @ SV580 @ emptyset ) )
| ( in @ SV580 @ ( setadjoin @ SV295 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1597,plain,
! [SV581: $i,SV296: $i] :
( ( ~ ~ ( subset @ SV296 @ SV581 )
| ( SV296 != SV581 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1598,plain,
! [SV582: $i,SV297: $i] :
( ( ~ ( breln1 @ SV297 @ SV582 )
| ! [SY3680: $i] :
( ~ ( breln1 @ SV297 @ SY3680 )
| ( ( binunion @ SV582 @ SY3680 )
= ( binunion @ SY3680 @ SV582 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1599,plain,
! [SV583: $i,SV298: $i] :
( ( ! [SY3681: $i,SY3682: $o] :
( ~ ( in @ SY3681 @ ( binunion @ SV298 @ SV583 ) )
| ~ ( ~ ( in @ SY3681 @ SV298 )
| SY3682 )
| ~ ( ~ ( in @ SY3681 @ SV583 )
| SY3682 )
| SY3682 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1600,plain,
! [SV299: $i,SV584: $i] :
( ( ~ ( in @ SV584 @ ( powerset @ SV299 ) )
| ! [SY3683: $i] :
( ~ ( in @ SY3683 @ ( powerset @ SV299 ) )
| ~ ! [SY3684: $i] :
( ~ ( in @ SY3684 @ SV299 )
| ~ ( in @ SY3684 @ SV584 )
| ( in @ SY3684 @ SY3683 ) )
| ~ ! [SY3685: $i] :
( ~ ( in @ SY3685 @ SV299 )
| ~ ( in @ SY3685 @ SY3683 )
| ( in @ SY3685 @ SV584 ) )
| ( SV584 = SY3683 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1601,plain,
! [SV585: $i,SV300: $i] :
( ( ~ ( breln1 @ SV300 @ SV585 )
| ! [SY3686: $i] :
( ~ ( breln1 @ SV300 @ SY3686 )
| ! [SY3687: $i] :
( ~ ( in @ SY3687 @ SV300 )
| ! [SY3688: $i] :
( ~ ( in @ SY3688 @ SV300 )
| ~ ( in @ ( kpair @ SY3687 @ SY3688 ) @ SV585 )
| ( in @ ( kpair @ SY3687 @ SY3688 ) @ ( binunion @ SV585 @ SY3686 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1602,plain,
! [SV586: $i,SV301: $i] :
( ( ! [SY3689: $i] :
( ~ ( func @ SV301 @ SV586 @ SY3689 )
| ! [SY3690: $i] :
( ~ ( func @ SV301 @ SV586 @ SY3690 )
| ~ ! [SY3691: $i] :
( ~ ( in @ SY3691 @ SV301 )
| ( ( ap @ SV301 @ SV586 @ SY3689 @ SY3691 )
= ( ap @ SV301 @ SV586 @ SY3690 @ SY3691 ) ) )
| ! [SY3692: $i] :
( ~ ( in @ SY3692 @ SV301 )
| ! [SY3693: $i] :
( ~ ( in @ SY3693 @ SV586 )
| ~ ( in @ ( kpair @ SY3692 @ SY3693 ) @ SY3690 )
| ( in @ ( kpair @ SY3692 @ SY3693 ) @ SY3689 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1603,plain,
! [SV302: $i,SV587: $i] :
( ( ~ ( in @ SV587 @ ( powerset @ SV302 ) )
| ! [SY3694: $i] :
( ~ ( in @ SY3694 @ ( powerset @ SV302 ) )
| ! [SY3695: $i] :
( ~ ( in @ SY3695 @ SV302 )
| ~ ( in @ SY3695 @ ( binunion @ ( setminus @ SV302 @ SV587 ) @ ( setminus @ SV302 @ SY3694 ) ) )
| ( in @ SY3695 @ ( setminus @ SV302 @ ( binintersect @ SV587 @ SY3694 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1604,plain,
! [SV303: $i] :
( ( ( ~ ( in @ SV303 @ emptyset ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1265]) ).
thf(1605,plain,
! [SV304: $i,SV588: $i] :
( ( ~ ( in @ SV588 @ ( powerset @ SV304 ) )
| ( SV588
= ( setminus @ SV304 @ ( setminus @ SV304 @ SV588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1606,plain,
! [SV305: $i,SV589: $i] :
( ( ~ ( in @ SV589 @ ( powerset @ SV305 ) )
| ! [SY3696: $i] :
( ~ ( in @ SY3696 @ ( powerset @ SV305 ) )
| ! [SY3697: $i] :
( ~ ( in @ SY3697 @ ( powerset @ SV305 ) )
| ( in @ ( binintersect @ SV589 @ SY3696 ) @ ( powerset @ ( binintersect @ ( binunion @ SV589 @ SY3697 ) @ ( binunion @ SY3696 @ SY3697 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1607,plain,
! [SV306: $i] :
( ( ( ~ ! [SY3165: $i] :
~ ( in @ SY3165 @ SV306 ) )
= $true )
| ( ( SV306 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1268]) ).
thf(1608,plain,
! [SV307: $i,SV590: $i] :
( ( ~ ( in @ SV590 @ ( powerset @ SV307 ) )
| ! [SY3698: $i] :
( ~ ( in @ SY3698 @ ( powerset @ SV307 ) )
| ! [SY3699: $i] :
( ~ ( in @ SY3699 @ SV307 )
| ~ ( in @ SY3699 @ ( binintersect @ ( setminus @ SV307 @ SV590 ) @ ( setminus @ SV307 @ SY3698 ) ) )
| ( in @ SY3699 @ ( setminus @ SV307 @ ( binunion @ SV590 @ SY3698 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1609,plain,
! [SV308: $i,SV591: $i] :
( ( ~ ( in @ SV591 @ ( powerset @ SV308 ) )
| ! [SY3700: $i] :
( ~ ( in @ SY3700 @ ( powerset @ SV308 ) )
| ~ ! [SY3701: $i] :
( ~ ( in @ SY3701 @ SV308 )
| ~ ( in @ SY3701 @ SV591 )
| ( in @ SY3701 @ SY3700 ) )
| ( in @ SV591 @ ( powerset @ SY3700 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1610,plain,
! [SV309: $i,SV592: $i] :
( ( ~ ( in @ SV592 @ ( powerset @ SV309 ) )
| ! [SY3702: $i] :
( ~ ( in @ SY3702 @ ( powerset @ SV309 ) )
| ! [SY3703: $i] :
( ~ ( in @ SY3703 @ SV309 )
| ~ ( in @ SY3703 @ ( setminus @ SV309 @ SV592 ) )
| ~ ( in @ SY3703 @ ( setminus @ SV309 @ SY3702 ) )
| ( in @ SY3703 @ ( setminus @ SV309 @ ( binunion @ SV592 @ SY3702 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1611,plain,
! [SV310: $i,SV593: $i] :
( ( ~ ( in @ SV593 @ ( powerset @ SV310 ) )
| ( in @ ( setminus @ SV310 @ SV593 ) @ ( powerset @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1612,plain,
! [SV594: $i,SV311: $i] :
( ( ~ ( ( SV311 != SV594 ) )
| ~ ( in @ SV594 @ ( setadjoin @ SV311 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1613,plain,
! [SV312: $i,SV595: $i] :
( ( ! [SY3704: $i] :
( ~ ( in @ SY3704 @ SV595 )
| ( in @ SY3704 @ ( binunion @ SV312 @ SV595 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1614,plain,
! [SV596: $i,SV313: $i] :
( ( ! [SY3705: $i] :
( ~ ( in @ SY3705 @ SV313 )
| ! [SY3706: $i] :
( ~ ( in @ SY3706 @ SV596 )
| ( in @ ( setadjoin @ SY3705 @ ( setadjoin @ SY3706 @ emptyset ) ) @ ( powerset @ ( binunion @ SV313 @ SV596 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1615,plain,
! [SV597: $i,SV314: $i] :
( ( ! [SY3707: $i] :
( ~ ( in @ SY3707 @ SV314 )
| ! [SY3708: $i] :
( ~ ( in @ SY3708 @ SV597 )
| ( ( ksnd @ ( kpair @ SY3707 @ SY3708 ) )
= SY3708 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1616,plain,
! [SV315: $i,SV598: $i] :
( ( ~ ( in @ SV598 @ ( powerset @ SV315 ) )
| ! [SY3709: $i] :
( ~ ( in @ SY3709 @ ( powerset @ SV315 ) )
| ! [SY3710: $i] :
( ~ ( in @ SY3710 @ SV315 )
| ~ ( in @ SY3710 @ ( setminus @ SV315 @ ( binunion @ SV598 @ SY3709 ) ) )
| ~ ( in @ SY3710 @ SV598 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1617,plain,
! [SV316: $i > $o] :
( ( ( ~ ~ ! [SY3188: $i] :
~ ~ ( ~ ( SV316 @ SY3188 )
| ~ ! [SY3189: $i] :
( ~ ( SV316 @ SY3189 )
| ( SY3188 = SY3189 ) ) ) )
= $true )
| ( ( ~ ! [SY3190: $i] :
~ ! [SY3191: $i] :
~ ( ~ ( ~ ( SV316 @ SY3191 )
| ( SY3191 = SY3190 ) )
| ~ ( ( SY3191 != SY3190 )
| ( SV316 @ SY3191 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1278]) ).
thf(1618,plain,
! [SV317: $i,SV599: $i] :
( ( ~ ( in @ SV599 @ ( powerset @ SV317 ) )
| ! [SY3711: $i] :
( ~ ( in @ SY3711 @ ( powerset @ SV317 ) )
| ! [SY3712: $i] :
( ~ ( in @ SY3712 @ ( powerset @ SV317 ) )
| ! [SY3713: $i] :
( ~ ( in @ SY3713 @ ( powerset @ SV317 ) )
| ~ ( subset @ SV599 @ SY3712 )
| ~ ( subset @ SY3711 @ SY3713 )
| ( subset @ ( binintersect @ SV599 @ SY3711 ) @ ( binintersect @ SY3712 @ SY3713 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1619,plain,
! [SV318: $i,SV600: $i] :
( ( ~ ( in @ SV600 @ ( powerset @ SV318 ) )
| ! [SY3714: $i] :
( ~ ( in @ SY3714 @ ( powerset @ SV318 ) )
| ! [SY3715: $i] :
( ~ ( in @ SY3715 @ SV318 )
| ~ ~ ( in @ SY3715 @ SY3714 )
| ~ ( in @ SY3715 @ ( binintersect @ SV600 @ SY3714 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1620,plain,
! [SV601: $i,SV319: $i] :
( ( ! [SY3716: $i] :
( ~ ( breln @ SV319 @ SV601 @ SY3716 )
| ! [SY3717: $i > $o] :
( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV319 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV601 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SY3716 )
| ( SY3717 @ ( kpair @ SY3718 @ SY3719 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3716 )
| ( SY3717 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1621,plain,
! [SV602: $i,SV320: $i] :
( ( ~ ! [SY3721: $i] :
( ~ ( in @ SY3721 @ SV320 )
| ( in @ SY3721 @ SV602 ) )
| ( subset @ SV320 @ SV602 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1622,plain,
! [SV603: $o,SV321: $i] :
( ( ! [SY3722: $i] :
( ~ ( in @ SY3722 @ SV321 )
| ! [SY3723: $i] :
( ~ ( in @ SY3723 @ SV321 )
| ~ ~ SV603
| ( ( if @ SV321 @ SV603 @ SY3722 @ SY3723 )
= SY3723 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1283]) ).
thf(1623,plain,
! [SV321: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV321 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV321 )
| ~ ~ $true
| ( ( if @ SV321 @ $true @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1283]) ).
thf(1624,plain,
! [SV321: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV321 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV321 )
| ~ ~ $false
| ( ( if @ SV321 @ $false @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1283]) ).
thf(1625,plain,
! [SV322: $i] :
( ( ( ~ ~ ! [SY3210: $i] :
~ ( in @ SY3210 @ SV322 ) )
= $true )
| ( ( ~ ! [SY3211: $i] :
~ ~ ( ~ ( in @ SY3211 @ SV322 )
| ~ ~ ~ ! [SY3212: $i] :
~ ~ ( ~ ( in @ SY3212 @ SY3211 )
| ~ ( in @ SY3212 @ SV322 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1284]) ).
thf(1626,plain,
! [SV604: $i,SV323: $i] :
( ( ! [SY3724: $i,SY3725: $i] :
( ~ ( in @ ( kpair @ SY3724 @ SY3725 ) @ ( cartprod @ SV323 @ SV604 ) )
| ( in @ SY3724 @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1627,plain,
! [SV605: $i,SV324: $i] :
( ( ~ ! [SY3726: $i] :
( ~ ( in @ SY3726 @ SV324 )
| ( in @ SY3726 @ SV605 ) )
| ( subset @ SV324 @ SV605 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1628,plain,
! [SV325: $i,SV606: $i] :
( ( ~ ( in @ SV606 @ ( powerset @ SV325 ) )
| ! [SY3727: $i] :
( ~ ( in @ SY3727 @ ( powerset @ SV325 ) )
| ! [SY3728: $i] :
( ~ ( in @ SY3728 @ ( powerset @ SV325 ) )
| ~ ( subset @ SV606 @ SY3727 )
| ~ ( subset @ SV606 @ SY3728 )
| ( subset @ SV606 @ ( binintersect @ SY3727 @ SY3728 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1629,plain,
! [SV607: $i > $i > $o,SV327: $i,SV3: $i] :
( ( breln @ SV3 @ SV327
@ ( dpsetconstr @ SV3 @ SV327
@ ^ [SY3729: $i,SY3730: $i] : ( SV607 @ SY3729 @ SY3730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1630,plain,
! [SV608: $i > $i > $o,SV328: $i,SV4: $i] :
( ( subset
@ ( dpsetconstr @ SV4 @ SV328
@ ^ [SY3731: $i,SY3732: $i] : ( SV608 @ SY3731 @ SY3732 ) )
@ ( cartprod @ SV4 @ SV328 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1631,plain,
! [SV609: $i,SV337: $i,SV16: $i] :
( ( ( binintersect @ SV16 @ ( binunion @ SV337 @ SV609 ) )
= ( binunion @ ( binintersect @ SV16 @ SV337 ) @ ( binintersect @ SV16 @ SV609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1632,plain,
! [SV349: $i,SV36: $i] :
( ( ( ~ ( in @ SV36 @ ( setadjoin @ SV349 @ emptyset ) ) )
= $true )
| ( ( SV36 = SV349 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1314]) ).
thf(1633,plain,
! [SV37: $i] :
( ( ( SV37 != emptyset )
= $false )
| ( ( ~ ! [SY2402: $i] :
~ ~ ( ~ ( in @ SY2402 @ SV37 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1315]) ).
thf(1634,plain,
! [SV38: $i] :
( ( ( in @ SV38 @ omega )
= $false )
| ( ( ! [SY2403: $i] :
( ~ ( in @ SY2403 @ omega )
| ( ( omegaS @ SV38 )
!= ( omegaS @ SY2403 ) )
| ( SV38 = SY2403 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1316]) ).
thf(1635,plain,
! [SV350: $i,SV610: $i > $i,SV39: $i] :
( ( ~ ! [SY3733: $i] :
( ~ ( in @ SY3733 @ SV39 )
| ( in @ ( SV610 @ SY3733 ) @ SV350 ) )
| ( func @ SV39 @ SV350
@ ( dpsetconstr @ SV39 @ SV350
@ ^ [SY3734: $i,SY3735: $i] :
( ( SV610 @ SY3734 )
= SY3735 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1636,plain,
! [SV40: $i > $o] :
( ( ( ~ ! [SY2409: $i] :
~ ~ ( ~ ( SV40 @ SY2409 )
| ~ ! [SY2410: $i] :
( ~ ( SV40 @ SY2410 )
| ( SY2409 = SY2410 ) ) ) )
= $false )
| ( ( ~ ! [SY2411: $i] :
~ ( SV40 @ SY2411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1637,plain,
! [SV351: $i,SV41: $i,SV611: $i] :
( ( ~ ( in @ SV611 @ SV41 )
| ! [SY3736: $i] :
( ~ ( in @ SY3736 @ SV351 )
| ( ( kpair @ SV611 @ SY3736 )
= ( kpair @ SV611 @ SY3736 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1638,plain,
! [SV42: $i > $o] :
( ( ( ~ ! [SY2415: $i] :
~ ~ ( ~ ( SV42 @ SY2415 )
| ~ ! [SY2416: $i] :
( ~ ( SV42 @ SY2416 )
| ( SY2415 = SY2416 ) ) ) )
= $false )
| ( ( SV42
@ ( descr
@ ^ [SY2417: $i] : ( SV42 @ SY2417 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1639,plain,
! [SV352: $i,SV43: $i] :
( ( ( SV43 != SV352 )
= $true )
| ( ( ( powerset @ SV43 )
= ( powerset @ SV352 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1321]) ).
thf(1640,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ( ~ ! [SY3238: $i] :
( ~ ( in @ SY3238 @ SV44 )
| ! [SY3239: $i] :
( ~ ( in @ SY3239 @ SV44 )
| ~ ( SV353 @ SY3238 )
| ~ ( SV353 @ SY3239 )
| ( SY3238 = SY3239 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) )
| ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1641,plain,
! [SV354: $i,SV45: $i,SV612: $i] :
( ( ~ ( in @ SV612 @ ( funcSet @ SV45 @ SV354 ) )
| ! [SY3737: $i] :
( ~ ( in @ SY3737 @ ( funcSet @ SV45 @ SV354 ) )
| ~ ! [SY3738: $i] :
( ~ ( in @ SY3738 @ SV45 )
| ( ( ap @ SV45 @ SV354 @ SV612 @ SY3738 )
= ( ap @ SV45 @ SV354 @ SY3737 @ SY3738 ) ) )
| ( SV612 = SY3737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1642,plain,
! [SV355: $i,SV46: $i,SV613: $i] :
( ( ~ ( in @ SV613 @ SV46 )
| ( in @ ( setadjoin @ SV613 @ emptyset ) @ ( powerset @ ( binunion @ SV46 @ SV355 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1643,plain,
! [SV356: $i,SV47: $i,SV614: $i] :
( ( ~ ( in @ SV614 @ ( funcSet @ SV47 @ SV356 ) )
| ! [SY3739: $i] :
( ~ ( in @ SY3739 @ SV47 )
| ( in @ ( kpair @ SY3739 @ ( ap @ SV47 @ SV356 @ SV614 @ SY3739 ) ) @ SV614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1644,plain,
! [SV615: $i,SV357: $i,SV48: $i] :
( ( ! [SY3740: $i] :
( ( ( setadjoin @ ( setadjoin @ SV48 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV48 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV615 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV615 @ ( setadjoin @ SY3740 @ emptyset ) ) @ emptyset ) ) )
| ( SV357 = SY3740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1645,plain,
! [SV358: $i,SV49: $i,SV616: $i] :
( ( ~ ( in @ SV616 @ ( funcSet @ SV49 @ SV358 ) )
| ! [SY3741: $i] :
( ~ ( in @ SY3741 @ SV49 )
| ( in @ ( ap @ SV49 @ SV358 @ SV616 @ SY3741 ) @ SV358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1646,plain,
! [SV359: $i,SV50: $i] :
( ( ( SV50 != SV359 )
= $true )
| ( ( ! [SY3252: $i,SY3253: $i] :
( ( SY3252 != SY3253 )
| ( ( setadjoin @ SV50 @ SY3252 )
= ( setadjoin @ SV359 @ SY3253 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1328]) ).
thf(1647,plain,
! [SV360: $i,SV51: $i,SV617: $i] :
( ( ~ ( in @ SV617 @ ( funcSet @ SV51 @ SV360 ) )
| ( func @ SV51 @ SV360 @ SV617 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1648,plain,
! [SV52: $i,SV361: $i] :
( ( ( ~ ( in @ SV361 @ ( powerset @ SV52 ) ) )
= $true )
| ( ( ! [SY3255: $i] :
( ~ ( in @ SY3255 @ ( powerset @ SV52 ) )
| ! [SY3256: $i] :
( ~ ( in @ SY3256 @ ( powerset @ SV52 ) )
| ! [SY3257: $i] :
( ~ ( in @ SY3257 @ SV52 )
| ~ ( in @ SY3257 @ ( binintersect @ SV361 @ SY3255 ) )
| ( in @ SY3257 @ ( binunion @ SY3255 @ SY3256 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1330]) ).
thf(1649,plain,
! [SV53: $i,SV362: $i] :
( ( ( ~ ( subset @ SV362 @ SV53 ) )
= $true )
| ( ( ( binintersect @ SV53 @ SV362 )
= SV362 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1650,plain,
! [SV363: $i,SV618: $i > $i,SV54: $i] :
( ( ~ ! [SY3742: $i] :
( ~ ( in @ SY3742 @ SV54 )
| ( in @ ( SV618 @ SY3742 ) @ SV363 ) )
| ( in
@ ( lam @ SV54 @ SV363
@ ^ [SY3743: $i] : ( SV618 @ SY3743 ) )
@ ( funcSet @ SV54 @ SV363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1651,plain,
! [SV55: $i,SV364: $i] :
( ( ( ~ ( in @ SV364 @ ( powerset @ SV55 ) ) )
= $true )
| ( ( ! [SY3261: $i] :
( ~ ( in @ SY3261 @ ( powerset @ SV55 ) )
| ~ ( subset @ SV364 @ ( setminus @ SV55 @ SY3261 ) )
| ( subset @ SY3261 @ ( setminus @ SV55 @ SV364 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1652,plain,
! [SV56: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ ( powerset @ SV56 ) ) )
= $true )
| ( ( ! [SY3262: $i] :
( ~ ( in @ SY3262 @ ( powerset @ SV56 ) )
| ! [SY3263: $i] :
( ~ ( in @ SY3263 @ ( powerset @ SV56 ) )
| ! [SY3264: $i] :
( ~ ( in @ SY3264 @ ( powerset @ SV56 ) )
| ( ( setminus @ SV56 @ ( binintersect @ ( binunion @ SV365 @ SY3262 ) @ ( binunion @ SY3263 @ SY3264 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV56 @ SV365 ) @ ( setminus @ SV56 @ SY3262 ) ) @ ( binintersect @ ( setminus @ SV56 @ SY3263 ) @ ( setminus @ SV56 @ SY3264 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1653,plain,
! [SV57: $i,SV366: $i] :
( ( ~ ( ~ ( in @ SV366 @ ( setunion @ SV57 ) )
| ~ ! [SY3265: $i] :
~ ~ ( ~ ( in @ SV366 @ SY3265 )
| ~ ( in @ SY3265 @ SV57 ) ) )
| ~ ( ~ ~ ! [SY3266: $i] :
~ ~ ( ~ ( in @ SV366 @ SY3266 )
| ~ ( in @ SY3266 @ SV57 ) )
| ( in @ SV366 @ ( setunion @ SV57 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1654,plain,
! [SV58: $i > $o] :
( ( ( ~ ! [SY2462: $i] :
~ ~ ( ~ ( SV58 @ SY2462 )
| ~ ! [SY2463: $i] :
( ~ ( SV58 @ SY2463 )
| ( SY2462 = SY2463 ) ) ) )
= $false )
| ( ( ! [SY2464: $i,SY2465: $i] :
( ~ ( SV58 @ SY2464 )
| ~ ( SV58 @ SY2465 )
| ( SY2464 = SY2465 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1655,plain,
! [SV59: $i > $o] :
( ( ( ~ ! [SY2466: $i] :
~ ! [SY2467: $i] :
~ ( ~ ( ~ ( SV59 @ SY2467 )
| ( SY2467 = SY2466 ) )
| ~ ( ( SY2467 != SY2466 )
| ( SV59 @ SY2467 ) ) ) )
= $false )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1656,plain,
! [SV60: $i > $o] :
( ( ( ~ ! [SY2470: $i] :
~ ~ ( ~ ( SV60 @ SY2470 )
| ~ ! [SY2471: $i] :
( ~ ( SV60 @ SY2471 )
| ( SY2470 = SY2471 ) ) ) )
= $false )
| ( ( ~ ! [SY2472: $i] :
~ ~ ( ~ ( SV60 @ SY2472 )
| ~ ! [SY2473: $i] :
( ~ ( SV60 @ SY2473 )
| ( SY2472 = SY2473 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1657,plain,
! [SV367: $i > $o,SV61: $i] :
( ( ( ~ ~ ! [SY3267: $i] :
( ~ ( in @ SY3267 @ SV61 )
| ( SV367 @ SY3267 ) ) )
= $true )
| ( ( ~ ! [SY3268: $i] :
~ ~ ( ~ ( in @ SY3268 @ SV61 )
| ~ ~ ( SV367 @ SY3268 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1339]) ).
thf(1658,plain,
! [SV62: $i > $o,SV368: $i] :
( ( ( ~ ( in @ SV368 @ emptyset ) )
= $true )
| ( ( SV62 @ SV368 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1659,plain,
! [SV619: $i,SV369: $i,SV63: $i] :
( ( ~ ( func @ SV63 @ SV369 @ SV619 )
| ! [SY3744: $i] :
( ~ ( in @ SY3744 @ SV63 )
| ( in @ ( ap @ SV63 @ SV369 @ SV619 @ SY3744 ) @ SV369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1660,plain,
! [SV370: $i,SV620: $i > $i,SV64: $i] :
( ( ~ ! [SY3745: $i] :
( ~ ( in @ SY3745 @ SV64 )
| ( in @ ( SV620 @ SY3745 ) @ SV370 ) )
| ( ( lam @ SV64 @ SV370
@ ^ [SY3746: $i] : ( SV620 @ SY3746 ) )
= ( lam @ SV64 @ SV370
@ ^ [SY3747: $i] : ( SV620 @ SY3747 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1661,plain,
! [SV371: $i,SV65: $i] :
( ( ( ~ ! [SY3275: $i] :
~ ( ~ ( ~ ( in @ SY3275 @ SV65 )
| ( in @ SY3275 @ SV371 ) )
| ~ ( ~ ( in @ SY3275 @ SV371 )
| ( in @ SY3275 @ SV65 ) ) ) )
= $true )
| ( ( SV65 = SV371 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1343]) ).
thf(1662,plain,
! [SV66: $i] :
( ( ( in @ SV66 @ emptyset )
= $false )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1344]) ).
thf(1663,plain,
! [SV67: $i] :
( ( ( subset @ SV67 @ emptyset )
= $false )
| ( ( SV67 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1345]) ).
thf(1664,plain,
! [SV68: $i,SV372: $i] :
( ( ( ~ ( in @ SV372 @ ( powerset @ SV68 ) ) )
= $true )
| ( ( ! [SY3276: $i] :
( ~ ( in @ SY3276 @ ( powerset @ SV68 ) )
| ~ ( subset @ SV372 @ ( setminus @ SV68 @ SY3276 ) )
| ! [SY3277: $i] :
( ~ ( in @ SY3277 @ SV68 )
| ~ ( in @ SY3277 @ SY3276 )
| ( in @ SY3277 @ ( setminus @ SV68 @ SV372 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1346]) ).
thf(1665,plain,
! [SV69: $i,SV373: $i] :
( ( ( ~ ( in @ SV373 @ ( powerset @ SV69 ) ) )
= $true )
| ( ( ! [SY3278: $i] :
( ~ ( in @ SY3278 @ ( powerset @ SV69 ) )
| ! [SY3279: $i] :
( ~ ( in @ SY3279 @ SV69 )
| ~ ( in @ SY3279 @ ( setminus @ SV69 @ ( binintersect @ SV373 @ SY3278 ) ) )
| ( in @ SY3279 @ ( binunion @ ( setminus @ SV69 @ SV373 ) @ ( setminus @ SV69 @ SY3278 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1347]) ).
thf(1666,plain,
! [SV374: $i,SV70: $i] :
( ( ( SV70 != SV374 )
= $true )
| ( ( in @ SV70 @ ( setadjoin @ SV374 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1348]) ).
thf(1667,plain,
! [SV71: $i,SV375: $i] :
( ( ( ~ ( in @ SV375 @ ( powerset @ SV71 ) ) )
= $true )
| ( ( ! [SY3280: $i] :
( ~ ( in @ SY3280 @ ( powerset @ SV71 ) )
| ( in @ ( binunion @ SV375 @ SY3280 ) @ ( powerset @ SV71 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1349]) ).
thf(1668,plain,
! [SV376: $i,SV72: $i,SV621: $i] :
( ( ~ ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
| ! [SY3748: $o] :
( ~ ( ( SV621 != SV72 )
| SY3748 )
| ~ ( ~ ( in @ SV621 @ SV376 )
| SY3748 )
| SY3748 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1669,plain,
! [SV377: $i,SV73: $i] :
( ( ( ~ ( breln1 @ SV73 @ SV377 ) )
= $true )
| ( ( ! [SY3283: $i] :
( ~ ( breln1 @ SV73 @ SY3283 )
| ( breln1 @ SV73 @ ( breln1compset @ SV73 @ SV377 @ SY3283 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1351]) ).
thf(1670,plain,
! [SV378: $i,SV74: $i] :
( ( ( ~ ( breln1 @ SV74 @ SV378 ) )
= $true )
| ( ( SV378
= ( breln1invset @ SV74 @ ( breln1invset @ SV74 @ SV378 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1352]) ).
thf(1671,plain,
! [SV75: $i,SV379: $i] :
( ( ( ~ ( in @ SV379 @ ( powerset @ SV75 ) ) )
= $true )
| ( ( ! [SY3284: $i] :
( ~ ( in @ SY3284 @ ( powerset @ SV75 ) )
| ! [SY3285: $i] :
( ~ ( in @ SY3285 @ SV75 )
| ~ ( in @ SY3285 @ ( setminus @ SV75 @ ( binunion @ SV379 @ SY3284 ) ) )
| ( in @ SY3285 @ ( setminus @ SV75 @ SY3284 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1353]) ).
thf(1672,plain,
! [SV380: $i > $i,SV76: $i,SV622: $i] :
( ( ~ ( ~ ( ~ ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3287: $i] : ( SV380 @ SY3287 ) ) )
| ~ ! [SY3750: $i] :
~ ~ ( ~ ( in @ SY3750 @ SV76 )
| ( SV622
!= ( SV380 @ SY3750 ) ) ) )
| ~ ( ~ ~ ! [SY3751: $i] :
~ ~ ( ~ ( in @ SY3751 @ SV76 )
| ( SV622
!= ( SV380 @ SY3751 ) ) )
| ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3290: $i] : ( SV380 @ SY3290 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1673,plain,
! [SV381: $i > $i,SV623: $i,SV77: $i] :
( ( ~ ~ ! [SY3753: $i] :
~ ~ ( ~ ( in @ SY3753 @ SV77 )
| ( SV623
!= ( SV381 @ SY3753 ) ) )
| ( in @ SV623
@ ( image1 @ SV77
@ ^ [SY3293: $i] : ( SV381 @ SY3293 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1674,plain,
! [SV382: $i,SV78: $i] :
( ( ( ~ ( breln1 @ SV78 @ SV382 ) )
= $true )
| ( ( ! [SY3294: $i] :
( ~ ( breln1 @ SV78 @ SY3294 )
| ! [SY3295: $i] :
( ~ ( in @ SY3295 @ SV78 )
| ! [SY3296: $i] :
( ~ ( in @ SY3296 @ SV78 )
| ~ ( in @ ( kpair @ SY3295 @ SY3296 ) @ ( breln1compset @ SV78 @ SV382 @ SY3294 ) )
| ~ ! [SY3297: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3297 @ SV78 )
| ~ ( in @ ( kpair @ SY3295 @ SY3297 ) @ SV382 ) )
| ~ ( in @ ( kpair @ SY3297 @ SY3296 ) @ SY3294 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1675,plain,
! [SV383: $i,SV79: $i,SV624: $i] :
( ( ~ ( in @ SV624 @ ( cartprod @ SV79 @ SV383 ) )
| ( in @ ( kfst @ SV624 ) @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1676,plain,
! [SV384: $i,SV80: $i,SV625: $i] :
( ( ~ ( ~ ( ~ ( in @ SV625 @ ( setadjoin @ SV80 @ SV384 ) )
| ( SV625 = SV80 )
| ( in @ SV625 @ SV384 ) )
| ~ ( ~ ( ( SV625 = SV80 )
| ( in @ SV625 @ SV384 ) )
| ( in @ SV625 @ ( setadjoin @ SV80 @ SV384 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1677,plain,
! [SV81: $i,SV385: $i,SV626: $i] :
( ( ~ ( in @ SV626 @ SV385 )
| ( in @ SV626 @ ( setadjoin @ SV81 @ SV385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1678,plain,
! [SV386: $i,SV82: $i] :
( ( ( ~ ( breln1 @ SV82 @ SV386 ) )
= $true )
| ( ( ! [SY3301: $i] :
( ~ ( breln1 @ SV82 @ SY3301 )
| ! [SY3302: $i] :
( ~ ( in @ SY3302 @ SV82 )
| ! [SY3303: $i] :
( ~ ( in @ SY3303 @ SV82 )
| ~ ( in @ ( kpair @ SY3302 @ SY3303 ) @ ( binunion @ SV386 @ SY3301 ) )
| ( in @ ( kpair @ SY3302 @ SY3303 ) @ SV386 )
| ( in @ ( kpair @ SY3302 @ SY3303 ) @ SY3301 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1360]) ).
thf(1679,plain,
! [SV83: $i,SV387: $i] :
( ( ( ~ ( subset @ SV387 @ SV83 ) )
= $true )
| ( ( in @ SV387 @ ( powerset @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1361]) ).
thf(1680,plain,
! [SV84: $i] :
( ( ( in @ SV84 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV84 @ SV84 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1681,plain,
! [SV85: $i,SV388: $i] :
( ( ( ~ ( in @ SV388 @ ( powerset @ SV85 ) ) )
= $true )
| ( ( ! [SY3304: $i] :
( ~ ( in @ SY3304 @ ( powerset @ SV85 ) )
| ( ( setminus @ SV85 @ ( binintersect @ SV388 @ SY3304 ) )
= ( binunion @ ( setminus @ SV85 @ SV388 ) @ ( setminus @ SV85 @ SY3304 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1363]) ).
thf(1682,plain,
! [SV86: $i,SV389: $i] :
( ( ( ~ ( in @ SV389 @ ( powerset @ SV86 ) ) )
= $true )
| ( ( ! [SY3305: $i] :
( ~ ( in @ SY3305 @ ( powerset @ SV86 ) )
| ! [SY3306: $i] :
( ~ ( in @ SY3306 @ SV86 )
| ~ ( subset @ SV389 @ ( setminus @ SV86 @ SY3305 ) )
| ~ ( in @ SY3306 @ SY3305 )
| ~ ( in @ SY3306 @ SV389 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1364]) ).
thf(1683,plain,
! [SV87: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ ( powerset @ SV87 ) ) )
= $true )
| ( ( ! [SY3307: $i] :
( ~ ( in @ SY3307 @ ( powerset @ SV87 ) )
| ! [SY3308: $i] :
( ~ ( in @ SY3308 @ SV87 )
| ~ ( subset @ SV390 @ SY3307 )
| ~ ~ ( in @ SY3308 @ SY3307 )
| ~ ( in @ SY3308 @ SV390 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1365]) ).
thf(1684,plain,
! [SV88: $i,SV391: $i] :
( ( ( ~ ( in @ SV391 @ ( powerset @ SV88 ) ) )
= $true )
| ( ( ! [SY3309: $i] :
( ~ ( in @ SY3309 @ ( powerset @ SV88 ) )
| ( subset @ ( setminus @ SV88 @ SV391 ) @ ( setminus @ SV88 @ ( binintersect @ SV391 @ SY3309 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1685,plain,
! [SV89: $i,SV392: $i] :
( ( ( ~ ( in @ SV392 @ ( powerset @ SV89 ) ) )
= $true )
| ( ( subset @ SV392 @ ( setminus @ SV89 @ ( setminus @ SV89 @ SV392 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1686,plain,
! [SV90: $i,SV393: $i] :
( ( ( ~ ( in @ SV393 @ ( powerset @ SV90 ) ) )
= $true )
| ( ( ! [SY3310: $i] :
( ~ ( in @ SY3310 @ ( powerset @ SV90 ) )
| ! [SY3311: $i] :
( ~ ( in @ SY3311 @ ( powerset @ SV90 ) )
| ! [SY3312: $i] :
( ~ ( in @ SY3312 @ SV90 )
| ~ ( in @ SY3312 @ ( binintersect @ SV393 @ SY3310 ) )
| ( in @ SY3312 @ ( binintersect @ ( binunion @ SV393 @ SY3311 ) @ ( binunion @ SY3310 @ SY3311 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1687,plain,
! [SV91: $o] :
( ( SV91 = $false )
| ( ( in @ emptyset @ ( prop2set @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1688,plain,
( ( $true = $false )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1370]) ).
thf(1689,plain,
( ( $false = $false )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1690,plain,
! [SV394: $i,SV92: $i,SV627: $i] :
( ( ~ ( in @ SV627 @ SV92 )
| ~ ~ ( in @ SV627 @ SV394 )
| ( in @ SV627 @ ( setminus @ SV92 @ SV394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1691,plain,
! [SV93: $i,SV395: $i] :
( ( ( ~ ( in @ SV395 @ SV93 ) )
= $true )
| ( ( in @ ( setadjoin @ SV395 @ emptyset ) @ ( powerset @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1692,plain,
! [SV94: $o] :
( ( SV94 = $false )
| ( ( set2prop @ ( prop2set @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1693,plain,
( ( $true = $false )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1375]) ).
thf(1694,plain,
( ( $false = $false )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1695,plain,
! [SV396: $i,SV95: $i,SV628: $i] :
( ( ~ ( in @ SV628 @ ( funcSet @ SV95 @ SV396 ) )
| ! [SY3755: $i] :
( ~ ( in @ SY3755 @ SV95 )
| ( ( ap @ SV95 @ SV396 @ SV628 @ SY3755 )
= ( ap @ SV95 @ SV396 @ SV628 @ SY3755 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1696,plain,
! [SV397: $i,SV96: $i,SV629: $i] :
( ( ~ ~ ( in @ SV629 @ ( setminus @ SV96 @ SV397 ) )
| ~ ( in @ SV629 @ SV96 )
| ( in @ SV629 @ SV397 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1697,plain,
! [SV398: $i,SV97: $i,SV630: $i] :
( ( ~ ( in @ SV630 @ ( cartprod @ SV97 @ SV398 ) )
| ( iskpair @ SV630 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1698,plain,
! [SV98: $i,SV399: $i] :
( ( ( ~ ( in @ SV399 @ ( powerset @ SV98 ) ) )
= $true )
| ( ( in @ ( powerset @ SV399 ) @ ( powerset @ ( powerset @ SV98 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1380]) ).
thf(1699,plain,
! [SV99: $i,SV400: $i] :
( ( ( ~ ( in @ SV400 @ ( powerset @ SV99 ) ) )
= $true )
| ( ( ! [SY3318: $i] :
( ~ ( in @ SY3318 @ ( powerset @ SV99 ) )
| ! [SY3319: $i] :
( ~ ( in @ SY3319 @ SV99 )
| ~ ( in @ SY3319 @ ( setminus @ SV99 @ ( binunion @ SV400 @ SY3318 ) ) )
| ( in @ SY3319 @ ( setminus @ SV99 @ SV400 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1700,plain,
! [SV100: $i > $o] :
( ( ( ~ ! [SY2562: $i] :
~ ( SV100 @ SY2562 ) )
= $false )
| ( ( ~ ! [SY2563: $i,SY2564: $i] :
( ~ ( SV100 @ SY2563 )
| ~ ( SV100 @ SY2564 )
| ( SY2563 = SY2564 ) )
| ~ ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1382]) ).
thf(1701,plain,
! [SV401: $i,SV101: $i] :
( ( ( ( setadjoin @ SV101 @ emptyset )
!= ( setadjoin @ SV401 @ emptyset ) )
= $true )
| ( ( SV101 = SV401 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1383]) ).
thf(1702,plain,
! [SV402: $i,SV102: $i,SV631: $i] :
( ( ~ ~ ( in @ SV631 @ ( setminus @ SV102 @ SV402 ) )
| ~ ~ ( in @ SV631 @ SV402 )
| ~ ( in @ SV631 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1703,plain,
! [SV403: $i,SV103: $i,SV632: $i] :
( ( ~ ( in @ SV632 @ ( funcSet @ SV103 @ SV403 ) )
| ( ( lam @ SV103 @ SV403
@ ^ [SY3756: $i] : ( ap @ SV103 @ SV403 @ SV632 @ SY3756 ) )
= SV632 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1704,plain,
! [SV404: $i > $o,SV104: $i] :
( ( ( ~ ~ ! [SY3323: $i] :
~ ~ ( ~ ( in @ SY3323 @ SV104 )
| ~ ~ ( SV404 @ SY3323 ) ) )
= $true )
| ( ( ~ ! [SY3324: $i] :
( ~ ( in @ SY3324 @ SV104 )
| ( SV404 @ SY3324 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1705,plain,
! [SV105: $i,SV405: $i] :
( ( ( ~ ( in @ SV405 @ ( funcSet @ SV105 @ ( powerset @ SV105 ) ) ) )
= $true )
| ( ( ~ ( surjective @ SV105 @ ( powerset @ SV105 ) @ SV405 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1706,plain,
! [SV106: $i] :
( ( ( ~ ( ~ ( in @ emptyset @ SV106 )
| ~ ! [SY2577: $i] :
( ~ ~ ( ~ ( in @ SY2577 @ omega )
| ~ ( in @ SY2577 @ SV106 ) )
| ( in @ ( setadjoin @ SY2577 @ SY2577 ) @ SV106 ) ) ) )
= $false )
| ( ( ! [SY2578: $i] :
( ~ ( in @ SY2578 @ omega )
| ( in @ SY2578 @ SV106 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1707,plain,
! [SV107: $i] :
( ( ( iskpair @ SV107 )
= $false )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV107 )
@ ^ [SY2579: $i] : ( in @ ( setadjoin @ SY2579 @ emptyset ) @ SV107 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1708,plain,
! [SV633: $i,SV406: $i,SV108: $i] :
( ( ~ ( func @ SV108 @ SV406 @ SV633 )
| ! [SY3757: $i] :
( ~ ( in @ SY3757 @ SV108 )
| ( singleton
@ ( dsetconstr @ SV406
@ ^ [SY3758: $i] : ( in @ ( kpair @ SY3757 @ SY3758 ) @ SV633 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1709,plain,
! [SV109: $i,SV407: $i] :
( ( ( ~ ( in @ SV407 @ ( powerset @ SV109 ) ) )
= $true )
| ( ( ! [SY3328: $i] :
( ~ ( in @ SY3328 @ ( powerset @ SV109 ) )
| ~ ! [SY3329: $i] :
( ~ ( in @ SY3329 @ SV109 )
| ~ ( in @ SY3329 @ SV407 )
| ( in @ SY3329 @ SY3328 ) )
| ( subset @ SV407 @ SY3328 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1710,plain,
! [SV110: $i,SV408: $i] :
( ( ( ~ ( in @ SV408 @ ( powerset @ SV110 ) ) )
= $true )
| ( ( ! [SY3330: $i] :
( ~ ( in @ SY3330 @ ( powerset @ SV110 ) )
| ! [SY3331: $i] :
( ~ ( in @ SY3331 @ SV110 )
| ~ ~ ( in @ SY3331 @ SV408 )
| ~ ( in @ SY3331 @ ( binintersect @ SV408 @ SY3330 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1392]) ).
thf(1711,plain,
! [SV409: $i,SV111: $i,SV634: $i] :
( ( ~ ( in @ SV634 @ ( cartprod @ SV111 @ SV409 ) )
| ( in @ ( ksnd @ SV634 ) @ SV409 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1712,plain,
! [SV410: $i,SV112: $i,SV635: $i] :
( ( ~ ( in @ SV635 @ SV112 )
| ! [SY3759: $i] :
( ~ ( in @ SY3759 @ SV410 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV635 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV635 @ ( setadjoin @ SY3759 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV112 @ SV410 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1713,plain,
! [SV113: $i,SV411: $i] :
( ( ( ~ ( in @ SV411 @ ( powerset @ SV113 ) ) )
= $true )
| ( ( ! [SY3335: $i] :
( ~ ( in @ SY3335 @ ( powerset @ SV113 ) )
| ! [SY3336: $i] :
( ~ ( in @ SY3336 @ SV113 )
| ~ ( in @ SY3336 @ ( setminus @ SV113 @ SV411 ) )
| ( in @ SY3336 @ ( setminus @ SV113 @ ( binintersect @ SV411 @ SY3335 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1395]) ).
thf(1714,plain,
! [SV114: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ ( powerset @ SV114 ) ) )
= $true )
| ( ( ! [SY3337: $i] :
( ~ ( in @ SY3337 @ SV114 )
| ~ ( in @ SY3337 @ SV412 )
| ~ ( in @ SY3337 @ ( setminus @ SV114 @ SV412 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1396]) ).
thf(1715,plain,
! [SV636: $i > $i > $o,SV413: $i,SV115: $i] :
( ( ! [SY3760: $i,SY3761: $i] :
( ~ ( in @ ( kpair @ SY3760 @ SY3761 )
@ ( dpsetconstr @ SV115 @ SV413
@ ^ [SY3762: $i,SY3763: $i] : ( SV636 @ SY3762 @ SY3763 ) ) )
| ( in @ SY3760 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1716,plain,
! [SV637: $i > $i > $o,SV414: $i,SV116: $i] :
( ( ! [SY3764: $i,SY3765: $i] :
( ~ ( in @ ( kpair @ SY3764 @ SY3765 )
@ ( dpsetconstr @ SV116 @ SV414
@ ^ [SY3766: $i,SY3767: $i] : ( SV637 @ SY3766 @ SY3767 ) ) )
| ( in @ SY3765 @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1717,plain,
! [SV415: $i,SV117: $i,SV638: $i] :
( ( ~ ( in @ SV638 @ ( setminus @ SV117 @ SV415 ) )
| ~ ( in @ SV638 @ SV415 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1718,plain,
! [SV416: $i > $o,SV118: $i,SV639: $i] :
( ( ~ ( in @ SV639 @ SV118 )
| ~ ( SV416 @ SV639 )
| ~ ! [SY3768: $i] :
( ~ ( in @ SY3768 @ SV118 )
| ~ ( SV416 @ SY3768 )
| ( SY3768 = SV639 ) )
| ( ex1 @ SV118
@ ^ [SY3351: $i] : ( SV416 @ SY3351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(1719,plain,
! [SV417: $i,SV119: $i] :
( ( ( ( setminus @ SV119 @ SV417 )
!= emptyset )
= $true )
| ( ( subset @ SV119 @ SV417 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1401]) ).
thf(1720,plain,
! [SV418: $i,SV120: $i,SV640: $i] :
( ( ~ ~ ( in @ SV640 @ SV120 )
| ~ ~ ( in @ SV640 @ SV418 )
| ~ ( in @ SV640 @ ( symdiff @ SV120 @ SV418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1721,plain,
! [SV419: $i,SV641: $i > $i,SV121: $i] :
( ( ~ ! [SY3770: $i] :
( ~ ( in @ SY3770 @ SV121 )
| ( in @ ( SV641 @ SY3770 ) @ SV419 ) )
| ! [SY3771: $i] :
( ~ ( in @ SY3771 @ SV121 )
| ( ( ap @ SV121 @ SV419
@ ( lam @ SV121 @ SV419
@ ^ [SY3772: $i] : ( SV641 @ SY3772 ) )
@ SY3771 )
= ( SV641 @ SY3771 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1722,plain,
! [SV420: $i,SV122: $i] :
( ( ( SV122 != SV420 )
= $true )
| ( ( ! [SY3357: $i > $o,SY3358: $i > $o] :
( ~ ! [SY3359: $i] :
( ~ ( in @ SY3359 @ SV122 )
| ! [SY3360: $i] :
( ~ ( in @ SY3360 @ SV420 )
| ( SY3359 != SY3360 )
| ~ ( ~ ( ~ ( SY3357 @ SY3359 )
| ( SY3358 @ SY3360 ) )
| ~ ( ~ ( SY3358 @ SY3360 )
| ( SY3357 @ SY3359 ) ) ) ) )
| ( ( dsetconstr @ SV122
@ ^ [SX4: $i] : ( SY3357 @ SX4 ) )
= ( dsetconstr @ SV420
@ ^ [SX4: $i] : ( SY3358 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1404]) ).
thf(1723,plain,
! [SV421: $i > $o,SV123: $i] :
( ( ( ~ ( ex1 @ SV123
@ ^ [SY3363: $i] : ( SV421 @ SY3363 ) ) )
= $true )
| ( ( ! [SY3364: $i] :
( ~ ( in @ SY3364 @ SV123 )
| ! [SY3365: $i] :
( ~ ( in @ SY3365 @ SV123 )
| ~ ( SV421 @ SY3364 )
| ~ ( SV421 @ SY3365 )
| ( SY3364 = SY3365 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1724,plain,
! [SV422: $i,SV124: $i] :
( ( ( ~ ( in @ SV124 @ SV422 ) )
= $true )
| ( ( ~ ( in @ SV422 @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1725,plain,
! [SV423: $i,SV125: $i] :
( ( ( ~ ( breln1 @ SV125 @ SV423 ) )
= $true )
| ( ( ! [SY3366: $i] :
( ~ ( breln1 @ SV125 @ SY3366 )
| ! [SY3367: $i] :
( ~ ( in @ SY3367 @ SV125 )
| ! [SY3368: $i] :
( ~ ( in @ SY3368 @ SV125 )
| ~ ( in @ ( kpair @ SY3367 @ SY3368 ) @ SY3366 )
| ( in @ ( kpair @ SY3367 @ SY3368 ) @ ( binunion @ SV423 @ SY3366 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1407]) ).
thf(1726,plain,
! [SV424: $o,SV126: $i,SV642: $i] :
( ( ~ ( in @ SV642 @ SV126 )
| ! [SY3773: $i] :
( ~ ( in @ SY3773 @ SV126 )
| ~ ~ SV424
| ( in @ SY3773
@ ( dsetconstr @ SV126
@ ^ [SY3774: $i] :
( ~ ( ~ SV424
| ( SY3774 != SV642 ) )
| ~ ( ~ ~ SV424
| ( SY3774 != SY3773 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1727,plain,
! [SV126: $i,SV643: $i] :
( ( ~ ( in @ SV643 @ SV126 )
| ! [SY3775: $i] :
( ~ ( in @ SY3775 @ SV126 )
| ~ ~ $true
| ( in @ SY3775
@ ( dsetconstr @ SV126
@ ^ [SY3776: $i] :
( ~ ( ~ $true
| ( SY3776 != SV643 ) )
| ~ ( ~ ~ $true
| ( SY3776 != SY3775 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1728,plain,
! [SV126: $i,SV644: $i] :
( ( ~ ( in @ SV644 @ SV126 )
| ! [SY3777: $i] :
( ~ ( in @ SY3777 @ SV126 )
| ~ ~ $false
| ( in @ SY3777
@ ( dsetconstr @ SV126
@ ^ [SY3778: $i] :
( ~ ( ~ $false
| ( SY3778 != SV644 ) )
| ~ ( ~ ~ $false
| ( SY3778 != SY3777 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1729,plain,
! [SV425: $i,SV127: $i,SV645: $i] :
( ( ~ ( in @ SV645 @ ( setadjoin @ SV127 @ SV425 ) )
| ( SV645 = SV127 )
| ( in @ SV645 @ SV425 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1730,plain,
! [SV426: $i,SV128: $i,SV646: $i] :
( ( ~ ( in @ SV646 @ SV128 )
| ~ ( in @ SV646 @ SV426 )
| ~ ( in @ SV646 @ ( symdiff @ SV128 @ SV426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1731,plain,
! [SV129: $i] :
( ( ( ~ ! [SY2650: $i] :
~ ( in @ SY2650 @ SV129 ) )
= $false )
| ( ( SV129 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1413]) ).
thf(1732,plain,
! [SV130: $i,SV427: $i] :
( ( ~ ( ~ ( in @ SV427 @ ( powerset @ SV130 ) )
| ! [SY3374: $i] :
( ~ ( in @ SY3374 @ SV427 )
| ( in @ SY3374 @ SV130 ) ) )
| ~ ( ~ ! [SY3375: $i] :
( ~ ( in @ SY3375 @ SV427 )
| ( in @ SY3375 @ SV130 ) )
| ( in @ SV427 @ ( powerset @ SV130 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1733,plain,
! [SV428: $i,SV131: $i] :
( ( ( ~ ( breln1 @ SV131 @ SV428 ) )
= $true )
| ( ( ! [SY3376: $i] :
( ~ ( breln1 @ SV131 @ SY3376 )
| ! [SY3377: $i] :
( ~ ( in @ SY3377 @ SV131 )
| ! [SY3378: $i] :
( ~ ( in @ SY3378 @ SV131 )
| ! [SY3379: $i] :
( ~ ( in @ SY3379 @ SV131 )
| ~ ( in @ ( kpair @ SY3377 @ SY3379 ) @ SV428 )
| ~ ( in @ ( kpair @ SY3379 @ SY3378 ) @ SY3376 )
| ( in @ ( kpair @ SY3377 @ SY3378 ) @ ( breln1compset @ SV131 @ SV428 @ SY3376 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1415]) ).
thf(1734,plain,
! [SV132: $i,SV429: $i] :
( ( ( ~ ( in @ SV429 @ ( powerset @ SV132 ) ) )
= $true )
| ( ( ! [SY3380: $i] :
( ~ ( in @ SY3380 @ ( powerset @ SV132 ) )
| ( in @ ( setminus @ SV132 @ ( binunion @ SV429 @ SY3380 ) ) @ ( powerset @ ( setminus @ SV132 @ SV429 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1416]) ).
thf(1735,plain,
! [SV430: $i,SV133: $i,SV647: $i] :
( ( ~ ( in @ ( setadjoin @ SV647 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV133 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV133 @ ( setadjoin @ SV430 @ emptyset ) ) @ emptyset ) ) )
| ( SV133 = SV647 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1736,plain,
! [SV648: $i,SV431: $i,SV134: $i] :
( ( ( ( setadjoin @ SV134 @ ( setadjoin @ SV431 @ emptyset ) )
!= ( setadjoin @ SV648 @ emptyset ) )
| ( SV134 = SV431 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1737,plain,
! [SV432: $i,SV135: $i] :
( ( ( ~ ( breln1 @ SV135 @ SV432 ) )
= $true )
| ( ( ! [SY3383: $i] :
( ~ ( breln1 @ SV135 @ SY3383 )
| ~ ! [SY3384: $i] :
( ~ ( in @ SY3384 @ SV135 )
| ! [SY3385: $i] :
( ~ ( in @ SY3385 @ SV135 )
| ~ ( in @ ( kpair @ SY3384 @ SY3385 ) @ SV432 )
| ( in @ ( kpair @ SY3384 @ SY3385 ) @ SY3383 ) ) )
| ( subset @ SV432 @ SY3383 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1419]) ).
thf(1738,plain,
! [SV136: $i] :
( ( ( SV136 != emptyset )
= $false )
| ( ( ~ ! [SY2669: $i] :
~ ~ ( ~ ( in @ SY2669 @ SV136 )
| ( ( binintersect @ SY2669 @ SV136 )
!= emptyset ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1420]) ).
thf(1739,plain,
! [SV433: $i,SV137: $i,SV649: $i] :
( ( ~ ( in @ SV649 @ ( cartprod @ SV137 @ SV433 ) )
| ( ( kpair @ ( kfst @ SV649 ) @ ( ksnd @ SV649 ) )
= SV649 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1740,plain,
! [SV434: $i,SV138: $i] :
( ( ( SV138 != SV434 )
= $true )
| ( ( ! [SY3387: $i,SY3388: $i] :
( ( SY3387 != SY3388 )
| ~ ( ~ ( ~ ( in @ SY3387 @ SV138 )
| ( in @ SY3388 @ SV434 ) )
| ~ ( ~ ( in @ SY3388 @ SV434 )
| ( in @ SY3387 @ SV138 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1422]) ).
thf(1741,plain,
! [SV139: $i,SV435: $i] :
( ( ( ~ ( in @ SV435 @ ( powerset @ SV139 ) ) )
= $true )
| ( ( ! [SY3389: $i] :
( ~ ( in @ SY3389 @ ( powerset @ SV139 ) )
| ! [SY3390: $i] :
( ~ ( in @ SY3390 @ ( powerset @ SV139 ) )
| ~ ( subset @ SV435 @ SY3390 )
| ( subset @ ( binintersect @ SV435 @ SY3389 ) @ SY3390 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1423]) ).
thf(1742,plain,
! [SV650: $i,SV436: $i,SV140: $i] :
( ( ~ ( breln @ SV140 @ SV436 @ SV650 )
| ! [SY3779: $i] :
( ~ ( breln @ SV140 @ SV436 @ SY3779 )
| ~ ! [SY3780: $i] :
( ~ ( in @ SY3780 @ SV140 )
| ! [SY3781: $i] :
( ~ ( in @ SY3781 @ SV436 )
| ~ ( in @ ( kpair @ SY3780 @ SY3781 ) @ SV650 )
| ( in @ ( kpair @ SY3780 @ SY3781 ) @ SY3779 ) ) )
| ~ ! [SY3782: $i] :
( ~ ( in @ SY3782 @ SV140 )
| ! [SY3783: $i] :
( ~ ( in @ SY3783 @ SV436 )
| ~ ( in @ ( kpair @ SY3782 @ SY3783 ) @ SY3779 )
| ( in @ ( kpair @ SY3782 @ SY3783 ) @ SV650 ) ) )
| ( SV650 = SY3779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1743,plain,
! [SV437: $i,SV141: $i,SV651: $i] :
( ( ~ ( in @ SV651 @ SV141 )
| ! [SY3784: $i] :
( ~ ( in @ SY3784 @ SV437 )
| ( in @ ( kpair @ SV651 @ SY3784 ) @ ( cartprod @ SV141 @ SV437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1744,plain,
! [SV438: $i,SV142: $i,SV652: $i] :
( ( ~ ( in @ SV652 @ SV142 )
| ! [SY3785: $i] :
( ~ ( in @ SY3785 @ SV438 )
| ( in @ ( kpair @ SV652 @ SY3785 ) @ ( powerset @ ( powerset @ ( binunion @ SV142 @ SV438 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1745,plain,
! [SV439: $i,SV143: $i,SV653: $i] :
( ( ~ ( in @ SV653 @ ( binintersect @ SV143 @ SV439 ) )
| ( in @ SV653 @ SV439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1746,plain,
! [SV440: $i,SV654: $i > $i,SV144: $i] :
( ( ~ ! [SY3786: $i] :
( ~ ( in @ SY3786 @ SV144 )
| ( in @ ( SV654 @ SY3786 ) @ SV440 ) )
| ! [SY3787: $i] :
( ~ ( in @ SY3787 @ ( funcSet @ SV440 @ SV144 ) )
| ~ ! [SY3788: $i] :
( ~ ( in @ SY3788 @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SY3787 @ ( SV654 @ SY3788 ) )
= SY3788 ) )
| ( surjective @ SV440 @ SV144 @ SY3787 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1747,plain,
! [SV145: $i,SV441: $i] :
( ( ( ~ ( in @ SV441 @ ( powerset @ SV145 ) ) )
= $true )
| ( ( ! [SY3406: $i] :
( ~ ( in @ SY3406 @ SV145 )
| ~ ( in @ SY3406 @ SV441 )
| ( in @ SY3406 @ ( setminus @ SV145 @ ( setminus @ SV145 @ SV441 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1429]) ).
thf(1748,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ( ~ ! [SY3407: $i] :
( ~ ( in @ SY3407 @ SV146 )
| ! [SY3408: $i] :
( ~ ( in @ SY3408 @ SV146 )
| ~ ( SV442 @ SY3407 )
| ~ ( SV442 @ SY3408 )
| ( SY3407 = SY3408 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) )
| ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1430]) ).
thf(1749,plain,
! [SV147: $i,SV443: $i] :
( ( ( ~ ( in @ SV443 @ ( powerset @ SV147 ) ) )
= $true )
| ( ( ! [SY3411: $i] :
( ~ ( in @ SY3411 @ ( powerset @ SV147 ) )
| ! [SY3412: $i] :
( ~ ( in @ SY3412 @ SV147 )
| ~ ( in @ SY3412 @ ( setminus @ SV147 @ SV443 ) )
| ~ ( in @ SY3412 @ ( binintersect @ SV443 @ SY3411 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1431]) ).
thf(1750,plain,
! [SV148: $i,SV444: $i] :
( ( ( ~ ( in @ SV444 @ ( powerset @ SV148 ) ) )
= $true )
| ( ( ! [SY3413: $i] :
( ~ ( in @ SY3413 @ ( powerset @ SV148 ) )
| ! [SY3414: $i] :
( ~ ( in @ SY3414 @ ( powerset @ SV148 ) )
| ! [SY3415: $i] :
( ~ ( in @ SY3415 @ SV148 )
| ~ ( in @ SY3415 @ ( binintersect @ SV444 @ SY3413 ) )
| ( in @ SY3415 @ ( binunion @ SV444 @ SY3414 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1432]) ).
thf(1751,plain,
! [SV445: $i > $o,SV149: $i] :
( ( ( ~ ( ex1 @ SV149
@ ^ [SY3416: $i] : ( SV445 @ SY3416 ) ) )
= $true )
| ( ( ~ ! [SY3417: $i] :
~ ~ ( ~ ( in @ SY3417 @ SV149 )
| ~ ( SV445 @ SY3417 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1433]) ).
thf(1752,plain,
! [SV446: $i,SV150: $i] :
( ( ( ~ ( breln1 @ SV150 @ SV446 ) )
= $true )
| ( ( ! [SY3418: $i] :
( ~ ( breln1 @ SV150 @ SY3418 )
| ! [SY3419: $i] :
( ~ ( breln1 @ SV150 @ SY3419 )
| ( ( breln1compset @ SV150 @ ( binunion @ SV446 @ SY3418 ) @ SY3419 )
= ( binunion @ ( breln1compset @ SV150 @ SV446 @ SY3419 ) @ ( breln1compset @ SV150 @ SY3418 @ SY3419 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1434]) ).
thf(1753,plain,
! [SV655: $i > $i > $o,SV447: $i,SV151: $i] :
( ( ! [SY3789: $i,SY3790: $i] :
( ~ ( in @ ( kpair @ SY3789 @ SY3790 )
@ ( dpsetconstr @ SV151 @ SV447
@ ^ [SY3791: $i,SY3792: $i] : ( SV655 @ SY3791 @ SY3792 ) ) )
| ( SV655 @ SY3789 @ SY3790 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1754,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ! [SY3425: $i,SY3426: $i] :
( ( SY3425 != SY3426 )
| ~ ( ~ ( ~ ( SV152 @ SY3425 )
| ( SV448 @ SY3426 ) )
| ~ ( ~ ( SV448 @ SY3426 )
| ( SV152 @ SY3425 ) ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1436]) ).
thf(1755,plain,
! [SV449: $i,SV153: $i] :
( ( ( ~ ( subset @ SV153 @ SV449 ) )
= $true )
| ( ( ~ ( subset @ SV449 @ SV153 )
| ( SV153 = SV449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1437]) ).
thf(1756,plain,
! [SV656: $i,SV450: $i,SV154: $i] :
( ( ~ ( func @ SV154 @ SV450 @ SV656 )
| ( in @ SV656 @ ( funcSet @ SV154 @ SV450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1757,plain,
! [SV451: $o,SV155: $i,SV657: $i] :
( ( ~ ( in @ SV657 @ SV155 )
| ! [SY3793: $i] :
( ~ ( in @ SY3793 @ SV155 )
| ~ ~ SV451
| ( ( dsetconstr @ SV155
@ ^ [SY3794: $i] :
( ~ ( ~ SV451
| ( SY3794 != SV657 ) )
| ~ ( ~ ~ SV451
| ( SY3794 != SY3793 ) ) ) )
= ( setadjoin @ SY3793 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1758,plain,
! [SV155: $i,SV658: $i] :
( ( ~ ( in @ SV658 @ SV155 )
| ! [SY3795: $i] :
( ~ ( in @ SY3795 @ SV155 )
| ~ ~ $true
| ( ( dsetconstr @ SV155
@ ^ [SY3796: $i] :
( ~ ( ~ $true
| ( SY3796 != SV658 ) )
| ~ ( ~ ~ $true
| ( SY3796 != SY3795 ) ) ) )
= ( setadjoin @ SY3795 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1759,plain,
! [SV155: $i,SV659: $i] :
( ( ~ ( in @ SV659 @ SV155 )
| ! [SY3797: $i] :
( ~ ( in @ SY3797 @ SV155 )
| ~ ~ $false
| ( ( dsetconstr @ SV155
@ ^ [SY3798: $i] :
( ~ ( ~ $false
| ( SY3798 != SV659 ) )
| ~ ( ~ ~ $false
| ( SY3798 != SY3797 ) ) ) )
= ( setadjoin @ SY3797 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1760,plain,
! [SV660: $i,SV156: $i,SV452: $i] :
( ( ~ ( in @ SV452 @ ( powerset @ SV156 ) )
| ~ ( in @ SV660 @ SV452 )
| ( in @ SV660 @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1761,plain,
! [SV453: $i,SV157: $i] :
( ( ( ~ ( breln1 @ SV157 @ SV453 ) )
= $true )
| ( ( ! [SY3438: $i] :
( ~ ( in @ SY3438 @ SV157 )
| ! [SY3439: $i] :
( ~ ( in @ SY3439 @ SV157 )
| ~ ( in @ ( kpair @ SY3438 @ SY3439 ) @ SV453 )
| ( in @ ( kpair @ SY3439 @ SY3438 ) @ ( breln1invset @ SV157 @ SV453 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1443]) ).
thf(1762,plain,
! [SV661: $i,SV454: $i,SV158: $i] :
( ( ~ ( subset @ SV158 @ SV454 )
| ~ ( subset @ SV454 @ SV661 )
| ( subset @ SV158 @ SV661 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1763,plain,
! [SV455: $i > $o,SV159: $i,SV662: $i] :
( ( ~ ( in @ SV662 @ SV159 )
| ~ ( SV455 @ SV662 )
| ( ( dsetconstr @ SV159
@ ^ [SY3442: $i] : ( SV455 @ SY3442 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1764,plain,
! [SV663: $i,SV456: $i,SV160: $i] :
( ( ~ ( subset @ SV160 @ SV456 )
| ~ ( in @ SV663 @ SV160 )
| ( in @ SV663 @ SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1765,plain,
! [SV457: $i,SV161: $i] :
( ( ( SV161 != SV457 )
= $true )
| ( ( ( setadjoin @ SV161 @ ( setadjoin @ SV457 @ emptyset ) )
= ( setadjoin @ SV161 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1447]) ).
thf(1766,plain,
! [SV162: $i,SV458: $i] :
( ( ( ~ ( in @ SV458 @ ( powerset @ SV162 ) ) )
= $true )
| ( ( ! [SY3444: $i] :
( ~ ( in @ SY3444 @ ( powerset @ SV162 ) )
| ( in @ ( setminus @ SV162 @ ( binunion @ SV458 @ SY3444 ) ) @ ( powerset @ ( setminus @ SV162 @ SV458 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1448]) ).
thf(1767,plain,
! [SV163: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ ( powerset @ SV163 ) ) )
= $true )
| ( ( ! [SY3445: $i] :
( ~ ( in @ SY3445 @ ( powerset @ SV163 ) )
| ! [SY3446: $i] :
( ~ ( in @ SY3446 @ ( powerset @ SV163 ) )
| ~ ( subset @ SY3445 @ SY3446 )
| ( subset @ ( binintersect @ SV459 @ SY3445 ) @ SY3446 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1768,plain,
! [SV460: $i,SV164: $i,SV664: $i] :
( ( ~ ~ ( in @ SV664 @ SV164 )
| ~ ( in @ SV664 @ ( setminus @ SV164 @ SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1769,plain,
! [SV461: $i,SV165: $i] :
( ( ( SV165 != SV461 )
= $true )
| ( ( ( setunion @ SV165 )
= ( setunion @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1451]) ).
thf(1770,plain,
! [SV166: $i,SV462: $i,SV665: $i] :
( ( ~ ( in @ SV665 @ SV462 )
| ~ ( in @ SV665 @ ( setminus @ SV166 @ SV462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1771,plain,
! [SV463: $i,SV167: $i] :
( ( ( SV167 != SV463 )
= $true )
| ( ( ! [SY3449: $i,SY3450: $i] :
( ( SY3449 != SY3450 )
| ~ ( in @ SY3449 @ SV167 )
| ( in @ SY3450 @ SV463 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1453]) ).
thf(1772,plain,
! [SV666: $i,SV464: $i,SV168: $i] :
( ( ~ ( breln @ SV168 @ SV464 @ SV666 )
| ! [SY3800: $i] :
( ~ ( breln @ SV168 @ SV464 @ SY3800 )
| ~ ! [SY3801: $i] :
( ~ ( in @ SY3801 @ SV168 )
| ! [SY3802: $i] :
( ~ ( in @ SY3802 @ SV464 )
| ~ ( in @ ( kpair @ SY3801 @ SY3802 ) @ SV666 )
| ( in @ ( kpair @ SY3801 @ SY3802 ) @ SY3800 ) ) )
| ( subset @ SV666 @ SY3800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1773,plain,
! [SV465: $i,SV169: $i] :
( ( ( ~ ( breln1 @ SV169 @ SV465 ) )
= $true )
| ( ( ! [SY3455: $i] :
( ~ ( breln1 @ SV169 @ SY3455 )
| ! [SY3456: $i] :
( ~ ( breln1 @ SV169 @ SY3456 )
| ( ( breln1compset @ SV169 @ ( binunion @ SV465 @ SY3455 ) @ SY3456 )
= ( binunion @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SY3456 ) @ ( breln1invset @ SV169 @ SY3455 ) ) ) @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SY3456 ) @ ( breln1invset @ SV169 @ SV465 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1455]) ).
thf(1774,plain,
! [SV170: $i] :
( ( ( iskpair @ SV170 )
= $false )
| ( ( ( kpair @ ( kfst @ SV170 ) @ ( ksnd @ SV170 ) )
= SV170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1456]) ).
thf(1775,plain,
! [SV171: $i,SV466: $i] :
( ( ( ~ ( in @ SV466 @ ( powerset @ SV171 ) ) )
= $true )
| ( ( ! [SY3457: $i] :
( ~ ( in @ SY3457 @ ( powerset @ SV171 ) )
| ! [SY3458: $i] :
( ~ ( in @ SY3458 @ ( binintersect @ SV466 @ SY3457 ) )
| ( in @ SY3458 @ SV171 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1457]) ).
thf(1776,plain,
! [SV467: $i,SV172: $i] :
( ( ( SV172 != SV467 )
= $true )
| ( ( subset @ SV467 @ SV172 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1777,plain,
! [SV173: $i,SV468: $i] :
( ( ( ~ ( in @ SV468 @ ( powerset @ SV173 ) ) )
= $true )
| ( ( ! [SY3459: $i] :
( ~ ( in @ SY3459 @ ( powerset @ SV173 ) )
| ~ ( subset @ SV468 @ ( setminus @ SV173 @ SY3459 ) )
| ( subset @ SY3459 @ ( setminus @ SV173 @ SV468 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1459]) ).
thf(1778,plain,
! [SV667: $i,SV469: $i,SV174: $i] :
( ( ! [SY3803: $i] :
( ( ( kpair @ SV174 @ SV469 )
!= ( kpair @ SV667 @ SY3803 ) )
| ( SV174 = SV667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1779,plain,
! [SV470: $i > $i,SV175: $i] :
( ( ! [SY3462: $i] :
~ ~ ( ~ ! [SY3463: $i] :
~ ( ~ ( ~ ( in @ SY3463 @ SY3462 )
| ~ ! [SY3464: $i] :
~ ~ ( ~ ( in @ SY3464 @ SV175 )
| ( SY3463
!= ( SV470 @ SY3464 ) ) ) )
| ~ ( ~ ~ ! [SY3465: $i] :
~ ~ ( ~ ( in @ SY3465 @ SV175 )
| ( SY3463
!= ( SV470 @ SY3465 ) ) )
| ( in @ SY3463 @ SY3462 ) ) )
| ~ ! [SY3466: $i] :
( ~ ! [SY3467: $i] :
~ ( ~ ( ~ ( in @ SY3467 @ SY3466 )
| ~ ! [SY3468: $i] :
~ ~ ( ~ ( in @ SY3468 @ SV175 )
| ( SY3467
!= ( SV470 @ SY3468 ) ) ) )
| ~ ( ~ ~ ! [SY3469: $i] :
~ ~ ( ~ ( in @ SY3469 @ SV175 )
| ( SY3467
!= ( SV470 @ SY3469 ) ) )
| ( in @ SY3467 @ SY3466 ) ) )
| ( SY3462 = SY3466 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1780,plain,
! [SV176: $i,SV471: $i] :
( ( ( ~ ( in @ SV471 @ ( powerset @ SV176 ) ) )
= $true )
| ( ( ! [SY3470: $i] :
( ~ ( in @ SY3470 @ ( powerset @ SV176 ) )
| ( in @ ( setminus @ SV471 @ SY3470 ) @ ( powerset @ SV176 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1781,plain,
! [SV472: $i,SV177: $i,SV668: $i] :
( ( ~ ( in @ SV668 @ ( funcSet @ SV177 @ SV472 ) )
| ~ ( injective @ SV177 @ SV472 @ SV668 )
| ( in @ SV668 @ ( injFuncSet @ SV177 @ SV472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1782,plain,
! [SV473: $i,SV178: $i] :
( ( ( ~ ( breln1 @ SV178 @ SV473 ) )
= $true )
| ( ( ! [SY3472: $i] :
( ~ ( breln1 @ SV178 @ SY3472 )
| ( ( breln1invset @ SV178 @ ( breln1compset @ SV178 @ SV473 @ SY3472 ) )
= ( breln1compset @ SV178 @ ( breln1invset @ SV178 @ SY3472 ) @ ( breln1invset @ SV178 @ SV473 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1783,plain,
! [SV474: $i > $o,SV179: $i,SV669: $i] :
( ( ~ ( in @ SV669
@ ( dsetconstr @ SV179
@ ^ [SY3474: $i] : ( SV474 @ SY3474 ) ) )
| ( in @ SV669 @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1784,plain,
! [SV670: $i > $i > $o,SV475: $i,SV180: $i] :
( ( ~ ! [SY3805: $i] :
( ~ ( in @ SY3805 @ SV180 )
| ~ ! [SY3806: $i] :
~ ~ ( ~ ( in @ SY3806 @ SV475 )
| ~ ( SV670 @ SY3805 @ SY3806 ) ) )
| ! [SY3807: $i] :
( ~ ( in @ SY3807 @ ( breln1Set @ SV475 ) )
| ~ ( reflwellordering @ SV475 @ SY3807 )
| ! [SY3808: $i] :
( ~ ( in @ SY3808 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY3809: $i] :
~ ( ~ ( SV670 @ SY3808 @ SY3809 )
| ~ ! [SY3810: $i] :
( ~ ( in @ SY3810 @ SV475 )
| ~ ( SV670 @ SY3808 @ SY3810 )
| ( in @ ( kpair @ SY3809 @ SY3810 ) @ SY3807 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1785,plain,
! [SV476: $i,SV181: $i,SV671: $i] :
( ( ~ ( in @ SV671 @ SV181 )
| ! [SY3811: $i] :
( ~ ( in @ SY3811 @ SV476 )
| ( in @ ( setadjoin @ ( setadjoin @ SV671 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV671 @ ( setadjoin @ SY3811 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV181 @ SV476 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1786,plain,
! [SV477: $i,SV672: $i > $i,SV182: $i] :
( ( ~ ! [SY3812: $i] :
( ~ ( in @ SY3812 @ SV182 )
| ( in @ ( SV672 @ SY3812 ) @ SV477 ) )
| ! [SY3813: $i] :
( ~ ( in @ SY3813 @ SV182 )
| ( ( ap @ SV182 @ SV477
@ ( lam @ SV182 @ SV477
@ ^ [SY3814: $i] : ( SV672 @ SY3814 ) )
@ SY3813 )
= ( SV672 @ SY3813 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1787,plain,
! [SV478: $i,SV183: $i,SV673: $i] :
( ( ~ ( in @ SV673 @ SV183 )
| ~ ~ ( in @ SV673 @ SV478 )
| ~ ( subset @ SV183 @ SV478 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1788,plain,
! [SV479: $i,SV184: $i,SV674: $i] :
( ( ~ ( in @ SV674 @ SV184 )
| ~ ~ ( in @ SV674 @ SV479 )
| ( SV184 != SV479 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1789,plain,
! [SV185: $i,SV480: $i] :
( ( ( ~ ( in @ SV480 @ ( powerset @ SV185 ) ) )
= $true )
| ( ( ! [SY3490: $i] :
( ~ ( in @ SY3490 @ ( powerset @ SV185 ) )
| ( in @ ( binintersect @ SV480 @ SY3490 ) @ ( powerset @ SV185 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1471]) ).
thf(1790,plain,
! [SV186: $i,SV481: $i] :
( ( ( ~ ( in @ SV481 @ ( powerset @ SV186 ) ) )
= $true )
| ( ( ! [SY3491: $i] :
( ~ ( in @ SY3491 @ ( powerset @ SV186 ) )
| ! [SY3492: $i] :
( ~ ( in @ SY3492 @ SV186 )
| ~ ( in @ SV481 @ ( powerset @ SY3491 ) )
| ~ ( in @ SY3492 @ SV481 )
| ( in @ SY3492 @ SY3491 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1472]) ).
thf(1791,plain,
! [SV482: $i,SV187: $i] :
( ( ( ( binintersect @ SV187 @ SV482 )
!= SV187 )
= $true )
| ( ( subset @ SV187 @ SV482 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1473]) ).
thf(1792,plain,
! [SV483: $i > $o,SV188: $i,SV675: $i] :
( ( ~ ( in @ SV675 @ SV188 )
| ~ ( ~ ( ~ ( in @ SV675
@ ( dsetconstr @ SV188
@ ^ [SY3494: $i] : ( SV483 @ SY3494 ) ) )
| ( SV483 @ SV675 ) )
| ~ ( ~ ( SV483 @ SV675 )
| ( in @ SV675
@ ( dsetconstr @ SV188
@ ^ [SY3495: $i] : ( SV483 @ SY3495 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1793,plain,
! [SV484: $i > $o,SV189: $i] :
( ( ( ~ ~ ! [SY3496: $i] :
( ~ ( in @ SY3496 @ SV189 )
| ( SV484 @ SY3496 ) ) )
= $true )
| ( ( ~ ! [SY3497: $i] :
~ ~ ( ~ ( in @ SY3497 @ SV189 )
| ~ ~ ( SV484 @ SY3497 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1475]) ).
thf(1794,plain,
! [SV190: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ ( setunion @ SV190 ) ) )
= $true )
| ( ( ! [SY3498: $o] :
( ~ ! [SY3499: $i] :
( ~ ( in @ SV485 @ SY3499 )
| ~ ( in @ SY3499 @ SV190 )
| SY3498 )
| SY3498 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1476]) ).
thf(1795,plain,
! [SV486: $i,SV191: $i,SV676: $i] :
( ( ~ ( in @ SV676 @ ( funcSet @ SV191 @ SV486 ) )
| ! [SY3817: $i] :
( ~ ( in @ SY3817 @ SV191 )
| ! [SY3818: $i] :
( ~ ( in @ SY3818 @ SV486 )
| ~ ( in @ ( kpair @ SY3817 @ SY3818 ) @ SV676 )
| ( ( ap @ SV191 @ SV486 @ SV676 @ SY3817 )
= SY3818 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1796,plain,
! [SV487: $i,SV192: $i,SV677: $i] :
( ( ~ ( subset @ SV677 @ SV192 )
| ~ ( subset @ SV677 @ SV487 )
| ( subset @ SV677 @ ( binintersect @ SV192 @ SV487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1797,plain,
! [SV488: $i > $i,SV193: $i] :
( ( ! [SY3504: $i] :
~ ! [SY3505: $i] :
~ ( ~ ( ~ ( in @ SY3505 @ SY3504 )
| ~ ! [SY3506: $i] :
~ ~ ( ~ ( in @ SY3506 @ SV193 )
| ( SY3505
!= ( SV488 @ SY3506 ) ) ) )
| ~ ( ~ ~ ! [SY3507: $i] :
~ ~ ( ~ ( in @ SY3507 @ SV193 )
| ( SY3505
!= ( SV488 @ SY3507 ) ) )
| ( in @ SY3505 @ SY3504 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1798,plain,
! [SV194: $i,SV489: $i] :
( ( ( ~ ( in @ SV489 @ ( powerset @ SV194 ) ) )
= $true )
| ( ( ! [SY3508: $i] :
( ~ ( in @ SY3508 @ SV194 )
| ~ ~ ( in @ SY3508 @ ( setminus @ SV194 @ SV489 ) )
| ( in @ SY3508 @ SV489 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1799,plain,
! [SV678: $i,SV490: $i,SV195: $i] :
( ( ~ ( func @ SV195 @ SV490 @ SV678 )
| ( ( lam @ SV195 @ SV490
@ ^ [SY3819: $i] : ( ap @ SV195 @ SV490 @ SV678 @ SY3819 ) )
= SV678 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(1800,plain,
( ( ~ ! [SY3511: $i] :
( ~ ( in @ SY3511 @ sK1_SX0 )
| ( subset @ SY3511 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1482]) ).
thf(1801,plain,
( ( ! [SY3512: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY3512 )
| ( subset @ SX2 @ SY3512 ) )
| ! [SY3514: $i] :
( ~ ( in @ SY3514 @ ( binintersect @ sK1_SX0 @ SY3512 ) )
| ( subset @ SY3514 @ ( binintersect @ sK1_SX0 @ SY3512 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1482]) ).
thf(1802,plain,
! [SV196: $i > $o] :
( ( ( ~ ! [SY2853: $i] :
~ ~ ( ~ ( SV196 @ SY2853 )
| ~ ! [SY2854: $i] :
( ~ ( SV196 @ SY2854 )
| ( SY2853 = SY2854 ) ) ) )
= $false )
| ( ( ~ ! [SY2855: $i] :
~ ~ ( ~ ( SV196 @ SY2855 )
| ~ ! [SY2856: $i] :
( ~ ( SV196 @ SY2856 )
| ( SY2855 = SY2856 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1803,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ! [SY3515: $i,SY3516: $i] :
( ( SY3515 != SY3516 )
| ~ ( ~ ( ~ ( SV197 @ SY3515 )
| ( SV491 @ SY3516 ) )
| ~ ( ~ ( SV491 @ SY3516 )
| ( SV197 @ SY3515 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1484]) ).
thf(1804,plain,
! [SV198: $i] :
( ( ( ! [SY2868: $i] :
~ ( in @ SY2868 @ SV198 ) )
= $false )
| ( ( SV198 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1485]) ).
thf(1805,plain,
! [SV492: $i,SV199: $i,SV679: $i] :
( ( ~ ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) )
| ~ ! [SY3820: $i] :
~ ~ ( ~ ( in @ SY3820 @ SV199 )
| ~ ~ ! [SY3821: $i] :
~ ~ ( ~ ( in @ SY3821 @ SV492 )
| ( SV679
!= ( kpair @ SY3820 @ SY3821 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1806,plain,
! [SV200: $i,SV493: $i] :
( ( ( ~ ( in @ SV493 @ ( powerset @ SV200 ) ) )
= $true )
| ( ( ! [SY3528: $i] :
( ~ ( in @ SY3528 @ ( powerset @ SV200 ) )
| ! [SY3529: $i] :
( ~ ( in @ SY3529 @ SV200 )
| ~ ~ ( in @ SY3529 @ ( binunion @ SV493 @ SY3528 ) )
| ~ ( in @ SY3529 @ SY3528 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1487]) ).
thf(1807,plain,
! [SV494: $i,SV201: $i] :
( ( ( SV201 != SV494 )
= $true )
| ( ( subset @ SV201 @ SV494 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1488]) ).
thf(1808,plain,
! [SV495: $o,SV202: $i,SV680: $i] :
( ( ~ ( in @ SV680 @ SV202 )
| ! [SY3822: $i] :
( ~ ( in @ SY3822 @ SV202 )
| ( in @ ( if @ SV202 @ SV495 @ SV680 @ SY3822 ) @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1809,plain,
! [SV202: $i,SV681: $i] :
( ( ~ ( in @ SV681 @ SV202 )
| ! [SY3823: $i] :
( ~ ( in @ SY3823 @ SV202 )
| ( in @ ( if @ SV202 @ $true @ SV681 @ SY3823 ) @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1810,plain,
! [SV202: $i,SV682: $i] :
( ( ~ ( in @ SV682 @ SV202 )
| ! [SY3824: $i] :
( ~ ( in @ SY3824 @ SV202 )
| ( in @ ( if @ SV202 @ $false @ SV682 @ SY3824 ) @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1811,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ~ ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
| ! [SY3825: $o] :
( ~ ( ~ ( in @ SV683 @ SV203 )
| ~ ~ ( in @ SV683 @ SV496 )
| SY3825 )
| ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SY3825 )
| SY3825 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1812,plain,
! [SV497: $i,SV684: $i > $i,SV204: $i] :
( ( ~ ! [SY3826: $i] :
( ~ ( in @ SY3826 @ SV204 )
| ( in @ ( SV684 @ SY3826 ) @ SV497 ) )
| ( func @ SV204 @ SV497
@ ( lam @ SV204 @ SV497
@ ^ [SY3827: $i] : ( SV684 @ SY3827 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1813,plain,
! [SV498: $i,SV685: $i,SV205: $i] :
( ( ~ ( subset @ SV205 @ SV685 )
| ( subset @ SV205 @ ( setadjoin @ SV498 @ SV685 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1814,plain,
! [SV499: $o,SV206: $i,SV686: $i] :
( ( ~ ( in @ SV686 @ SV206 )
| ! [SY3828: $i] :
( ~ ( in @ SY3828 @ SV206 )
| ( in @ ( if @ SV206 @ SV499 @ SV686 @ SY3828 ) @ ( setadjoin @ SV686 @ ( setadjoin @ SY3828 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1815,plain,
! [SV206: $i,SV687: $i] :
( ( ~ ( in @ SV687 @ SV206 )
| ! [SY3829: $i] :
( ~ ( in @ SY3829 @ SV206 )
| ( in @ ( if @ SV206 @ $true @ SV687 @ SY3829 ) @ ( setadjoin @ SV687 @ ( setadjoin @ SY3829 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1816,plain,
! [SV206: $i,SV688: $i] :
( ( ~ ( in @ SV688 @ SV206 )
| ! [SY3830: $i] :
( ~ ( in @ SY3830 @ SV206 )
| ( in @ ( if @ SV206 @ $false @ SV688 @ SY3830 ) @ ( setadjoin @ SV688 @ ( setadjoin @ SY3830 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1817,plain,
! [SV500: $i > $o,SV207: $i] :
( ( ( ~ ~ ~ ! [SY3540: $i] :
~ ~ ( ~ ( in @ SY3540 @ SV207 )
| ~ ( SV500 @ SY3540 ) ) )
= $true )
| ( ( ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SV207 )
| ~ ( SV500 @ SY3541 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1498]) ).
thf(1818,plain,
! [SV208: $i,SV501: $i] :
( ( ( ~ ( in @ SV501 @ ( powerset @ SV208 ) ) )
= $true )
| ( ( ! [SY3542: $i] :
( ~ ( in @ SY3542 @ ( powerset @ SV208 ) )
| ! [SY3543: $o,SY3544: $i] :
( ~ ( in @ SY3544 @ SV208 )
| ~ ( in @ SY3544 @ ( binunion @ SV501 @ SY3542 ) )
| ~ ( ~ ( in @ SY3544 @ SV501 )
| SY3543 )
| ~ ( ~ ( in @ SY3544 @ SY3542 )
| SY3543 )
| SY3543 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1499]) ).
thf(1819,plain,
! [SV689: $i,SV502: $i,SV209: $i] :
( ( ~ ( breln @ SV209 @ SV502 @ SV689 )
| ! [SY3831: $i > $o] :
( ~ ! [SY3832: $i] :
( ~ ( in @ SY3832 @ SV209 )
| ! [SY3833: $i] :
( ~ ( in @ SY3833 @ SV502 )
| ~ ( in @ ( kpair @ SY3832 @ SY3833 ) @ SV689 )
| ( SY3831 @ ( kpair @ SY3832 @ SY3833 ) ) ) )
| ! [SY3834: $i] :
( ~ ( in @ SY3834 @ SV689 )
| ( SY3831 @ SY3834 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1820,plain,
! [SV503: $o,SV210: $i,SV690: $i] :
( ( ~ ( in @ SV690 @ SV210 )
| ! [SY3835: $i] :
( ~ ( in @ SY3835 @ SV210 )
| ~ SV503
| ( in @ SV690
@ ( dsetconstr @ SV210
@ ^ [SY3836: $i] :
( ~ ( ~ SV503
| ( SY3836 != SV690 ) )
| ~ ( ~ ~ SV503
| ( SY3836 != SY3835 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1821,plain,
! [SV210: $i,SV691: $i] :
( ( ~ ( in @ SV691 @ SV210 )
| ! [SY3837: $i] :
( ~ ( in @ SY3837 @ SV210 )
| ~ $true
| ( in @ SV691
@ ( dsetconstr @ SV210
@ ^ [SY3838: $i] :
( ~ ( ~ $true
| ( SY3838 != SV691 ) )
| ~ ( ~ ~ $true
| ( SY3838 != SY3837 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1822,plain,
! [SV210: $i,SV692: $i] :
( ( ~ ( in @ SV692 @ SV210 )
| ! [SY3839: $i] :
( ~ ( in @ SY3839 @ SV210 )
| ~ $false
| ( in @ SV692
@ ( dsetconstr @ SV210
@ ^ [SY3840: $i] :
( ~ ( ~ $false
| ( SY3840 != SV692 ) )
| ~ ( ~ ~ $false
| ( SY3840 != SY3839 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1823,plain,
! [SV211: $i] :
( ( ( in @ SV211 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV211 @ SV211 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1504]) ).
thf(1824,plain,
! [SV693: $i,SV504: $i,SV212: $i] :
( ( ~ ( subset @ SV212 @ SV504 )
| ~ ~ ( in @ SV693 @ SV504 )
| ~ ( in @ SV693 @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1825,plain,
! [SV694: $i,SV505: $i,SV213: $i] :
( ( ! [SY3841: $i] :
( ( ( setadjoin @ ( setadjoin @ SV213 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV213 @ ( setadjoin @ SV505 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV694 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV694 @ ( setadjoin @ SY3841 @ emptyset ) ) @ emptyset ) ) )
| ( SV213 = SV694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1826,plain,
! [SV506: $i,SV214: $i,SV695: $i] :
( ( ~ ( in @ SV695 @ ( injFuncSet @ SV214 @ SV506 ) )
| ( injective @ SV214 @ SV506 @ SV695 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1827,plain,
! [SV215: $i,SV507: $i] :
( ( ( ~ ( in @ SV507 @ SV215 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV507 @ emptyset ) @ SV215 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1508]) ).
thf(1828,plain,
! [SV508: $i,SV216: $i] :
( ( ( ~ ( breln1 @ SV216 @ SV508 ) )
= $true )
| ( ( ! [SY3557: $i] :
( ~ ( breln1 @ SV216 @ SY3557 )
| ! [SY3558: $i] :
( ~ ( in @ SY3558 @ SV216 )
| ! [SY3559: $i] :
( ~ ( in @ SY3559 @ SV216 )
| ~ ( in @ ( kpair @ SY3558 @ SY3559 ) @ ( binunion @ SV508 @ SY3557 ) )
| ! [SY3560: $o] :
( ~ ( ~ ( in @ ( kpair @ SY3558 @ SY3559 ) @ SV508 )
| SY3560 )
| ~ ( ~ ( in @ ( kpair @ SY3558 @ SY3559 ) @ SY3557 )
| SY3560 )
| SY3560 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1509]) ).
thf(1829,plain,
! [SV217: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ ( powerset @ SV217 ) ) )
= $true )
| ( ( ! [SY3561: $i] :
( ~ ( in @ SY3561 @ ( powerset @ SV217 ) )
| ! [SY3562: $i] :
( ~ ( in @ SY3562 @ SV217 )
| ~ ( in @ SY3562 @ ( setminus @ SV217 @ ( binunion @ SV509 @ SY3561 ) ) )
| ( in @ SY3562 @ ( binintersect @ ( setminus @ SV217 @ SV509 ) @ ( setminus @ SV217 @ SY3561 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1510]) ).
thf(1830,plain,
! [SV510: $i > $i,SV218: $i,SV696: $i] :
( ( ~ ( in @ SV696
@ ( image1 @ SV218
@ ^ [SY3564: $i] : ( SV510 @ SY3564 ) ) )
| ~ ! [SY3843: $i] :
~ ~ ( ~ ( in @ SY3843 @ SV218 )
| ( SV696
!= ( SV510 @ SY3843 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1831,plain,
! [SV219: $i] :
( ( ( in @ SV219 @ omega )
= $false )
| ( ( ( omegaS @ SV219 )
!= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1832,plain,
! [SV511: $i,SV220: $i,SV697: $i] :
( ( ~ ( in @ SV697 @ ( setadjoin @ SV220 @ ( setadjoin @ SV511 @ emptyset ) ) )
| ( SV697 = SV220 )
| ( SV697 = SV511 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1833,plain,
! [SV512: $i,SV221: $i,SV698: $i] :
( ( ~ ( in @ SV698 @ ( surjFuncSet @ SV221 @ SV512 ) )
| ( in @ SV698 @ ( funcSet @ SV221 @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1834,plain,
! [SV513: $i,SV222: $i] :
( ( ( ~ ( subset @ SV222 @ SV513 ) )
= $true )
| ( ( in @ SV222 @ ( powerset @ SV513 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1515]) ).
thf(1835,plain,
! [SV514: $o,SV223: $i,SV699: $i] :
( ( ~ ( in @ SV699 @ SV223 )
| ! [SY3844: $i] :
( ~ ( in @ SY3844 @ SV223 )
| ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY3845: $i] :
( ~ ( ~ SV514
| ( SY3845 != SV699 ) )
| ~ ( ~ ~ SV514
| ( SY3845 != SY3844 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1836,plain,
! [SV223: $i,SV700: $i] :
( ( ~ ( in @ SV700 @ SV223 )
| ! [SY3846: $i] :
( ~ ( in @ SY3846 @ SV223 )
| ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY3847: $i] :
( ~ ( ~ $true
| ( SY3847 != SV700 ) )
| ~ ( ~ ~ $true
| ( SY3847 != SY3846 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1837,plain,
! [SV223: $i,SV701: $i] :
( ( ~ ( in @ SV701 @ SV223 )
| ! [SY3848: $i] :
( ~ ( in @ SY3848 @ SV223 )
| ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY3849: $i] :
( ~ ( ~ $false
| ( SY3849 != SV701 ) )
| ~ ( ~ ~ $false
| ( SY3849 != SY3848 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1838,plain,
! [SV224: $i,SV515: $i] :
( ( ( ~ ( in @ SV515 @ ( powerset @ SV224 ) ) )
= $true )
| ( ( ! [SY3571: $i] :
( ~ ( in @ SY3571 @ ( powerset @ SV224 ) )
| ~ ( subset @ SV515 @ SY3571 )
| ( subset @ ( setminus @ SV224 @ SY3571 ) @ ( setminus @ SV224 @ SV515 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1519]) ).
thf(1839,plain,
! [SV702: $i,SV516: $i,SV225: $i] :
( ( ! [SY3850: $i] :
( ( ( kpair @ SV225 @ SV516 )
!= ( kpair @ SV702 @ SY3850 ) )
| ( SV516 = SY3850 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1840,plain,
! [SV226: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY3851: $i] :
( ~ ( in @ SY3851 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY2945: $i] :
( ~ ( in @ SY2945 @ SY3851 )
| ( in @ SY2945 @ SV226 ) ) )
| ~ ! [SY3853: $i,SY3854: $i] :
( ~ ~ ( ~ ( in @ SY3853 @ SV226 )
| ~ ( in @ SY3854 @ SV226 ) )
| ~ ! [SY3855: $i] :
( ~ ( in @ SY3855 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SY3853 @ SY3855 )
| ( in @ SY3854 @ SY3855 ) )
| ~ ( ~ ( in @ SY3854 @ SY3855 )
| ( in @ SY3853 @ SY3855 ) ) ) )
| ( SY3853 = SY3854 ) ) )
| ~ ! [SY3856: $i,SY3857: $i] :
( ~ ~ ( ~ ( in @ SY3856 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY3857 @ ( sK2_SY2943 @ SV226 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3856 )
| ( in @ SX4 @ SY3857 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3857 )
| ( in @ SX4 @ SY3856 ) ) ) )
| ~ ! [SY3860: $i] :
( ~ ~ ( ~ ! [SY2954: $i] :
( ~ ( in @ SY2954 @ SY3860 )
| ( in @ SY2954 @ SV226 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY3860 ) )
| ~ ! [SY3863: $i] :
~ ~ ! [SY3864: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3863 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY3864 @ SY3860 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY3863 )
| ~ ( in @ SX5 @ SY3860 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY3863 ) )
| ( in @ SY3864 @ SY3866 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1521]) ).
thf(1841,plain,
! [SV703: $i > $i > $o,SV517: $i,SV227: $i] :
( ( ! [SY3868: $i] :
( ~ ( in @ SY3868 @ SV227 )
| ! [SY3869: $i] :
( ~ ( in @ SY3869 @ SV517 )
| ~ ( in @ ( kpair @ SY3868 @ SY3869 )
@ ( dpsetconstr @ SV227 @ SV517
@ ^ [SY3870: $i,SY3871: $i] : ( SV703 @ SY3870 @ SY3871 ) ) )
| ( SV703 @ SY3868 @ SY3869 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1842,plain,
! [SV228: $i,SV704: $i,SV518: $i] :
( ( ~ ( in @ SV518 @ SV704 )
| ~ ( in @ SV704 @ SV228 )
| ( in @ SV518 @ ( setunion @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1843,plain,
! [SV229: $i,SV519: $i] :
( ( ( ~ ( in @ SV519 @ ( powerset @ SV229 ) ) )
= $true )
| ( ( ! [SY3580: $i] :
( ~ ( in @ SY3580 @ ( powerset @ SV229 ) )
| ! [SY3581: $i] :
( ~ ( in @ SY3581 @ SV229 )
| ~ ~ ( in @ SY3581 @ ( binunion @ SV519 @ SY3580 ) )
| ~ ( in @ SY3581 @ SV519 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1524]) ).
thf(1844,plain,
! [SV230: $i > $i > $o,SV520: $i] :
( ( ( ~ ! [SY3582: $i] :
( ~ ( in @ SY3582 @ SV520 )
| ~ ! [SY2974: $i] :
~ ~ ( ~ ( SV230 @ SY3582 @ SY2974 )
| ~ ! [SY2975: $i] :
( ~ ( SV230 @ SY3582 @ SY2975 )
| ( SY2974 = SY2975 ) ) ) ) )
= $true )
| ( ( ~ ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1525]) ).
thf(1845,plain,
! [SV705: $i,SV521: $i,SV231: $i] :
( ( ~ ( func @ SV231 @ SV521 @ SV705 )
| ! [SY3872: $i] :
( ~ ( func @ SV231 @ SV521 @ SY3872 )
| ~ ! [SY3873: $i] :
( ~ ( in @ SY3873 @ SV231 )
| ( ( ap @ SV231 @ SV521 @ SV705 @ SY3873 )
= ( ap @ SV231 @ SV521 @ SY3872 @ SY3873 ) ) )
| ( SV705 = SY3872 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1846,plain,
! [SV522: $o,SV232: $i,SV706: $i] :
( ( ~ ( in @ SV706 @ SV232 )
| ! [SY3874: $i] :
( ~ ( in @ SY3874 @ SV232 )
| ~ SV522
| ( ( if @ SV232 @ SV522 @ SV706 @ SY3874 )
= SV706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1847,plain,
! [SV232: $i,SV707: $i] :
( ( ~ ( in @ SV707 @ SV232 )
| ! [SY3875: $i] :
( ~ ( in @ SY3875 @ SV232 )
| ~ $true
| ( ( if @ SV232 @ $true @ SV707 @ SY3875 )
= SV707 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1848,plain,
! [SV232: $i,SV708: $i] :
( ( ~ ( in @ SV708 @ SV232 )
| ! [SY3876: $i] :
( ~ ( in @ SY3876 @ SV232 )
| ~ $false
| ( ( if @ SV232 @ $false @ SV708 @ SY3876 )
= SV708 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1849,plain,
! [SV523: $i,SV233: $i] :
( ( ( ~ ( breln1 @ SV233 @ SV523 ) )
= $true )
| ( ( ! [SY3594: $i > $o] :
( ~ ! [SY3595: $i] :
( ~ ( in @ SY3595 @ SV233 )
| ! [SY3596: $i] :
( ~ ( in @ SY3596 @ SV233 )
| ~ ( in @ ( kpair @ SY3595 @ SY3596 ) @ SV523 )
| ( SY3594 @ ( kpair @ SY3595 @ SY3596 ) ) ) )
| ! [SY3597: $i] :
( ~ ( in @ SY3597 @ SV523 )
| ( SY3594 @ SY3597 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1530]) ).
thf(1850,plain,
! [SV234: $i,SV524: $i] :
( ( ( ~ ! [SY3598: $i] :
( ~ ( in @ SY3598 @ SV524 )
| ( in @ SY3598 @ SV234 ) ) )
= $true )
| ( ( in @ SV524 @ ( powerset @ SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1531]) ).
thf(1851,plain,
! [SV235: $i,SV525: $i] :
( ( ( ~ ( in @ SV525 @ ( setunion @ SV235 ) ) )
= $true )
| ( ( ~ ! [SY3599: $i] :
~ ~ ( ~ ( in @ SY3599 @ SV235 )
| ~ ( in @ SV525 @ SY3599 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1852,plain,
! [SV236: $i] :
( ( ( singleton @ SV236 )
= $false )
| ( ( in @ ( setunion @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1853,plain,
! [SV526: $i,SV237: $i,SV709: $i] :
( ( ~ ( in @ SV709 @ ( setminus @ SV237 @ SV526 ) )
| ( in @ SV709 @ SV237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1854,plain,
! [SV527: $i,SV238: $i] :
( ( ( SV238 != SV527 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV238 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV238 @ ( setadjoin @ SV527 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV238 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1535]) ).
thf(1855,plain,
! [SV528: $i,SV239: $i,SV710: $i] :
( ( ~ ( in @ SV710 @ ( binunion @ SV239 @ SV528 ) )
| ( in @ SV710 @ SV239 )
| ( in @ SV710 @ SV528 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1856,plain,
! [SV711: $i,SV529: $i,SV240: $i] :
( ( ~ ( func @ SV240 @ SV529 @ SV711 )
| ! [SY3877: $i] :
( ~ ( in @ SY3877 @ SV240 )
| ( in @ ( kpair @ SY3877 @ ( ap @ SV240 @ SV529 @ SV711 @ SY3877 ) ) @ SV711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1857,plain,
! [SV241: $i,SV530: $i] :
( ( ( ~ ( in @ SV530 @ ( powerset @ SV241 ) ) )
= $true )
| ( ( ! [SY3604: $i] :
( ~ ( in @ SY3604 @ ( powerset @ SV241 ) )
| ( in @ ( setminus @ SV241 @ SV530 ) @ ( powerset @ ( setminus @ SV241 @ ( binintersect @ SV530 @ SY3604 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1538]) ).
thf(1858,plain,
! [SV242: $i] :
( ( ( SV242 != emptyset )
= $false )
| ( ( ~ ! [SY3006: $i] :
~ ( in @ SY3006 @ SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1859,plain,
! [SV243: $i,SV531: $i] :
( ( ( ~ ( in @ SV531 @ ( powerset @ SV243 ) ) )
= $true )
| ( ( ! [SY3605: $i] :
( ~ ( in @ SY3605 @ ( powerset @ SV243 ) )
| ! [SY3606: $i] :
( ~ ( in @ SY3606 @ ( powerset @ SV243 ) )
| ( in @ ( binintersect @ SV531 @ SY3605 ) @ ( powerset @ ( binintersect @ ( binunion @ SV531 @ SY3606 ) @ ( binunion @ SY3605 @ SY3606 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1540]) ).
thf(1860,plain,
! [SV244: $i,SV532: $i] :
( ( ( ~ ( in @ SV532 @ ( powerset @ SV244 ) ) )
= $true )
| ( ( ! [SY3607: $i] :
( ~ ( in @ SY3607 @ SV244 )
| ~ ( in @ SY3607 @ ( setminus @ SV244 @ ( setminus @ SV244 @ SV532 ) ) )
| ( in @ SY3607 @ SV532 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1541]) ).
thf(1861,plain,
! [SV533: $i > $o,SV245: $i] :
( ( ( ~ ~ ! [SY3608: $i] :
~ ~ ( ~ ( in @ SY3608 @ SV245 )
| ~ ( SV533 @ SY3608 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV245
@ ^ [SY3609: $i] : ( SV533 @ SY3609 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1542]) ).
thf(1862,plain,
! [SV712: $i,SV534: $i,SV246: $i] :
( ( ~ ( func @ SV246 @ SV534 @ SV712 )
| ! [SY3878: $i] :
( ~ ( in @ SY3878 @ SV246 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV534
@ ^ [SY3879: $i] : ( in @ ( kpair @ SY3878 @ SY3879 ) @ SV712 ) ) )
@ SV534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1863,plain,
! [SV535: $i,SV247: $i] :
( ( ( ~ ( breln1 @ SV247 @ SV535 ) )
= $true )
| ( ( ! [SY3613: $i] :
( ~ ( in @ SY3613 @ SV247 )
| ! [SY3614: $i] :
( ~ ( in @ SY3614 @ SV247 )
| ~ ( in @ ( kpair @ SY3614 @ SY3613 ) @ ( breln1invset @ SV247 @ SV535 ) )
| ( in @ ( kpair @ SY3613 @ SY3614 ) @ SV535 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1544]) ).
thf(1864,plain,
! [SV536: $i,SV248: $i] :
( ( ( ( binintersect @ SV248 @ SV536 )
!= SV536 )
= $true )
| ( ( subset @ SV536 @ SV248 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1545]) ).
thf(1865,plain,
! [SV249: $i] :
( ( ( ! [SY3023: $i] :
( ~ ( in @ SY3023 @ SV249 )
| ( subset @ SY3023 @ SV249 ) ) )
= $false )
| ( ( ! [SY3024: $i] :
( ~ ( in @ SY3024 @ SV249 )
| ( subset @ SY3024 @ SV249 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1866,plain,
! [SV537: $i,SV250: $i,SV713: $i] :
( ( ~ ( in @ SV713 @ ( setadjoin @ SV250 @ ( setadjoin @ SV537 @ emptyset ) ) )
| ( SV713 = SV250 )
| ( SV713 = SV537 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1867,plain,
! [SV251: $i,SV538: $i] :
( ( ( ~ ( in @ SV538 @ ( powerset @ SV251 ) ) )
= $true )
| ( ( ! [SY3616: $i] :
( ~ ( in @ SY3616 @ ( powerset @ SV251 ) )
| ! [SY3617: $i] :
( ~ ( in @ SY3617 @ SV251 )
| ~ ~ ( in @ SY3617 @ SV538 )
| ~ ~ ( in @ SY3617 @ SY3616 )
| ~ ( in @ SY3617 @ ( binunion @ SV538 @ SY3616 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1548]) ).
thf(1868,plain,
! [SV539: $o,SV252: $i,SV714: $i] :
( ( ~ ( in @ SV714 @ SV252 )
| ! [SY3880: $i] :
( ~ ( in @ SY3880 @ SV252 )
| ~ SV539
| ( ( dsetconstr @ SV252
@ ^ [SY3881: $i] :
( ~ ( ~ SV539
| ( SY3881 != SV714 ) )
| ~ ( ~ ~ SV539
| ( SY3881 != SY3880 ) ) ) )
= ( setadjoin @ SV714 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1869,plain,
! [SV252: $i,SV715: $i] :
( ( ~ ( in @ SV715 @ SV252 )
| ! [SY3882: $i] :
( ~ ( in @ SY3882 @ SV252 )
| ~ $true
| ( ( dsetconstr @ SV252
@ ^ [SY3883: $i] :
( ~ ( ~ $true
| ( SY3883 != SV715 ) )
| ~ ( ~ ~ $true
| ( SY3883 != SY3882 ) ) ) )
= ( setadjoin @ SV715 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1870,plain,
! [SV252: $i,SV716: $i] :
( ( ~ ( in @ SV716 @ SV252 )
| ! [SY3884: $i] :
( ~ ( in @ SY3884 @ SV252 )
| ~ $false
| ( ( dsetconstr @ SV252
@ ^ [SY3885: $i] :
( ~ ( ~ $false
| ( SY3885 != SV716 ) )
| ~ ( ~ ~ $false
| ( SY3885 != SY3884 ) ) ) )
= ( setadjoin @ SV716 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1871,plain,
! [SV253: $i,SV540: $i] :
( ( ( ~ ( in @ SV540 @ ( breln1Set @ SV253 ) ) )
= $true )
| ( ( breln1 @ SV253 @ SV540 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1552]) ).
thf(1872,plain,
! [SV717: $i,SV541: $i,SV254: $i] :
( ( ~ ( func @ SV254 @ SV541 @ SV717 )
| ! [SY3886: $i] :
( ~ ( in @ SY3886 @ SV254 )
| ( ( ap @ SV254 @ SV541 @ SV717 @ SY3886 )
= ( ap @ SV254 @ SV541 @ SV717 @ SY3886 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1873,plain,
! [SV542: $i,SV255: $i] :
( ( ( ~ ( subset @ SV255 @ SV542 ) )
= $true )
| ( ( subset @ ( powerset @ SV255 ) @ ( powerset @ SV542 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1554]) ).
thf(1874,plain,
! [SV718: $i,SV543: $i,SV256: $i] :
( ( ! [SY3887: $i] :
( ( ( setadjoin @ ( setadjoin @ SV256 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV256 @ ( setadjoin @ SV543 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV718 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV718 @ ( setadjoin @ SY3887 @ emptyset ) ) @ emptyset ) ) )
| ( SV718 != SY3887 )
| ( SV543 = SY3887 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(1875,plain,
! [SV257: $i,SV544: $i] :
( ( ( ~ ( in @ SV544 @ ( powerset @ SV257 ) ) )
= $true )
| ( ( subset @ SV544 @ SV257 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1556]) ).
thf(1876,plain,
! [SV258: $o,SV545: $i] :
( ( ( ~ ( in @ SV545 @ ( prop2set @ SV258 ) ) )
= $true )
| ( SV258 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1557]) ).
thf(1877,plain,
! [SV546: $i] :
( ( ( ~ ( in @ SV546 @ ( prop2set @ $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1558]) ).
thf(1878,plain,
! [SV547: $i] :
( ( ( ~ ( in @ SV547 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1559]) ).
thf(1879,plain,
! [SV719: $i,SV548: $i,SV259: $i] :
( ( ~ ( func @ SV259 @ SV548 @ SV719 )
| ! [SY3888: $i] :
( ~ ( in @ SY3888 @ SV259 )
| ! [SY3889: $i] :
( ~ ( in @ SY3889 @ SV548 )
| ~ ( in @ ( kpair @ SY3888 @ SY3889 ) @ SV719 )
| ( ( ap @ SV259 @ SV548 @ SV719 @ SY3888 )
= SY3889 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1880,plain,
! [SV549: $i,SV260: $i] :
( ( ( ~ ( breln1 @ SV260 @ SV549 ) )
= $true )
| ( ( ! [SY3628: $i] :
( ~ ( breln1 @ SV260 @ SY3628 )
| ~ ! [SY3629: $i] :
( ~ ( in @ SY3629 @ SV260 )
| ! [SY3630: $i] :
( ~ ( in @ SY3630 @ SV260 )
| ~ ( in @ ( kpair @ SY3629 @ SY3630 ) @ SV549 )
| ( in @ ( kpair @ SY3629 @ SY3630 ) @ SY3628 ) ) )
| ~ ! [SY3631: $i] :
( ~ ( in @ SY3631 @ SV260 )
| ! [SY3632: $i] :
( ~ ( in @ SY3632 @ SV260 )
| ~ ( in @ ( kpair @ SY3631 @ SY3632 ) @ SY3628 )
| ( in @ ( kpair @ SY3631 @ SY3632 ) @ SV549 ) ) )
| ( SV549 = SY3628 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1561]) ).
thf(1881,plain,
! [SV550: $i,SV261: $i] :
( ( ( ~ ( breln1 @ SV261 @ SV550 ) )
= $true )
| ( ( breln1 @ SV261 @ ( breln1invset @ SV261 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1562]) ).
thf(1882,plain,
! [SV551: $i > $o,SV262: $i,SV720: $i] :
( ( ~ ( in @ SV720
@ ( dsetconstr @ SV262
@ ^ [SY3634: $i] : ( SV551 @ SY3634 ) ) )
| ( SV551 @ SV720 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(1883,plain,
! [SV552: $i,SV263: $i,SV721: $i] :
( ( ~ ( in @ SV721 @ SV263 )
| ~ ( in @ SV721 @ SV552 )
| ( in @ SV721 @ ( binintersect @ SV263 @ SV552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1884,plain,
! [SV553: $i,SV264: $i] :
( ( ( ~ ( breln1 @ SV264 @ SV553 ) )
= $true )
| ( ( ! [SY3636: $i] :
( ~ ( breln1 @ SV264 @ SY3636 )
| ! [SY3637: $i] :
( ~ ( in @ SY3637 @ SV264 )
| ! [SY3638: $i] :
( ~ ( in @ SY3638 @ SV264 )
| ~ ( ( in @ ( kpair @ SY3637 @ SY3638 ) @ SV553 )
| ( in @ ( kpair @ SY3637 @ SY3638 ) @ SY3636 ) )
| ( in @ ( kpair @ SY3637 @ SY3638 ) @ ( binunion @ SV553 @ SY3636 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1565]) ).
thf(1885,plain,
! [SV554: $i,SV265: $i,SV722: $i] :
( ( ~ ( in @ SV722 @ SV265 )
| ! [SY3891: $i] :
( ~ ( in @ SY3891 @ SV554 )
| ( subset @ ( setadjoin @ SV722 @ ( setadjoin @ SY3891 @ emptyset ) ) @ ( binunion @ SV265 @ SV554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1886,plain,
! [SV266: $i,SV555: $i] :
( ( ( ~ ( in @ SV555 @ ( powerset @ SV266 ) ) )
= $true )
| ( ( ! [SY3641: $i] :
( ~ ( in @ SY3641 @ ( powerset @ SV266 ) )
| ( in @ ( setminus @ SV266 @ SV555 ) @ ( powerset @ ( setminus @ SV266 @ ( binintersect @ SV555 @ SY3641 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1567]) ).
thf(1887,plain,
! [SV556: $i,SV267: $i,SV723: $i] :
( ( ~ ( in @ SV723 @ ( injFuncSet @ SV267 @ SV556 ) )
| ( in @ SV723 @ ( funcSet @ SV267 @ SV556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1888,plain,
! [SV557: $i,SV268: $i,SV724: $i] :
( ( ~ ( in @ SV724 @ ( surjFuncSet @ SV268 @ SV557 ) )
| ( surjective @ SV268 @ SV557 @ SV724 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(1889,plain,
! [SV269: $i] :
( ( ( in @ SV269 @ omega )
= $false )
| ( ( in @ ( omegaS @ SV269 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1570]) ).
thf(1890,plain,
! [SV270: $i,SV558: $i] :
( ( ( ~ ( in @ SV558 @ ( powerset @ SV270 ) ) )
= $true )
| ( ( ! [SY3644: $i] :
( ~ ( in @ SY3644 @ ( powerset @ SV270 ) )
| ( ( setminus @ SV270 @ ( binunion @ SV558 @ SY3644 ) )
= ( binintersect @ ( setminus @ SV270 @ SV558 ) @ ( setminus @ SV270 @ SY3644 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1571]) ).
thf(1891,plain,
! [SV559: $i,SV271: $i] :
( ( ( ~ ( breln1 @ SV271 @ SV559 ) )
= $true )
| ( ( ! [SY3645: $i > $o] :
( ~ ! [SY3646: $i] :
( ~ ( in @ SY3646 @ SV271 )
| ! [SY3647: $i] :
( ~ ( in @ SY3647 @ SV271 )
| ~ ( in @ ( kpair @ SY3646 @ SY3647 ) @ SV559 )
| ( SY3645 @ ( kpair @ SY3646 @ SY3647 ) ) ) )
| ! [SY3648: $i] :
( ~ ( in @ SY3648 @ SV559 )
| ( SY3645 @ SY3648 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1572]) ).
thf(1892,plain,
! [SV560: $i,SV272: $i,SV725: $i] :
( ( ~ ( in @ SV725 @ SV272 )
| ~ ~ ( in @ SV725 @ SV560 )
| ( in @ SV725 @ ( symdiff @ SV272 @ SV560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1893,plain,
! [SV561: $i,SV273: $i,SV726: $i] :
( ( ~ ( in @ SV726 @ SV273 )
| ! [SY3892: $i] :
( ~ ( in @ SY3892 @ SV561 )
| ( ( kfst @ ( kpair @ SV726 @ SY3892 ) )
= SV726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1894,plain,
! [SV274: $i,SV562: $i] :
( ( ( ~ ( in @ SV562 @ ( powerset @ SV274 ) ) )
= $true )
| ( ( ! [SY3652: $i] :
( ~ ( in @ SY3652 @ ( powerset @ SV274 ) )
| ~ ( subset @ ( setminus @ SV274 @ SY3652 ) @ ( setminus @ SV274 @ SV562 ) )
| ( subset @ SV562 @ SY3652 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1575]) ).
thf(1895,plain,
! [SV563: $i > $o,SV275: $i] :
( ( ( ~ ! [SY3653: $i] :
( ~ ( in @ SY3653 @ SV275 )
| ~ ( SV563 @ SY3653 ) ) )
= $true )
| ( ( ~ ~ ! [SY3654: $i] :
~ ~ ( ~ ( in @ SY3654 @ SV275 )
| ~ ( SV563 @ SY3654 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1576]) ).
thf(1896,plain,
! [SV564: $i,SV276: $i] :
( ( ( ~ ( subset @ SV276 @ SV564 ) )
= $true )
| ( ( ( setminus @ SV276 @ SV564 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1577]) ).
thf(1897,plain,
! [SV277: $i,SV565: $i] :
( ( ( ~ ( in @ SV565 @ ( powerset @ SV277 ) ) )
= $true )
| ( ( ! [SY3655: $i] :
( ~ ( in @ SY3655 @ ( powerset @ SV277 ) )
| ! [SY3656: $i] :
( ~ ( in @ SY3656 @ SV277 )
| ~ ( in @ SY3656 @ ( setminus @ SV277 @ ( binunion @ SV565 @ SY3655 ) ) )
| ( in @ SY3656 @ ( setminus @ SV277 @ SV565 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1578]) ).
thf(1898,plain,
! [SV566: $i,SV278: $i] :
( ( ( ~ ! [SY3657: $i] :
( ~ ( in @ SY3657 @ SV278 )
| ( in @ SY3657 @ SV566 ) ) )
= $true )
| ( ( ~ ! [SY3658: $i] :
( ~ ( in @ SY3658 @ SV566 )
| ( in @ SY3658 @ SV278 ) )
| ( SV278 = SV566 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1579]) ).
thf(1899,plain,
! [SV567: $i,SV279: $i,SV727: $i] :
( ( ~ ( in @ SV727 @ ( binintersect @ SV279 @ SV567 ) )
| ( in @ SV727 @ SV279 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1900,plain,
! [SV568: $i,SV280: $i] :
( ( ( ~ ( breln1 @ SV280 @ SV568 ) )
= $true )
| ( ( ! [SY3660: $i] :
( ~ ( breln1 @ SV280 @ SY3660 )
| ! [SY3661: $i] :
( ~ ( in @ SY3661 @ SV280 )
| ! [SY3662: $i] :
( ~ ( in @ SY3662 @ SV280 )
| ~ ( in @ ( kpair @ SY3661 @ SY3662 ) @ ( breln1compset @ SV280 @ SV568 @ SY3660 ) )
| ! [SY3663: $o] :
( ~ ! [SY3664: $i] :
( ~ ( in @ SY3664 @ SV280 )
| ~ ( in @ ( kpair @ SY3661 @ SY3664 ) @ SV568 )
| ~ ( in @ ( kpair @ SY3664 @ SY3662 ) @ SY3660 )
| SY3663 )
| SY3663 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1581]) ).
thf(1901,plain,
! [SV569: $i,SV281: $i] :
( ( ( ~ ( subset @ SV281 @ SV569 ) )
= $true )
| ( ( ( binintersect @ SV281 @ SV569 )
= SV281 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1582]) ).
thf(1902,plain,
! [SV570: $i,SV282: $i,SV728: $i] :
( ( ~ ~ ( in @ SV728 @ SV282 )
| ~ ( in @ SV728 @ SV570 )
| ( in @ SV728 @ ( symdiff @ SV282 @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(1903,plain,
! [SV571: $i,SV283: $i,SV729: $i] :
( ( ! [SY3893: $i] :
( ~ ( in @ ( kpair @ SV729 @ SY3893 ) @ ( cartprod @ SV283 @ SV571 ) )
| ( in @ SY3893 @ SV571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1904,plain,
! [SV572: $i,SV284: $i] :
( ( ( ~ ~ ~ ! [SY3668: $i] :
~ ~ ( ~ ( in @ SY3668 @ SV284 )
| ~ ( in @ SY3668 @ SV572 ) ) )
= $true )
| ( ( ( binintersect @ SV284 @ SV572 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1585]) ).
thf(1905,plain,
! [SV573: $i,SV285: $i,SV730: $i] :
( ( ~ ( in @ SV730 @ SV285 )
| ( in @ SV730 @ ( binunion @ SV285 @ SV573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1906,plain,
! [SV286: $i,SV574: $i] :
( ( ( ~ ( in @ SV574 @ SV286 ) )
= $true )
| ( ( in @ SV574 @ ( powerset @ ( setunion @ SV286 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1587]) ).
thf(1907,plain,
! [SV287: $i] :
( ( ( iskpair @ SV287 )
= $false )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV287 )
@ ^ [SY3116: $i] :
( SV287
= ( kpair @ ( kfst @ SV287 ) @ SY3116 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1588]) ).
thf(1908,plain,
! [SV288: $i > $o] :
( ( ( ~ ! [SY3117: $i] :
~ ~ ( ~ ( SV288 @ SY3117 )
| ~ ! [SY3118: $i] :
( ~ ( SV288 @ SY3118 )
| ( SY3117 = SY3118 ) ) ) )
= $false )
| ( ( ! [SY3119: $i,SY3120: $i] :
( ~ ( SV288 @ SY3119 )
| ~ ( SV288 @ SY3120 )
| ( SY3119 = SY3120 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1909,plain,
! [SV575: $i > $o,SV289: $i] :
( ( ( ~ ~ ~ ! [SY3670: $i] :
~ ~ ( ~ ( in @ SY3670 @ SV289 )
| ~ ( SV575 @ SY3670 ) ) )
= $true )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV289 )
| ~ ( SV575 @ SY3671 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1590]) ).
thf(1910,plain,
! [SV290: $i,SV576: $i] :
( ( ( ~ ( in @ SV576 @ ( powerset @ SV290 ) ) )
= $true )
| ( ( subset @ ( setminus @ SV290 @ ( setminus @ SV290 @ SV576 ) ) @ SV576 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1591]) ).
thf(1911,plain,
! [SV577: $i > $o,SV291: $i,SV731: $i] :
( ( ~ ( in @ SV731 @ SV291 )
| ~ ( SV577 @ SV731 )
| ( in @ SV731
@ ( dsetconstr @ SV291
@ ^ [SY3673: $i] : ( SV577 @ SY3673 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(1912,plain,
! [SV578: $i,SV292: $i] :
( ( ( ~ ( breln1 @ SV292 @ SV578 ) )
= $true )
| ( ( ! [SY3674: $i] :
( ~ ( breln1 @ SV292 @ SY3674 )
| ( breln1 @ SV292 @ ( binunion @ SV578 @ SY3674 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1593]) ).
thf(1913,plain,
! [SV732: $i > $i > $o,SV579: $i,SV293: $i] :
( ( ! [SY3895: $i] :
( ~ ( in @ SY3895 @ SV293 )
| ! [SY3896: $i] :
( ~ ( in @ SY3896 @ SV579 )
| ~ ( SV732 @ SY3895 @ SY3896 )
| ( in @ ( kpair @ SY3895 @ SY3896 )
@ ( dpsetconstr @ SV293 @ SV579
@ ^ [SY3897: $i,SY3898: $i] : ( SV732 @ SY3897 @ SY3898 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(1914,plain,
! [SV294: $i] :
( ( ( singleton @ SV294 )
= $false )
| ( ( ! [SY3136: $i] :
( ~ ( in @ SY3136 @ SV294 )
| ( ( setunion @ SV294 )
= SY3136 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1915,plain,
! [SV580: $i,SV295: $i] :
( ( ( ~ ( in @ SV295 @ ( setadjoin @ SV580 @ emptyset ) ) )
= $true )
| ( ( in @ SV580 @ ( setadjoin @ SV295 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1596]) ).
thf(1916,plain,
! [SV581: $i,SV296: $i] :
( ( ( ~ ~ ( subset @ SV296 @ SV581 ) )
= $true )
| ( ( SV296 != SV581 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1597]) ).
thf(1917,plain,
! [SV582: $i,SV297: $i] :
( ( ( ~ ( breln1 @ SV297 @ SV582 ) )
= $true )
| ( ( ! [SY3680: $i] :
( ~ ( breln1 @ SV297 @ SY3680 )
| ( ( binunion @ SV582 @ SY3680 )
= ( binunion @ SY3680 @ SV582 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1598]) ).
thf(1918,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( ! [SY3899: $o] :
( ~ ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
| ~ ( ~ ( in @ SV733 @ SV298 )
| SY3899 )
| ~ ( ~ ( in @ SV733 @ SV583 )
| SY3899 )
| SY3899 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(1919,plain,
! [SV299: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ ( powerset @ SV299 ) ) )
= $true )
| ( ( ! [SY3683: $i] :
( ~ ( in @ SY3683 @ ( powerset @ SV299 ) )
| ~ ! [SY3684: $i] :
( ~ ( in @ SY3684 @ SV299 )
| ~ ( in @ SY3684 @ SV584 )
| ( in @ SY3684 @ SY3683 ) )
| ~ ! [SY3685: $i] :
( ~ ( in @ SY3685 @ SV299 )
| ~ ( in @ SY3685 @ SY3683 )
| ( in @ SY3685 @ SV584 ) )
| ( SV584 = SY3683 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1600]) ).
thf(1920,plain,
! [SV585: $i,SV300: $i] :
( ( ( ~ ( breln1 @ SV300 @ SV585 ) )
= $true )
| ( ( ! [SY3686: $i] :
( ~ ( breln1 @ SV300 @ SY3686 )
| ! [SY3687: $i] :
( ~ ( in @ SY3687 @ SV300 )
| ! [SY3688: $i] :
( ~ ( in @ SY3688 @ SV300 )
| ~ ( in @ ( kpair @ SY3687 @ SY3688 ) @ SV585 )
| ( in @ ( kpair @ SY3687 @ SY3688 ) @ ( binunion @ SV585 @ SY3686 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1601]) ).
thf(1921,plain,
! [SV734: $i,SV586: $i,SV301: $i] :
( ( ~ ( func @ SV301 @ SV586 @ SV734 )
| ! [SY3900: $i] :
( ~ ( func @ SV301 @ SV586 @ SY3900 )
| ~ ! [SY3901: $i] :
( ~ ( in @ SY3901 @ SV301 )
| ( ( ap @ SV301 @ SV586 @ SV734 @ SY3901 )
= ( ap @ SV301 @ SV586 @ SY3900 @ SY3901 ) ) )
| ! [SY3902: $i] :
( ~ ( in @ SY3902 @ SV301 )
| ! [SY3903: $i] :
( ~ ( in @ SY3903 @ SV586 )
| ~ ( in @ ( kpair @ SY3902 @ SY3903 ) @ SY3900 )
| ( in @ ( kpair @ SY3902 @ SY3903 ) @ SV734 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1922,plain,
! [SV302: $i,SV587: $i] :
( ( ( ~ ( in @ SV587 @ ( powerset @ SV302 ) ) )
= $true )
| ( ( ! [SY3694: $i] :
( ~ ( in @ SY3694 @ ( powerset @ SV302 ) )
| ! [SY3695: $i] :
( ~ ( in @ SY3695 @ SV302 )
| ~ ( in @ SY3695 @ ( binunion @ ( setminus @ SV302 @ SV587 ) @ ( setminus @ SV302 @ SY3694 ) ) )
| ( in @ SY3695 @ ( setminus @ SV302 @ ( binintersect @ SV587 @ SY3694 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1603]) ).
thf(1923,plain,
! [SV303: $i] :
( ( ( in @ SV303 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1604]) ).
thf(1924,plain,
! [SV304: $i,SV588: $i] :
( ( ( ~ ( in @ SV588 @ ( powerset @ SV304 ) ) )
= $true )
| ( ( SV588
= ( setminus @ SV304 @ ( setminus @ SV304 @ SV588 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1605]) ).
thf(1925,plain,
! [SV305: $i,SV589: $i] :
( ( ( ~ ( in @ SV589 @ ( powerset @ SV305 ) ) )
= $true )
| ( ( ! [SY3696: $i] :
( ~ ( in @ SY3696 @ ( powerset @ SV305 ) )
| ! [SY3697: $i] :
( ~ ( in @ SY3697 @ ( powerset @ SV305 ) )
| ( in @ ( binintersect @ SV589 @ SY3696 ) @ ( powerset @ ( binintersect @ ( binunion @ SV589 @ SY3697 ) @ ( binunion @ SY3696 @ SY3697 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1606]) ).
thf(1926,plain,
! [SV306: $i] :
( ( ( ! [SY3165: $i] :
~ ( in @ SY3165 @ SV306 ) )
= $false )
| ( ( SV306 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1927,plain,
! [SV307: $i,SV590: $i] :
( ( ( ~ ( in @ SV590 @ ( powerset @ SV307 ) ) )
= $true )
| ( ( ! [SY3698: $i] :
( ~ ( in @ SY3698 @ ( powerset @ SV307 ) )
| ! [SY3699: $i] :
( ~ ( in @ SY3699 @ SV307 )
| ~ ( in @ SY3699 @ ( binintersect @ ( setminus @ SV307 @ SV590 ) @ ( setminus @ SV307 @ SY3698 ) ) )
| ( in @ SY3699 @ ( setminus @ SV307 @ ( binunion @ SV590 @ SY3698 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1608]) ).
thf(1928,plain,
! [SV308: $i,SV591: $i] :
( ( ( ~ ( in @ SV591 @ ( powerset @ SV308 ) ) )
= $true )
| ( ( ! [SY3700: $i] :
( ~ ( in @ SY3700 @ ( powerset @ SV308 ) )
| ~ ! [SY3701: $i] :
( ~ ( in @ SY3701 @ SV308 )
| ~ ( in @ SY3701 @ SV591 )
| ( in @ SY3701 @ SY3700 ) )
| ( in @ SV591 @ ( powerset @ SY3700 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1609]) ).
thf(1929,plain,
! [SV309: $i,SV592: $i] :
( ( ( ~ ( in @ SV592 @ ( powerset @ SV309 ) ) )
= $true )
| ( ( ! [SY3702: $i] :
( ~ ( in @ SY3702 @ ( powerset @ SV309 ) )
| ! [SY3703: $i] :
( ~ ( in @ SY3703 @ SV309 )
| ~ ( in @ SY3703 @ ( setminus @ SV309 @ SV592 ) )
| ~ ( in @ SY3703 @ ( setminus @ SV309 @ SY3702 ) )
| ( in @ SY3703 @ ( setminus @ SV309 @ ( binunion @ SV592 @ SY3702 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1610]) ).
thf(1930,plain,
! [SV310: $i,SV593: $i] :
( ( ( ~ ( in @ SV593 @ ( powerset @ SV310 ) ) )
= $true )
| ( ( in @ ( setminus @ SV310 @ SV593 ) @ ( powerset @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1611]) ).
thf(1931,plain,
! [SV594: $i,SV311: $i] :
( ( ( ~ ( ( SV311 != SV594 ) ) )
= $true )
| ( ( ~ ( in @ SV594 @ ( setadjoin @ SV311 @ emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1612]) ).
thf(1932,plain,
! [SV312: $i,SV595: $i,SV735: $i] :
( ( ~ ( in @ SV735 @ SV595 )
| ( in @ SV735 @ ( binunion @ SV312 @ SV595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1933,plain,
! [SV596: $i,SV313: $i,SV736: $i] :
( ( ~ ( in @ SV736 @ SV313 )
| ! [SY3904: $i] :
( ~ ( in @ SY3904 @ SV596 )
| ( in @ ( setadjoin @ SV736 @ ( setadjoin @ SY3904 @ emptyset ) ) @ ( powerset @ ( binunion @ SV313 @ SV596 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(1934,plain,
! [SV597: $i,SV314: $i,SV737: $i] :
( ( ~ ( in @ SV737 @ SV314 )
| ! [SY3905: $i] :
( ~ ( in @ SY3905 @ SV597 )
| ( ( ksnd @ ( kpair @ SV737 @ SY3905 ) )
= SY3905 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(1935,plain,
! [SV315: $i,SV598: $i] :
( ( ( ~ ( in @ SV598 @ ( powerset @ SV315 ) ) )
= $true )
| ( ( ! [SY3709: $i] :
( ~ ( in @ SY3709 @ ( powerset @ SV315 ) )
| ! [SY3710: $i] :
( ~ ( in @ SY3710 @ SV315 )
| ~ ( in @ SY3710 @ ( setminus @ SV315 @ ( binunion @ SV598 @ SY3709 ) ) )
| ~ ( in @ SY3710 @ SV598 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1616]) ).
thf(1936,plain,
! [SV316: $i > $o] :
( ( ( ~ ! [SY3188: $i] :
~ ~ ( ~ ( SV316 @ SY3188 )
| ~ ! [SY3189: $i] :
( ~ ( SV316 @ SY3189 )
| ( SY3188 = SY3189 ) ) ) )
= $false )
| ( ( ~ ! [SY3190: $i] :
~ ! [SY3191: $i] :
~ ( ~ ( ~ ( SV316 @ SY3191 )
| ( SY3191 = SY3190 ) )
| ~ ( ( SY3191 != SY3190 )
| ( SV316 @ SY3191 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1937,plain,
! [SV317: $i,SV599: $i] :
( ( ( ~ ( in @ SV599 @ ( powerset @ SV317 ) ) )
= $true )
| ( ( ! [SY3711: $i] :
( ~ ( in @ SY3711 @ ( powerset @ SV317 ) )
| ! [SY3712: $i] :
( ~ ( in @ SY3712 @ ( powerset @ SV317 ) )
| ! [SY3713: $i] :
( ~ ( in @ SY3713 @ ( powerset @ SV317 ) )
| ~ ( subset @ SV599 @ SY3712 )
| ~ ( subset @ SY3711 @ SY3713 )
| ( subset @ ( binintersect @ SV599 @ SY3711 ) @ ( binintersect @ SY3712 @ SY3713 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1618]) ).
thf(1938,plain,
! [SV318: $i,SV600: $i] :
( ( ( ~ ( in @ SV600 @ ( powerset @ SV318 ) ) )
= $true )
| ( ( ! [SY3714: $i] :
( ~ ( in @ SY3714 @ ( powerset @ SV318 ) )
| ! [SY3715: $i] :
( ~ ( in @ SY3715 @ SV318 )
| ~ ~ ( in @ SY3715 @ SY3714 )
| ~ ( in @ SY3715 @ ( binintersect @ SV600 @ SY3714 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1619]) ).
thf(1939,plain,
! [SV738: $i,SV601: $i,SV319: $i] :
( ( ~ ( breln @ SV319 @ SV601 @ SV738 )
| ! [SY3906: $i > $o] :
( ~ ! [SY3907: $i] :
( ~ ( in @ SY3907 @ SV319 )
| ! [SY3908: $i] :
( ~ ( in @ SY3908 @ SV601 )
| ~ ( in @ ( kpair @ SY3907 @ SY3908 ) @ SV738 )
| ( SY3906 @ ( kpair @ SY3907 @ SY3908 ) ) ) )
| ! [SY3909: $i] :
( ~ ( in @ SY3909 @ SV738 )
| ( SY3906 @ SY3909 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(1940,plain,
! [SV602: $i,SV320: $i] :
( ( ( ~ ! [SY3721: $i] :
( ~ ( in @ SY3721 @ SV320 )
| ( in @ SY3721 @ SV602 ) ) )
= $true )
| ( ( subset @ SV320 @ SV602 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1621]) ).
thf(1941,plain,
! [SV603: $o,SV321: $i,SV739: $i] :
( ( ~ ( in @ SV739 @ SV321 )
| ! [SY3910: $i] :
( ~ ( in @ SY3910 @ SV321 )
| ~ ~ SV603
| ( ( if @ SV321 @ SV603 @ SV739 @ SY3910 )
= SY3910 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(1942,plain,
! [SV321: $i,SV740: $i] :
( ( ~ ( in @ SV740 @ SV321 )
| ! [SY3911: $i] :
( ~ ( in @ SY3911 @ SV321 )
| ~ ~ $true
| ( ( if @ SV321 @ $true @ SV740 @ SY3911 )
= SY3911 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(1943,plain,
! [SV321: $i,SV741: $i] :
( ( ~ ( in @ SV741 @ SV321 )
| ! [SY3912: $i] :
( ~ ( in @ SY3912 @ SV321 )
| ~ ~ $false
| ( ( if @ SV321 @ $false @ SV741 @ SY3912 )
= SY3912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(1944,plain,
! [SV322: $i] :
( ( ( ~ ! [SY3210: $i] :
~ ( in @ SY3210 @ SV322 ) )
= $false )
| ( ( ~ ! [SY3211: $i] :
~ ~ ( ~ ( in @ SY3211 @ SV322 )
| ~ ~ ~ ! [SY3212: $i] :
~ ~ ( ~ ( in @ SY3212 @ SY3211 )
| ~ ( in @ SY3212 @ SV322 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1945,plain,
! [SV604: $i,SV323: $i,SV742: $i] :
( ( ! [SY3913: $i] :
( ~ ( in @ ( kpair @ SV742 @ SY3913 ) @ ( cartprod @ SV323 @ SV604 ) )
| ( in @ SV742 @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(1946,plain,
! [SV605: $i,SV324: $i] :
( ( ( ~ ! [SY3726: $i] :
( ~ ( in @ SY3726 @ SV324 )
| ( in @ SY3726 @ SV605 ) ) )
= $true )
| ( ( subset @ SV324 @ SV605 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1947,plain,
! [SV325: $i,SV606: $i] :
( ( ( ~ ( in @ SV606 @ ( powerset @ SV325 ) ) )
= $true )
| ( ( ! [SY3727: $i] :
( ~ ( in @ SY3727 @ ( powerset @ SV325 ) )
| ! [SY3728: $i] :
( ~ ( in @ SY3728 @ ( powerset @ SV325 ) )
| ~ ( subset @ SV606 @ SY3727 )
| ~ ( subset @ SV606 @ SY3728 )
| ( subset @ SV606 @ ( binintersect @ SY3727 @ SY3728 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1628]) ).
thf(1948,plain,
! [SV349: $i,SV36: $i] :
( ( ( in @ SV36 @ ( setadjoin @ SV349 @ emptyset ) )
= $false )
| ( ( SV36 = SV349 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1632]) ).
thf(1949,plain,
! [SV37: $i] :
( ( ( SV37 = emptyset )
= $true )
| ( ( ~ ! [SY2402: $i] :
~ ~ ( ~ ( in @ SY2402 @ SV37 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1633]) ).
thf(1950,plain,
! [SV38: $i,SV743: $i] :
( ( ( ~ ( in @ SV743 @ omega )
| ( ( omegaS @ SV38 )
!= ( omegaS @ SV743 ) )
| ( SV38 = SV743 ) )
= $true )
| ( ( in @ SV38 @ omega )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1951,plain,
! [SV350: $i,SV610: $i > $i,SV39: $i] :
( ( ( ~ ! [SY3733: $i] :
( ~ ( in @ SY3733 @ SV39 )
| ( in @ ( SV610 @ SY3733 ) @ SV350 ) ) )
= $true )
| ( ( func @ SV39 @ SV350
@ ( dpsetconstr @ SV39 @ SV350
@ ^ [SY3734: $i,SY3735: $i] :
( ( SV610 @ SY3734 )
= SY3735 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1635]) ).
thf(1952,plain,
! [SV40: $i > $o] :
( ( ( ! [SY2409: $i] :
~ ~ ( ~ ( SV40 @ SY2409 )
| ~ ! [SY2410: $i] :
( ~ ( SV40 @ SY2410 )
| ( SY2409 = SY2410 ) ) ) )
= $true )
| ( ( ~ ! [SY2411: $i] :
~ ( SV40 @ SY2411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1636]) ).
thf(1953,plain,
! [SV351: $i,SV41: $i,SV611: $i] :
( ( ( ~ ( in @ SV611 @ SV41 ) )
= $true )
| ( ( ! [SY3736: $i] :
( ~ ( in @ SY3736 @ SV351 )
| ( ( kpair @ SV611 @ SY3736 )
= ( kpair @ SV611 @ SY3736 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1637]) ).
thf(1954,plain,
! [SV42: $i > $o] :
( ( ( ! [SY2415: $i] :
~ ~ ( ~ ( SV42 @ SY2415 )
| ~ ! [SY2416: $i] :
( ~ ( SV42 @ SY2416 )
| ( SY2415 = SY2416 ) ) ) )
= $true )
| ( ( SV42
@ ( descr
@ ^ [SY2417: $i] : ( SV42 @ SY2417 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1638]) ).
thf(1955,plain,
! [SV352: $i,SV43: $i] :
( ( ( SV43 = SV352 )
= $false )
| ( ( ( powerset @ SV43 )
= ( powerset @ SV352 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1956,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ( ! [SY3238: $i] :
( ~ ( in @ SY3238 @ SV44 )
| ! [SY3239: $i] :
( ~ ( in @ SY3239 @ SV44 )
| ~ ( SV353 @ SY3238 )
| ~ ( SV353 @ SY3239 )
| ( SY3238 = SY3239 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) )
| ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1640]) ).
thf(1957,plain,
! [SV354: $i,SV45: $i,SV612: $i] :
( ( ( ~ ( in @ SV612 @ ( funcSet @ SV45 @ SV354 ) ) )
= $true )
| ( ( ! [SY3737: $i] :
( ~ ( in @ SY3737 @ ( funcSet @ SV45 @ SV354 ) )
| ~ ! [SY3738: $i] :
( ~ ( in @ SY3738 @ SV45 )
| ( ( ap @ SV45 @ SV354 @ SV612 @ SY3738 )
= ( ap @ SV45 @ SV354 @ SY3737 @ SY3738 ) ) )
| ( SV612 = SY3737 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1641]) ).
thf(1958,plain,
! [SV355: $i,SV46: $i,SV613: $i] :
( ( ( ~ ( in @ SV613 @ SV46 ) )
= $true )
| ( ( in @ ( setadjoin @ SV613 @ emptyset ) @ ( powerset @ ( binunion @ SV46 @ SV355 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1642]) ).
thf(1959,plain,
! [SV356: $i,SV47: $i,SV614: $i] :
( ( ( ~ ( in @ SV614 @ ( funcSet @ SV47 @ SV356 ) ) )
= $true )
| ( ( ! [SY3739: $i] :
( ~ ( in @ SY3739 @ SV47 )
| ( in @ ( kpair @ SY3739 @ ( ap @ SV47 @ SV356 @ SV614 @ SY3739 ) ) @ SV614 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1643]) ).
thf(1960,plain,
! [SV744: $i,SV615: $i,SV357: $i,SV48: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV48 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV48 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV615 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV615 @ ( setadjoin @ SV744 @ emptyset ) ) @ emptyset ) ) )
| ( SV357 = SV744 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(1961,plain,
! [SV358: $i,SV49: $i,SV616: $i] :
( ( ( ~ ( in @ SV616 @ ( funcSet @ SV49 @ SV358 ) ) )
= $true )
| ( ( ! [SY3741: $i] :
( ~ ( in @ SY3741 @ SV49 )
| ( in @ ( ap @ SV49 @ SV358 @ SV616 @ SY3741 ) @ SV358 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1645]) ).
thf(1962,plain,
! [SV359: $i,SV50: $i] :
( ( ( SV50 = SV359 )
= $false )
| ( ( ! [SY3252: $i,SY3253: $i] :
( ( SY3252 != SY3253 )
| ( ( setadjoin @ SV50 @ SY3252 )
= ( setadjoin @ SV359 @ SY3253 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1963,plain,
! [SV360: $i,SV51: $i,SV617: $i] :
( ( ( ~ ( in @ SV617 @ ( funcSet @ SV51 @ SV360 ) ) )
= $true )
| ( ( func @ SV51 @ SV360 @ SV617 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1647]) ).
thf(1964,plain,
! [SV52: $i,SV361: $i] :
( ( ( in @ SV361 @ ( powerset @ SV52 ) )
= $false )
| ( ( ! [SY3255: $i] :
( ~ ( in @ SY3255 @ ( powerset @ SV52 ) )
| ! [SY3256: $i] :
( ~ ( in @ SY3256 @ ( powerset @ SV52 ) )
| ! [SY3257: $i] :
( ~ ( in @ SY3257 @ SV52 )
| ~ ( in @ SY3257 @ ( binintersect @ SV361 @ SY3255 ) )
| ( in @ SY3257 @ ( binunion @ SY3255 @ SY3256 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1648]) ).
thf(1965,plain,
! [SV53: $i,SV362: $i] :
( ( ( subset @ SV362 @ SV53 )
= $false )
| ( ( ( binintersect @ SV53 @ SV362 )
= SV362 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1649]) ).
thf(1966,plain,
! [SV363: $i,SV618: $i > $i,SV54: $i] :
( ( ( ~ ! [SY3742: $i] :
( ~ ( in @ SY3742 @ SV54 )
| ( in @ ( SV618 @ SY3742 ) @ SV363 ) ) )
= $true )
| ( ( in
@ ( lam @ SV54 @ SV363
@ ^ [SY3743: $i] : ( SV618 @ SY3743 ) )
@ ( funcSet @ SV54 @ SV363 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1650]) ).
thf(1967,plain,
! [SV55: $i,SV364: $i] :
( ( ( in @ SV364 @ ( powerset @ SV55 ) )
= $false )
| ( ( ! [SY3261: $i] :
( ~ ( in @ SY3261 @ ( powerset @ SV55 ) )
| ~ ( subset @ SV364 @ ( setminus @ SV55 @ SY3261 ) )
| ( subset @ SY3261 @ ( setminus @ SV55 @ SV364 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1651]) ).
thf(1968,plain,
! [SV56: $i,SV365: $i] :
( ( ( in @ SV365 @ ( powerset @ SV56 ) )
= $false )
| ( ( ! [SY3262: $i] :
( ~ ( in @ SY3262 @ ( powerset @ SV56 ) )
| ! [SY3263: $i] :
( ~ ( in @ SY3263 @ ( powerset @ SV56 ) )
| ! [SY3264: $i] :
( ~ ( in @ SY3264 @ ( powerset @ SV56 ) )
| ( ( setminus @ SV56 @ ( binintersect @ ( binunion @ SV365 @ SY3262 ) @ ( binunion @ SY3263 @ SY3264 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV56 @ SV365 ) @ ( setminus @ SV56 @ SY3262 ) ) @ ( binintersect @ ( setminus @ SV56 @ SY3263 ) @ ( setminus @ SV56 @ SY3264 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1969,plain,
! [SV57: $i,SV366: $i] :
( ( ~ ( ~ ( in @ SV366 @ ( setunion @ SV57 ) )
| ~ ! [SY3265: $i] :
~ ~ ( ~ ( in @ SV366 @ SY3265 )
| ~ ( in @ SY3265 @ SV57 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1653]) ).
thf(1970,plain,
! [SV57: $i,SV366: $i] :
( ( ~ ( ~ ~ ! [SY3266: $i] :
~ ~ ( ~ ( in @ SV366 @ SY3266 )
| ~ ( in @ SY3266 @ SV57 ) )
| ( in @ SV366 @ ( setunion @ SV57 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1653]) ).
thf(1971,plain,
! [SV58: $i > $o] :
( ( ( ! [SY2462: $i] :
~ ~ ( ~ ( SV58 @ SY2462 )
| ~ ! [SY2463: $i] :
( ~ ( SV58 @ SY2463 )
| ( SY2462 = SY2463 ) ) ) )
= $true )
| ( ( ! [SY2464: $i,SY2465: $i] :
( ~ ( SV58 @ SY2464 )
| ~ ( SV58 @ SY2465 )
| ( SY2464 = SY2465 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1654]) ).
thf(1972,plain,
! [SV59: $i > $o] :
( ( ( ! [SY2466: $i] :
~ ! [SY2467: $i] :
~ ( ~ ( ~ ( SV59 @ SY2467 )
| ( SY2467 = SY2466 ) )
| ~ ( ( SY2467 != SY2466 )
| ( SV59 @ SY2467 ) ) ) )
= $true )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1655]) ).
thf(1973,plain,
! [SV60: $i > $o] :
( ( ( ! [SY2470: $i] :
~ ~ ( ~ ( SV60 @ SY2470 )
| ~ ! [SY2471: $i] :
( ~ ( SV60 @ SY2471 )
| ( SY2470 = SY2471 ) ) ) )
= $true )
| ( ( ~ ! [SY2472: $i] :
~ ~ ( ~ ( SV60 @ SY2472 )
| ~ ! [SY2473: $i] :
( ~ ( SV60 @ SY2473 )
| ( SY2472 = SY2473 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1656]) ).
thf(1974,plain,
! [SV367: $i > $o,SV61: $i] :
( ( ( ~ ! [SY3267: $i] :
( ~ ( in @ SY3267 @ SV61 )
| ( SV367 @ SY3267 ) ) )
= $false )
| ( ( ~ ! [SY3268: $i] :
~ ~ ( ~ ( in @ SY3268 @ SV61 )
| ~ ~ ( SV367 @ SY3268 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1975,plain,
! [SV62: $i > $o,SV368: $i] :
( ( ( in @ SV368 @ emptyset )
= $false )
| ( ( SV62 @ SV368 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1658]) ).
thf(1976,plain,
! [SV619: $i,SV369: $i,SV63: $i] :
( ( ( ~ ( func @ SV63 @ SV369 @ SV619 ) )
= $true )
| ( ( ! [SY3744: $i] :
( ~ ( in @ SY3744 @ SV63 )
| ( in @ ( ap @ SV63 @ SV369 @ SV619 @ SY3744 ) @ SV369 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1659]) ).
thf(1977,plain,
! [SV370: $i,SV620: $i > $i,SV64: $i] :
( ( ( ~ ! [SY3745: $i] :
( ~ ( in @ SY3745 @ SV64 )
| ( in @ ( SV620 @ SY3745 ) @ SV370 ) ) )
= $true )
| ( ( ( lam @ SV64 @ SV370
@ ^ [SY3746: $i] : ( SV620 @ SY3746 ) )
= ( lam @ SV64 @ SV370
@ ^ [SY3747: $i] : ( SV620 @ SY3747 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1660]) ).
thf(1978,plain,
! [SV371: $i,SV65: $i] :
( ( ( ! [SY3275: $i] :
~ ( ~ ( ~ ( in @ SY3275 @ SV65 )
| ( in @ SY3275 @ SV371 ) )
| ~ ( ~ ( in @ SY3275 @ SV371 )
| ( in @ SY3275 @ SV65 ) ) ) )
= $false )
| ( ( SV65 = SV371 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1661]) ).
thf(1979,plain,
! [SV66: $i,SV745: $o] :
( ( SV745 = $true )
| ( ( in @ SV66 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1662]) ).
thf(1980,plain,
! [SV66: $i] :
( ( $true = $true )
| ( ( in @ SV66 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1662]) ).
thf(1981,plain,
! [SV66: $i] :
( ( $false = $true )
| ( ( in @ SV66 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1662]) ).
thf(1982,plain,
! [SV68: $i,SV372: $i] :
( ( ( in @ SV372 @ ( powerset @ SV68 ) )
= $false )
| ( ( ! [SY3276: $i] :
( ~ ( in @ SY3276 @ ( powerset @ SV68 ) )
| ~ ( subset @ SV372 @ ( setminus @ SV68 @ SY3276 ) )
| ! [SY3277: $i] :
( ~ ( in @ SY3277 @ SV68 )
| ~ ( in @ SY3277 @ SY3276 )
| ( in @ SY3277 @ ( setminus @ SV68 @ SV372 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1983,plain,
! [SV69: $i,SV373: $i] :
( ( ( in @ SV373 @ ( powerset @ SV69 ) )
= $false )
| ( ( ! [SY3278: $i] :
( ~ ( in @ SY3278 @ ( powerset @ SV69 ) )
| ! [SY3279: $i] :
( ~ ( in @ SY3279 @ SV69 )
| ~ ( in @ SY3279 @ ( setminus @ SV69 @ ( binintersect @ SV373 @ SY3278 ) ) )
| ( in @ SY3279 @ ( binunion @ ( setminus @ SV69 @ SV373 ) @ ( setminus @ SV69 @ SY3278 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1665]) ).
thf(1984,plain,
! [SV374: $i,SV70: $i] :
( ( ( SV70 = SV374 )
= $false )
| ( ( in @ SV70 @ ( setadjoin @ SV374 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1666]) ).
thf(1985,plain,
! [SV71: $i,SV375: $i] :
( ( ( in @ SV375 @ ( powerset @ SV71 ) )
= $false )
| ( ( ! [SY3280: $i] :
( ~ ( in @ SY3280 @ ( powerset @ SV71 ) )
| ( in @ ( binunion @ SV375 @ SY3280 ) @ ( powerset @ SV71 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1986,plain,
! [SV376: $i,SV72: $i,SV621: $i] :
( ( ( ~ ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) ) )
= $true )
| ( ( ! [SY3748: $o] :
( ~ ( ( SV621 != SV72 )
| SY3748 )
| ~ ( ~ ( in @ SV621 @ SV376 )
| SY3748 )
| SY3748 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1668]) ).
thf(1987,plain,
! [SV377: $i,SV73: $i] :
( ( ( breln1 @ SV73 @ SV377 )
= $false )
| ( ( ! [SY3283: $i] :
( ~ ( breln1 @ SV73 @ SY3283 )
| ( breln1 @ SV73 @ ( breln1compset @ SV73 @ SV377 @ SY3283 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1669]) ).
thf(1988,plain,
! [SV378: $i,SV74: $i] :
( ( ( breln1 @ SV74 @ SV378 )
= $false )
| ( ( SV378
= ( breln1invset @ SV74 @ ( breln1invset @ SV74 @ SV378 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1670]) ).
thf(1989,plain,
! [SV75: $i,SV379: $i] :
( ( ( in @ SV379 @ ( powerset @ SV75 ) )
= $false )
| ( ( ! [SY3284: $i] :
( ~ ( in @ SY3284 @ ( powerset @ SV75 ) )
| ! [SY3285: $i] :
( ~ ( in @ SY3285 @ SV75 )
| ~ ( in @ SY3285 @ ( setminus @ SV75 @ ( binunion @ SV379 @ SY3284 ) ) )
| ( in @ SY3285 @ ( setminus @ SV75 @ SY3284 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1671]) ).
thf(1990,plain,
! [SV380: $i > $i,SV76: $i,SV622: $i] :
( ( ~ ( ~ ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3287: $i] : ( SV380 @ SY3287 ) ) )
| ~ ! [SY3750: $i] :
~ ~ ( ~ ( in @ SY3750 @ SV76 )
| ( SV622
!= ( SV380 @ SY3750 ) ) ) )
| ~ ( ~ ~ ! [SY3751: $i] :
~ ~ ( ~ ( in @ SY3751 @ SV76 )
| ( SV622
!= ( SV380 @ SY3751 ) ) )
| ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3290: $i] : ( SV380 @ SY3290 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1672]) ).
thf(1991,plain,
! [SV381: $i > $i,SV623: $i,SV77: $i] :
( ( ( ~ ~ ! [SY3753: $i] :
~ ~ ( ~ ( in @ SY3753 @ SV77 )
| ( SV623
!= ( SV381 @ SY3753 ) ) ) )
= $true )
| ( ( in @ SV623
@ ( image1 @ SV77
@ ^ [SY3293: $i] : ( SV381 @ SY3293 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1673]) ).
thf(1992,plain,
! [SV382: $i,SV78: $i] :
( ( ( breln1 @ SV78 @ SV382 )
= $false )
| ( ( ! [SY3294: $i] :
( ~ ( breln1 @ SV78 @ SY3294 )
| ! [SY3295: $i] :
( ~ ( in @ SY3295 @ SV78 )
| ! [SY3296: $i] :
( ~ ( in @ SY3296 @ SV78 )
| ~ ( in @ ( kpair @ SY3295 @ SY3296 ) @ ( breln1compset @ SV78 @ SV382 @ SY3294 ) )
| ~ ! [SY3297: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3297 @ SV78 )
| ~ ( in @ ( kpair @ SY3295 @ SY3297 ) @ SV382 ) )
| ~ ( in @ ( kpair @ SY3297 @ SY3296 ) @ SY3294 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1993,plain,
! [SV383: $i,SV79: $i,SV624: $i] :
( ( ( ~ ( in @ SV624 @ ( cartprod @ SV79 @ SV383 ) ) )
= $true )
| ( ( in @ ( kfst @ SV624 ) @ SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1675]) ).
thf(1994,plain,
! [SV384: $i,SV80: $i,SV625: $i] :
( ( ~ ( ~ ( in @ SV625 @ ( setadjoin @ SV80 @ SV384 ) )
| ( SV625 = SV80 )
| ( in @ SV625 @ SV384 ) )
| ~ ( ~ ( ( SV625 = SV80 )
| ( in @ SV625 @ SV384 ) )
| ( in @ SV625 @ ( setadjoin @ SV80 @ SV384 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1676]) ).
thf(1995,plain,
! [SV81: $i,SV385: $i,SV626: $i] :
( ( ( ~ ( in @ SV626 @ SV385 ) )
= $true )
| ( ( in @ SV626 @ ( setadjoin @ SV81 @ SV385 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1677]) ).
thf(1996,plain,
! [SV386: $i,SV82: $i] :
( ( ( breln1 @ SV82 @ SV386 )
= $false )
| ( ( ! [SY3301: $i] :
( ~ ( breln1 @ SV82 @ SY3301 )
| ! [SY3302: $i] :
( ~ ( in @ SY3302 @ SV82 )
| ! [SY3303: $i] :
( ~ ( in @ SY3303 @ SV82 )
| ~ ( in @ ( kpair @ SY3302 @ SY3303 ) @ ( binunion @ SV386 @ SY3301 ) )
| ( in @ ( kpair @ SY3302 @ SY3303 ) @ SV386 )
| ( in @ ( kpair @ SY3302 @ SY3303 ) @ SY3301 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1997,plain,
! [SV83: $i,SV387: $i] :
( ( ( subset @ SV387 @ SV83 )
= $false )
| ( ( in @ SV387 @ ( powerset @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1998,plain,
! [SV85: $i,SV388: $i] :
( ( ( in @ SV388 @ ( powerset @ SV85 ) )
= $false )
| ( ( ! [SY3304: $i] :
( ~ ( in @ SY3304 @ ( powerset @ SV85 ) )
| ( ( setminus @ SV85 @ ( binintersect @ SV388 @ SY3304 ) )
= ( binunion @ ( setminus @ SV85 @ SV388 ) @ ( setminus @ SV85 @ SY3304 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1681]) ).
thf(1999,plain,
! [SV86: $i,SV389: $i] :
( ( ( in @ SV389 @ ( powerset @ SV86 ) )
= $false )
| ( ( ! [SY3305: $i] :
( ~ ( in @ SY3305 @ ( powerset @ SV86 ) )
| ! [SY3306: $i] :
( ~ ( in @ SY3306 @ SV86 )
| ~ ( subset @ SV389 @ ( setminus @ SV86 @ SY3305 ) )
| ~ ( in @ SY3306 @ SY3305 )
| ~ ( in @ SY3306 @ SV389 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1682]) ).
thf(2000,plain,
! [SV87: $i,SV390: $i] :
( ( ( in @ SV390 @ ( powerset @ SV87 ) )
= $false )
| ( ( ! [SY3307: $i] :
( ~ ( in @ SY3307 @ ( powerset @ SV87 ) )
| ! [SY3308: $i] :
( ~ ( in @ SY3308 @ SV87 )
| ~ ( subset @ SV390 @ SY3307 )
| ~ ~ ( in @ SY3308 @ SY3307 )
| ~ ( in @ SY3308 @ SV390 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1683]) ).
thf(2001,plain,
! [SV88: $i,SV391: $i] :
( ( ( in @ SV391 @ ( powerset @ SV88 ) )
= $false )
| ( ( ! [SY3309: $i] :
( ~ ( in @ SY3309 @ ( powerset @ SV88 ) )
| ( subset @ ( setminus @ SV88 @ SV391 ) @ ( setminus @ SV88 @ ( binintersect @ SV391 @ SY3309 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1684]) ).
thf(2002,plain,
! [SV89: $i,SV392: $i] :
( ( ( in @ SV392 @ ( powerset @ SV89 ) )
= $false )
| ( ( subset @ SV392 @ ( setminus @ SV89 @ ( setminus @ SV89 @ SV392 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(2003,plain,
! [SV90: $i,SV393: $i] :
( ( ( in @ SV393 @ ( powerset @ SV90 ) )
= $false )
| ( ( ! [SY3310: $i] :
( ~ ( in @ SY3310 @ ( powerset @ SV90 ) )
| ! [SY3311: $i] :
( ~ ( in @ SY3311 @ ( powerset @ SV90 ) )
| ! [SY3312: $i] :
( ~ ( in @ SY3312 @ SV90 )
| ~ ( in @ SY3312 @ ( binintersect @ SV393 @ SY3310 ) )
| ( in @ SY3312 @ ( binintersect @ ( binunion @ SV393 @ SY3311 ) @ ( binunion @ SY3310 @ SY3311 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1686]) ).
thf(2004,plain,
! [SV394: $i,SV92: $i,SV627: $i] :
( ( ( ~ ( in @ SV627 @ SV92 ) )
= $true )
| ( ( ~ ~ ( in @ SV627 @ SV394 )
| ( in @ SV627 @ ( setminus @ SV92 @ SV394 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1690]) ).
thf(2005,plain,
! [SV93: $i,SV395: $i] :
( ( ( in @ SV395 @ SV93 )
= $false )
| ( ( in @ ( setadjoin @ SV395 @ emptyset ) @ ( powerset @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1691]) ).
thf(2006,plain,
! [SV396: $i,SV95: $i,SV628: $i] :
( ( ( ~ ( in @ SV628 @ ( funcSet @ SV95 @ SV396 ) ) )
= $true )
| ( ( ! [SY3755: $i] :
( ~ ( in @ SY3755 @ SV95 )
| ( ( ap @ SV95 @ SV396 @ SV628 @ SY3755 )
= ( ap @ SV95 @ SV396 @ SV628 @ SY3755 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1695]) ).
thf(2007,plain,
! [SV397: $i,SV96: $i,SV629: $i] :
( ( ( ~ ~ ( in @ SV629 @ ( setminus @ SV96 @ SV397 ) ) )
= $true )
| ( ( ~ ( in @ SV629 @ SV96 )
| ( in @ SV629 @ SV397 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1696]) ).
thf(2008,plain,
! [SV398: $i,SV97: $i,SV630: $i] :
( ( ( ~ ( in @ SV630 @ ( cartprod @ SV97 @ SV398 ) ) )
= $true )
| ( ( iskpair @ SV630 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1697]) ).
thf(2009,plain,
! [SV98: $i,SV399: $i] :
( ( ( in @ SV399 @ ( powerset @ SV98 ) )
= $false )
| ( ( in @ ( powerset @ SV399 ) @ ( powerset @ ( powerset @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1698]) ).
thf(2010,plain,
! [SV99: $i,SV400: $i] :
( ( ( in @ SV400 @ ( powerset @ SV99 ) )
= $false )
| ( ( ! [SY3318: $i] :
( ~ ( in @ SY3318 @ ( powerset @ SV99 ) )
| ! [SY3319: $i] :
( ~ ( in @ SY3319 @ SV99 )
| ~ ( in @ SY3319 @ ( setminus @ SV99 @ ( binunion @ SV400 @ SY3318 ) ) )
| ( in @ SY3319 @ ( setminus @ SV99 @ SV400 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(2011,plain,
! [SV100: $i > $o] :
( ( ( ! [SY2562: $i] :
~ ( SV100 @ SY2562 ) )
= $true )
| ( ( ~ ! [SY2563: $i,SY2564: $i] :
( ~ ( SV100 @ SY2563 )
| ~ ( SV100 @ SY2564 )
| ( SY2563 = SY2564 ) )
| ~ ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1700]) ).
thf(2012,plain,
! [SV401: $i,SV101: $i] :
( ( ( ( setadjoin @ SV101 @ emptyset )
= ( setadjoin @ SV401 @ emptyset ) )
= $false )
| ( ( SV101 = SV401 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1701]) ).
thf(2013,plain,
! [SV402: $i,SV102: $i,SV631: $i] :
( ( ( ~ ~ ( in @ SV631 @ ( setminus @ SV102 @ SV402 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV631 @ SV402 )
| ~ ( in @ SV631 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1702]) ).
thf(2014,plain,
! [SV403: $i,SV103: $i,SV632: $i] :
( ( ( ~ ( in @ SV632 @ ( funcSet @ SV103 @ SV403 ) ) )
= $true )
| ( ( ( lam @ SV103 @ SV403
@ ^ [SY3756: $i] : ( ap @ SV103 @ SV403 @ SV632 @ SY3756 ) )
= SV632 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1703]) ).
thf(2015,plain,
! [SV404: $i > $o,SV104: $i] :
( ( ( ~ ! [SY3323: $i] :
~ ~ ( ~ ( in @ SY3323 @ SV104 )
| ~ ~ ( SV404 @ SY3323 ) ) )
= $false )
| ( ( ~ ! [SY3324: $i] :
( ~ ( in @ SY3324 @ SV104 )
| ( SV404 @ SY3324 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1704]) ).
thf(2016,plain,
! [SV105: $i,SV405: $i] :
( ( ( in @ SV405 @ ( funcSet @ SV105 @ ( powerset @ SV105 ) ) )
= $false )
| ( ( ~ ( surjective @ SV105 @ ( powerset @ SV105 ) @ SV405 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1705]) ).
thf(2017,plain,
! [SV106: $i] :
( ( ( ~ ( in @ emptyset @ SV106 )
| ~ ! [SY2577: $i] :
( ~ ~ ( ~ ( in @ SY2577 @ omega )
| ~ ( in @ SY2577 @ SV106 ) )
| ( in @ ( setadjoin @ SY2577 @ SY2577 ) @ SV106 ) ) )
= $true )
| ( ( ! [SY2578: $i] :
( ~ ( in @ SY2578 @ omega )
| ( in @ SY2578 @ SV106 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1706]) ).
thf(2018,plain,
! [SV633: $i,SV406: $i,SV108: $i] :
( ( ( ~ ( func @ SV108 @ SV406 @ SV633 ) )
= $true )
| ( ( ! [SY3757: $i] :
( ~ ( in @ SY3757 @ SV108 )
| ( singleton
@ ( dsetconstr @ SV406
@ ^ [SY3758: $i] : ( in @ ( kpair @ SY3757 @ SY3758 ) @ SV633 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1708]) ).
thf(2019,plain,
! [SV109: $i,SV407: $i] :
( ( ( in @ SV407 @ ( powerset @ SV109 ) )
= $false )
| ( ( ! [SY3328: $i] :
( ~ ( in @ SY3328 @ ( powerset @ SV109 ) )
| ~ ! [SY3329: $i] :
( ~ ( in @ SY3329 @ SV109 )
| ~ ( in @ SY3329 @ SV407 )
| ( in @ SY3329 @ SY3328 ) )
| ( subset @ SV407 @ SY3328 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(2020,plain,
! [SV110: $i,SV408: $i] :
( ( ( in @ SV408 @ ( powerset @ SV110 ) )
= $false )
| ( ( ! [SY3330: $i] :
( ~ ( in @ SY3330 @ ( powerset @ SV110 ) )
| ! [SY3331: $i] :
( ~ ( in @ SY3331 @ SV110 )
| ~ ~ ( in @ SY3331 @ SV408 )
| ~ ( in @ SY3331 @ ( binintersect @ SV408 @ SY3330 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1710]) ).
thf(2021,plain,
! [SV409: $i,SV111: $i,SV634: $i] :
( ( ( ~ ( in @ SV634 @ ( cartprod @ SV111 @ SV409 ) ) )
= $true )
| ( ( in @ ( ksnd @ SV634 ) @ SV409 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1711]) ).
thf(2022,plain,
! [SV410: $i,SV112: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV112 ) )
= $true )
| ( ( ! [SY3759: $i] :
( ~ ( in @ SY3759 @ SV410 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV635 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV635 @ ( setadjoin @ SY3759 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV112 @ SV410 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1712]) ).
thf(2023,plain,
! [SV113: $i,SV411: $i] :
( ( ( in @ SV411 @ ( powerset @ SV113 ) )
= $false )
| ( ( ! [SY3335: $i] :
( ~ ( in @ SY3335 @ ( powerset @ SV113 ) )
| ! [SY3336: $i] :
( ~ ( in @ SY3336 @ SV113 )
| ~ ( in @ SY3336 @ ( setminus @ SV113 @ SV411 ) )
| ( in @ SY3336 @ ( setminus @ SV113 @ ( binintersect @ SV411 @ SY3335 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1713]) ).
thf(2024,plain,
! [SV114: $i,SV412: $i] :
( ( ( in @ SV412 @ ( powerset @ SV114 ) )
= $false )
| ( ( ! [SY3337: $i] :
( ~ ( in @ SY3337 @ SV114 )
| ~ ( in @ SY3337 @ SV412 )
| ~ ( in @ SY3337 @ ( setminus @ SV114 @ SV412 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1714]) ).
thf(2025,plain,
! [SV636: $i > $i > $o,SV413: $i,SV115: $i,SV746: $i] :
( ( ! [SY3914: $i] :
( ~ ( in @ ( kpair @ SV746 @ SY3914 )
@ ( dpsetconstr @ SV115 @ SV413
@ ^ [SY3762: $i,SY3763: $i] : ( SV636 @ SY3762 @ SY3763 ) ) )
| ( in @ SV746 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2026,plain,
! [SV637: $i > $i > $o,SV414: $i,SV116: $i,SV747: $i] :
( ( ! [SY3917: $i] :
( ~ ( in @ ( kpair @ SV747 @ SY3917 )
@ ( dpsetconstr @ SV116 @ SV414
@ ^ [SY3766: $i,SY3767: $i] : ( SV637 @ SY3766 @ SY3767 ) ) )
| ( in @ SY3917 @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(2027,plain,
! [SV415: $i,SV117: $i,SV638: $i] :
( ( ( ~ ( in @ SV638 @ ( setminus @ SV117 @ SV415 ) ) )
= $true )
| ( ( ~ ( in @ SV638 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1717]) ).
thf(2028,plain,
! [SV416: $i > $o,SV118: $i,SV639: $i] :
( ( ( ~ ( in @ SV639 @ SV118 ) )
= $true )
| ( ( ~ ( SV416 @ SV639 )
| ~ ! [SY3768: $i] :
( ~ ( in @ SY3768 @ SV118 )
| ~ ( SV416 @ SY3768 )
| ( SY3768 = SV639 ) )
| ( ex1 @ SV118
@ ^ [SY3351: $i] : ( SV416 @ SY3351 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1718]) ).
thf(2029,plain,
! [SV417: $i,SV119: $i] :
( ( ( ( setminus @ SV119 @ SV417 )
= emptyset )
= $false )
| ( ( subset @ SV119 @ SV417 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(2030,plain,
! [SV418: $i,SV120: $i,SV640: $i] :
( ( ( ~ ~ ( in @ SV640 @ SV120 ) )
= $true )
| ( ( ~ ~ ( in @ SV640 @ SV418 )
| ~ ( in @ SV640 @ ( symdiff @ SV120 @ SV418 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1720]) ).
thf(2031,plain,
! [SV419: $i,SV641: $i > $i,SV121: $i] :
( ( ( ~ ! [SY3770: $i] :
( ~ ( in @ SY3770 @ SV121 )
| ( in @ ( SV641 @ SY3770 ) @ SV419 ) ) )
= $true )
| ( ( ! [SY3771: $i] :
( ~ ( in @ SY3771 @ SV121 )
| ( ( ap @ SV121 @ SV419
@ ( lam @ SV121 @ SV419
@ ^ [SY3772: $i] : ( SV641 @ SY3772 ) )
@ SY3771 )
= ( SV641 @ SY3771 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1721]) ).
thf(2032,plain,
! [SV420: $i,SV122: $i] :
( ( ( SV122 = SV420 )
= $false )
| ( ( ! [SY3357: $i > $o,SY3358: $i > $o] :
( ~ ! [SY3359: $i] :
( ~ ( in @ SY3359 @ SV122 )
| ! [SY3360: $i] :
( ~ ( in @ SY3360 @ SV420 )
| ( SY3359 != SY3360 )
| ~ ( ~ ( ~ ( SY3357 @ SY3359 )
| ( SY3358 @ SY3360 ) )
| ~ ( ~ ( SY3358 @ SY3360 )
| ( SY3357 @ SY3359 ) ) ) ) )
| ( ( dsetconstr @ SV122
@ ^ [SX4: $i] : ( SY3357 @ SX4 ) )
= ( dsetconstr @ SV420
@ ^ [SX4: $i] : ( SY3358 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(2033,plain,
! [SV421: $i > $o,SV123: $i] :
( ( ( ex1 @ SV123
@ ^ [SY3363: $i] : ( SV421 @ SY3363 ) )
= $false )
| ( ( ! [SY3364: $i] :
( ~ ( in @ SY3364 @ SV123 )
| ! [SY3365: $i] :
( ~ ( in @ SY3365 @ SV123 )
| ~ ( SV421 @ SY3364 )
| ~ ( SV421 @ SY3365 )
| ( SY3364 = SY3365 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1723]) ).
thf(2034,plain,
! [SV422: $i,SV124: $i] :
( ( ( in @ SV124 @ SV422 )
= $false )
| ( ( ~ ( in @ SV422 @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(2035,plain,
! [SV423: $i,SV125: $i] :
( ( ( breln1 @ SV125 @ SV423 )
= $false )
| ( ( ! [SY3366: $i] :
( ~ ( breln1 @ SV125 @ SY3366 )
| ! [SY3367: $i] :
( ~ ( in @ SY3367 @ SV125 )
| ! [SY3368: $i] :
( ~ ( in @ SY3368 @ SV125 )
| ~ ( in @ ( kpair @ SY3367 @ SY3368 ) @ SY3366 )
| ( in @ ( kpair @ SY3367 @ SY3368 ) @ ( binunion @ SV423 @ SY3366 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1725]) ).
thf(2036,plain,
! [SV424: $o,SV126: $i,SV642: $i] :
( ( ( ~ ( in @ SV642 @ SV126 ) )
= $true )
| ( ( ! [SY3773: $i] :
( ~ ( in @ SY3773 @ SV126 )
| ~ ~ SV424
| ( in @ SY3773
@ ( dsetconstr @ SV126
@ ^ [SY3774: $i] :
( ~ ( ~ SV424
| ( SY3774 != SV642 ) )
| ~ ( ~ ~ SV424
| ( SY3774 != SY3773 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1726]) ).
thf(2037,plain,
! [SV126: $i,SV643: $i] :
( ( ( ~ ( in @ SV643 @ SV126 ) )
= $true )
| ( ( ! [SY3775: $i] :
( ~ ( in @ SY3775 @ SV126 )
| ~ ~ $true
| ( in @ SY3775
@ ( dsetconstr @ SV126
@ ^ [SY3776: $i] :
( ~ ( ~ $true
| ( SY3776 != SV643 ) )
| ~ ( ~ ~ $true
| ( SY3776 != SY3775 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(2038,plain,
! [SV126: $i,SV644: $i] :
( ( ( ~ ( in @ SV644 @ SV126 ) )
= $true )
| ( ( ! [SY3777: $i] :
( ~ ( in @ SY3777 @ SV126 )
| ~ ~ $false
| ( in @ SY3777
@ ( dsetconstr @ SV126
@ ^ [SY3778: $i] :
( ~ ( ~ $false
| ( SY3778 != SV644 ) )
| ~ ( ~ ~ $false
| ( SY3778 != SY3777 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1728]) ).
thf(2039,plain,
! [SV425: $i,SV127: $i,SV645: $i] :
( ( ( ~ ( in @ SV645 @ ( setadjoin @ SV127 @ SV425 ) ) )
= $true )
| ( ( ( SV645 = SV127 )
| ( in @ SV645 @ SV425 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1729]) ).
thf(2040,plain,
! [SV426: $i,SV128: $i,SV646: $i] :
( ( ( ~ ( in @ SV646 @ SV128 ) )
= $true )
| ( ( ~ ( in @ SV646 @ SV426 )
| ~ ( in @ SV646 @ ( symdiff @ SV128 @ SV426 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1730]) ).
thf(2041,plain,
! [SV129: $i] :
( ( ( ! [SY2650: $i] :
~ ( in @ SY2650 @ SV129 ) )
= $true )
| ( ( SV129 != emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1731]) ).
thf(2042,plain,
! [SV130: $i,SV427: $i] :
( ( ~ ( ~ ( in @ SV427 @ ( powerset @ SV130 ) )
| ! [SY3374: $i] :
( ~ ( in @ SY3374 @ SV427 )
| ( in @ SY3374 @ SV130 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1732]) ).
thf(2043,plain,
! [SV130: $i,SV427: $i] :
( ( ~ ( ~ ! [SY3375: $i] :
( ~ ( in @ SY3375 @ SV427 )
| ( in @ SY3375 @ SV130 ) )
| ( in @ SV427 @ ( powerset @ SV130 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1732]) ).
thf(2044,plain,
! [SV428: $i,SV131: $i] :
( ( ( breln1 @ SV131 @ SV428 )
= $false )
| ( ( ! [SY3376: $i] :
( ~ ( breln1 @ SV131 @ SY3376 )
| ! [SY3377: $i] :
( ~ ( in @ SY3377 @ SV131 )
| ! [SY3378: $i] :
( ~ ( in @ SY3378 @ SV131 )
| ! [SY3379: $i] :
( ~ ( in @ SY3379 @ SV131 )
| ~ ( in @ ( kpair @ SY3377 @ SY3379 ) @ SV428 )
| ~ ( in @ ( kpair @ SY3379 @ SY3378 ) @ SY3376 )
| ( in @ ( kpair @ SY3377 @ SY3378 ) @ ( breln1compset @ SV131 @ SV428 @ SY3376 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(2045,plain,
! [SV132: $i,SV429: $i] :
( ( ( in @ SV429 @ ( powerset @ SV132 ) )
= $false )
| ( ( ! [SY3380: $i] :
( ~ ( in @ SY3380 @ ( powerset @ SV132 ) )
| ( in @ ( setminus @ SV132 @ ( binunion @ SV429 @ SY3380 ) ) @ ( powerset @ ( setminus @ SV132 @ SV429 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1734]) ).
thf(2046,plain,
! [SV430: $i,SV133: $i,SV647: $i] :
( ( ( ~ ( in @ ( setadjoin @ SV647 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV133 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV133 @ ( setadjoin @ SV430 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( SV133 = SV647 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1735]) ).
thf(2047,plain,
! [SV648: $i,SV431: $i,SV134: $i] :
( ( ( ( setadjoin @ SV134 @ ( setadjoin @ SV431 @ emptyset ) )
!= ( setadjoin @ SV648 @ emptyset ) )
= $true )
| ( ( SV134 = SV431 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1736]) ).
thf(2048,plain,
! [SV432: $i,SV135: $i] :
( ( ( breln1 @ SV135 @ SV432 )
= $false )
| ( ( ! [SY3383: $i] :
( ~ ( breln1 @ SV135 @ SY3383 )
| ~ ! [SY3384: $i] :
( ~ ( in @ SY3384 @ SV135 )
| ! [SY3385: $i] :
( ~ ( in @ SY3385 @ SV135 )
| ~ ( in @ ( kpair @ SY3384 @ SY3385 ) @ SV432 )
| ( in @ ( kpair @ SY3384 @ SY3385 ) @ SY3383 ) ) )
| ( subset @ SV432 @ SY3383 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(2049,plain,
! [SV136: $i] :
( ( ( SV136 = emptyset )
= $true )
| ( ( ~ ! [SY2669: $i] :
~ ~ ( ~ ( in @ SY2669 @ SV136 )
| ( ( binintersect @ SY2669 @ SV136 )
!= emptyset ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1738]) ).
thf(2050,plain,
! [SV433: $i,SV137: $i,SV649: $i] :
( ( ( ~ ( in @ SV649 @ ( cartprod @ SV137 @ SV433 ) ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV649 ) @ ( ksnd @ SV649 ) )
= SV649 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1739]) ).
thf(2051,plain,
! [SV434: $i,SV138: $i] :
( ( ( SV138 = SV434 )
= $false )
| ( ( ! [SY3387: $i,SY3388: $i] :
( ( SY3387 != SY3388 )
| ~ ( ~ ( ~ ( in @ SY3387 @ SV138 )
| ( in @ SY3388 @ SV434 ) )
| ~ ( ~ ( in @ SY3388 @ SV434 )
| ( in @ SY3387 @ SV138 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(2052,plain,
! [SV139: $i,SV435: $i] :
( ( ( in @ SV435 @ ( powerset @ SV139 ) )
= $false )
| ( ( ! [SY3389: $i] :
( ~ ( in @ SY3389 @ ( powerset @ SV139 ) )
| ! [SY3390: $i] :
( ~ ( in @ SY3390 @ ( powerset @ SV139 ) )
| ~ ( subset @ SV435 @ SY3390 )
| ( subset @ ( binintersect @ SV435 @ SY3389 ) @ SY3390 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(2053,plain,
! [SV650: $i,SV436: $i,SV140: $i] :
( ( ( ~ ( breln @ SV140 @ SV436 @ SV650 ) )
= $true )
| ( ( ! [SY3779: $i] :
( ~ ( breln @ SV140 @ SV436 @ SY3779 )
| ~ ! [SY3780: $i] :
( ~ ( in @ SY3780 @ SV140 )
| ! [SY3781: $i] :
( ~ ( in @ SY3781 @ SV436 )
| ~ ( in @ ( kpair @ SY3780 @ SY3781 ) @ SV650 )
| ( in @ ( kpair @ SY3780 @ SY3781 ) @ SY3779 ) ) )
| ~ ! [SY3782: $i] :
( ~ ( in @ SY3782 @ SV140 )
| ! [SY3783: $i] :
( ~ ( in @ SY3783 @ SV436 )
| ~ ( in @ ( kpair @ SY3782 @ SY3783 ) @ SY3779 )
| ( in @ ( kpair @ SY3782 @ SY3783 ) @ SV650 ) ) )
| ( SV650 = SY3779 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1742]) ).
thf(2054,plain,
! [SV437: $i,SV141: $i,SV651: $i] :
( ( ( ~ ( in @ SV651 @ SV141 ) )
= $true )
| ( ( ! [SY3784: $i] :
( ~ ( in @ SY3784 @ SV437 )
| ( in @ ( kpair @ SV651 @ SY3784 ) @ ( cartprod @ SV141 @ SV437 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1743]) ).
thf(2055,plain,
! [SV438: $i,SV142: $i,SV652: $i] :
( ( ( ~ ( in @ SV652 @ SV142 ) )
= $true )
| ( ( ! [SY3785: $i] :
( ~ ( in @ SY3785 @ SV438 )
| ( in @ ( kpair @ SV652 @ SY3785 ) @ ( powerset @ ( powerset @ ( binunion @ SV142 @ SV438 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1744]) ).
thf(2056,plain,
! [SV439: $i,SV143: $i,SV653: $i] :
( ( ( ~ ( in @ SV653 @ ( binintersect @ SV143 @ SV439 ) ) )
= $true )
| ( ( in @ SV653 @ SV439 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1745]) ).
thf(2057,plain,
! [SV440: $i,SV654: $i > $i,SV144: $i] :
( ( ( ~ ! [SY3786: $i] :
( ~ ( in @ SY3786 @ SV144 )
| ( in @ ( SV654 @ SY3786 ) @ SV440 ) ) )
= $true )
| ( ( ! [SY3787: $i] :
( ~ ( in @ SY3787 @ ( funcSet @ SV440 @ SV144 ) )
| ~ ! [SY3788: $i] :
( ~ ( in @ SY3788 @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SY3787 @ ( SV654 @ SY3788 ) )
= SY3788 ) )
| ( surjective @ SV440 @ SV144 @ SY3787 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1746]) ).
thf(2058,plain,
! [SV145: $i,SV441: $i] :
( ( ( in @ SV441 @ ( powerset @ SV145 ) )
= $false )
| ( ( ! [SY3406: $i] :
( ~ ( in @ SY3406 @ SV145 )
| ~ ( in @ SY3406 @ SV441 )
| ( in @ SY3406 @ ( setminus @ SV145 @ ( setminus @ SV145 @ SV441 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(2059,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ( ! [SY3407: $i] :
( ~ ( in @ SY3407 @ SV146 )
| ! [SY3408: $i] :
( ~ ( in @ SY3408 @ SV146 )
| ~ ( SV442 @ SY3407 )
| ~ ( SV442 @ SY3408 )
| ( SY3407 = SY3408 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) )
| ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(2060,plain,
! [SV147: $i,SV443: $i] :
( ( ( in @ SV443 @ ( powerset @ SV147 ) )
= $false )
| ( ( ! [SY3411: $i] :
( ~ ( in @ SY3411 @ ( powerset @ SV147 ) )
| ! [SY3412: $i] :
( ~ ( in @ SY3412 @ SV147 )
| ~ ( in @ SY3412 @ ( setminus @ SV147 @ SV443 ) )
| ~ ( in @ SY3412 @ ( binintersect @ SV443 @ SY3411 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(2061,plain,
! [SV148: $i,SV444: $i] :
( ( ( in @ SV444 @ ( powerset @ SV148 ) )
= $false )
| ( ( ! [SY3413: $i] :
( ~ ( in @ SY3413 @ ( powerset @ SV148 ) )
| ! [SY3414: $i] :
( ~ ( in @ SY3414 @ ( powerset @ SV148 ) )
| ! [SY3415: $i] :
( ~ ( in @ SY3415 @ SV148 )
| ~ ( in @ SY3415 @ ( binintersect @ SV444 @ SY3413 ) )
| ( in @ SY3415 @ ( binunion @ SV444 @ SY3414 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1750]) ).
thf(2062,plain,
! [SV445: $i > $o,SV149: $i] :
( ( ( ex1 @ SV149
@ ^ [SY3416: $i] : ( SV445 @ SY3416 ) )
= $false )
| ( ( ~ ! [SY3417: $i] :
~ ~ ( ~ ( in @ SY3417 @ SV149 )
| ~ ( SV445 @ SY3417 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1751]) ).
thf(2063,plain,
! [SV446: $i,SV150: $i] :
( ( ( breln1 @ SV150 @ SV446 )
= $false )
| ( ( ! [SY3418: $i] :
( ~ ( breln1 @ SV150 @ SY3418 )
| ! [SY3419: $i] :
( ~ ( breln1 @ SV150 @ SY3419 )
| ( ( breln1compset @ SV150 @ ( binunion @ SV446 @ SY3418 ) @ SY3419 )
= ( binunion @ ( breln1compset @ SV150 @ SV446 @ SY3419 ) @ ( breln1compset @ SV150 @ SY3418 @ SY3419 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1752]) ).
thf(2064,plain,
! [SV655: $i > $i > $o,SV447: $i,SV151: $i,SV748: $i] :
( ( ! [SY3920: $i] :
( ~ ( in @ ( kpair @ SV748 @ SY3920 )
@ ( dpsetconstr @ SV151 @ SV447
@ ^ [SY3791: $i,SY3792: $i] : ( SV655 @ SY3791 @ SY3792 ) ) )
| ( SV655 @ SV748 @ SY3920 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2065,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ! [SY3425: $i,SY3426: $i] :
( ( SY3425 != SY3426 )
| ~ ( ~ ( ~ ( SV152 @ SY3425 )
| ( SV448 @ SY3426 ) )
| ~ ( ~ ( SV448 @ SY3426 )
| ( SV152 @ SY3425 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1754]) ).
thf(2066,plain,
! [SV449: $i,SV153: $i] :
( ( ( subset @ SV153 @ SV449 )
= $false )
| ( ( ~ ( subset @ SV449 @ SV153 )
| ( SV153 = SV449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(2067,plain,
! [SV656: $i,SV450: $i,SV154: $i] :
( ( ( ~ ( func @ SV154 @ SV450 @ SV656 ) )
= $true )
| ( ( in @ SV656 @ ( funcSet @ SV154 @ SV450 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1756]) ).
thf(2068,plain,
! [SV451: $o,SV155: $i,SV657: $i] :
( ( ( ~ ( in @ SV657 @ SV155 ) )
= $true )
| ( ( ! [SY3793: $i] :
( ~ ( in @ SY3793 @ SV155 )
| ~ ~ SV451
| ( ( dsetconstr @ SV155
@ ^ [SY3794: $i] :
( ~ ( ~ SV451
| ( SY3794 != SV657 ) )
| ~ ( ~ ~ SV451
| ( SY3794 != SY3793 ) ) ) )
= ( setadjoin @ SY3793 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1757]) ).
thf(2069,plain,
! [SV155: $i,SV658: $i] :
( ( ( ~ ( in @ SV658 @ SV155 ) )
= $true )
| ( ( ! [SY3795: $i] :
( ~ ( in @ SY3795 @ SV155 )
| ~ ~ $true
| ( ( dsetconstr @ SV155
@ ^ [SY3796: $i] :
( ~ ( ~ $true
| ( SY3796 != SV658 ) )
| ~ ( ~ ~ $true
| ( SY3796 != SY3795 ) ) ) )
= ( setadjoin @ SY3795 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1758]) ).
thf(2070,plain,
! [SV155: $i,SV659: $i] :
( ( ( ~ ( in @ SV659 @ SV155 ) )
= $true )
| ( ( ! [SY3797: $i] :
( ~ ( in @ SY3797 @ SV155 )
| ~ ~ $false
| ( ( dsetconstr @ SV155
@ ^ [SY3798: $i] :
( ~ ( ~ $false
| ( SY3798 != SV659 ) )
| ~ ( ~ ~ $false
| ( SY3798 != SY3797 ) ) ) )
= ( setadjoin @ SY3797 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1759]) ).
thf(2071,plain,
! [SV660: $i,SV156: $i,SV452: $i] :
( ( ( ~ ( in @ SV452 @ ( powerset @ SV156 ) ) )
= $true )
| ( ( ~ ( in @ SV660 @ SV452 )
| ( in @ SV660 @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(2072,plain,
! [SV453: $i,SV157: $i] :
( ( ( breln1 @ SV157 @ SV453 )
= $false )
| ( ( ! [SY3438: $i] :
( ~ ( in @ SY3438 @ SV157 )
| ! [SY3439: $i] :
( ~ ( in @ SY3439 @ SV157 )
| ~ ( in @ ( kpair @ SY3438 @ SY3439 ) @ SV453 )
| ( in @ ( kpair @ SY3439 @ SY3438 ) @ ( breln1invset @ SV157 @ SV453 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1761]) ).
thf(2073,plain,
! [SV661: $i,SV454: $i,SV158: $i] :
( ( ( ~ ( subset @ SV158 @ SV454 ) )
= $true )
| ( ( ~ ( subset @ SV454 @ SV661 )
| ( subset @ SV158 @ SV661 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1762]) ).
thf(2074,plain,
! [SV455: $i > $o,SV159: $i,SV662: $i] :
( ( ( ~ ( in @ SV662 @ SV159 ) )
= $true )
| ( ( ~ ( SV455 @ SV662 )
| ( ( dsetconstr @ SV159
@ ^ [SY3442: $i] : ( SV455 @ SY3442 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1763]) ).
thf(2075,plain,
! [SV663: $i,SV456: $i,SV160: $i] :
( ( ( ~ ( subset @ SV160 @ SV456 ) )
= $true )
| ( ( ~ ( in @ SV663 @ SV160 )
| ( in @ SV663 @ SV456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1764]) ).
thf(2076,plain,
! [SV457: $i,SV161: $i] :
( ( ( SV161 = SV457 )
= $false )
| ( ( ( setadjoin @ SV161 @ ( setadjoin @ SV457 @ emptyset ) )
= ( setadjoin @ SV161 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(2077,plain,
! [SV162: $i,SV458: $i] :
( ( ( in @ SV458 @ ( powerset @ SV162 ) )
= $false )
| ( ( ! [SY3444: $i] :
( ~ ( in @ SY3444 @ ( powerset @ SV162 ) )
| ( in @ ( setminus @ SV162 @ ( binunion @ SV458 @ SY3444 ) ) @ ( powerset @ ( setminus @ SV162 @ SV458 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1766]) ).
thf(2078,plain,
! [SV163: $i,SV459: $i] :
( ( ( in @ SV459 @ ( powerset @ SV163 ) )
= $false )
| ( ( ! [SY3445: $i] :
( ~ ( in @ SY3445 @ ( powerset @ SV163 ) )
| ! [SY3446: $i] :
( ~ ( in @ SY3446 @ ( powerset @ SV163 ) )
| ~ ( subset @ SY3445 @ SY3446 )
| ( subset @ ( binintersect @ SV459 @ SY3445 ) @ SY3446 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1767]) ).
thf(2079,plain,
! [SV460: $i,SV164: $i,SV664: $i] :
( ( ( ~ ~ ( in @ SV664 @ SV164 ) )
= $true )
| ( ( ~ ( in @ SV664 @ ( setminus @ SV164 @ SV460 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(2080,plain,
! [SV461: $i,SV165: $i] :
( ( ( SV165 = SV461 )
= $false )
| ( ( ( setunion @ SV165 )
= ( setunion @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(2081,plain,
! [SV166: $i,SV462: $i,SV665: $i] :
( ( ( ~ ( in @ SV665 @ SV462 ) )
= $true )
| ( ( ~ ( in @ SV665 @ ( setminus @ SV166 @ SV462 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1770]) ).
thf(2082,plain,
! [SV463: $i,SV167: $i] :
( ( ( SV167 = SV463 )
= $false )
| ( ( ! [SY3449: $i,SY3450: $i] :
( ( SY3449 != SY3450 )
| ~ ( in @ SY3449 @ SV167 )
| ( in @ SY3450 @ SV463 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1771]) ).
thf(2083,plain,
! [SV666: $i,SV464: $i,SV168: $i] :
( ( ( ~ ( breln @ SV168 @ SV464 @ SV666 ) )
= $true )
| ( ( ! [SY3800: $i] :
( ~ ( breln @ SV168 @ SV464 @ SY3800 )
| ~ ! [SY3801: $i] :
( ~ ( in @ SY3801 @ SV168 )
| ! [SY3802: $i] :
( ~ ( in @ SY3802 @ SV464 )
| ~ ( in @ ( kpair @ SY3801 @ SY3802 ) @ SV666 )
| ( in @ ( kpair @ SY3801 @ SY3802 ) @ SY3800 ) ) )
| ( subset @ SV666 @ SY3800 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1772]) ).
thf(2084,plain,
! [SV465: $i,SV169: $i] :
( ( ( breln1 @ SV169 @ SV465 )
= $false )
| ( ( ! [SY3455: $i] :
( ~ ( breln1 @ SV169 @ SY3455 )
| ! [SY3456: $i] :
( ~ ( breln1 @ SV169 @ SY3456 )
| ( ( breln1compset @ SV169 @ ( binunion @ SV465 @ SY3455 ) @ SY3456 )
= ( binunion @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SY3456 ) @ ( breln1invset @ SV169 @ SY3455 ) ) ) @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SY3456 ) @ ( breln1invset @ SV169 @ SV465 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1773]) ).
thf(2085,plain,
! [SV171: $i,SV466: $i] :
( ( ( in @ SV466 @ ( powerset @ SV171 ) )
= $false )
| ( ( ! [SY3457: $i] :
( ~ ( in @ SY3457 @ ( powerset @ SV171 ) )
| ! [SY3458: $i] :
( ~ ( in @ SY3458 @ ( binintersect @ SV466 @ SY3457 ) )
| ( in @ SY3458 @ SV171 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1775]) ).
thf(2086,plain,
! [SV467: $i,SV172: $i] :
( ( ( SV172 = SV467 )
= $false )
| ( ( subset @ SV467 @ SV172 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(2087,plain,
! [SV173: $i,SV468: $i] :
( ( ( in @ SV468 @ ( powerset @ SV173 ) )
= $false )
| ( ( ! [SY3459: $i] :
( ~ ( in @ SY3459 @ ( powerset @ SV173 ) )
| ~ ( subset @ SV468 @ ( setminus @ SV173 @ SY3459 ) )
| ( subset @ SY3459 @ ( setminus @ SV173 @ SV468 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1777]) ).
thf(2088,plain,
! [SV749: $i,SV667: $i,SV469: $i,SV174: $i] :
( ( ( ( kpair @ SV174 @ SV469 )
!= ( kpair @ SV667 @ SV749 ) )
| ( SV174 = SV667 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2089,plain,
! [SV175: $i,SV470: $i > $i] :
( ( ~ ~ ( ~ ! [SY3923: $i] :
~ ( ~ ( ~ ( in @ SY3923 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
| ~ ! [SY3464: $i] :
~ ~ ( ~ ( in @ SY3464 @ SV175 )
| ( SY3923
!= ( SV470 @ SY3464 ) ) ) )
| ~ ( ~ ~ ! [SY3465: $i] :
~ ~ ( ~ ( in @ SY3465 @ SV175 )
| ( SY3923
!= ( SV470 @ SY3465 ) ) )
| ( in @ SY3923 @ ( sK3_SY3462 @ SV470 @ SV175 ) ) ) )
| ~ ! [SY3926: $i] :
( ~ ! [SY3467: $i] :
~ ( ~ ( ~ ( in @ SY3467 @ SY3926 )
| ~ ! [SY3468: $i] :
~ ~ ( ~ ( in @ SY3468 @ SV175 )
| ( SY3467
!= ( SV470 @ SY3468 ) ) ) )
| ~ ( ~ ~ ! [SY3469: $i] :
~ ~ ( ~ ( in @ SY3469 @ SV175 )
| ( SY3467
!= ( SV470 @ SY3469 ) ) )
| ( in @ SY3467 @ SY3926 ) ) )
| ( ( sK3_SY3462 @ SV470 @ SV175 )
= SY3926 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1779]) ).
thf(2090,plain,
! [SV176: $i,SV471: $i] :
( ( ( in @ SV471 @ ( powerset @ SV176 ) )
= $false )
| ( ( ! [SY3470: $i] :
( ~ ( in @ SY3470 @ ( powerset @ SV176 ) )
| ( in @ ( setminus @ SV471 @ SY3470 ) @ ( powerset @ SV176 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1780]) ).
thf(2091,plain,
! [SV472: $i,SV177: $i,SV668: $i] :
( ( ( ~ ( in @ SV668 @ ( funcSet @ SV177 @ SV472 ) ) )
= $true )
| ( ( ~ ( injective @ SV177 @ SV472 @ SV668 )
| ( in @ SV668 @ ( injFuncSet @ SV177 @ SV472 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1781]) ).
thf(2092,plain,
! [SV473: $i,SV178: $i] :
( ( ( breln1 @ SV178 @ SV473 )
= $false )
| ( ( ! [SY3472: $i] :
( ~ ( breln1 @ SV178 @ SY3472 )
| ( ( breln1invset @ SV178 @ ( breln1compset @ SV178 @ SV473 @ SY3472 ) )
= ( breln1compset @ SV178 @ ( breln1invset @ SV178 @ SY3472 ) @ ( breln1invset @ SV178 @ SV473 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(2093,plain,
! [SV474: $i > $o,SV179: $i,SV669: $i] :
( ( ( ~ ( in @ SV669
@ ( dsetconstr @ SV179
@ ^ [SY3474: $i] : ( SV474 @ SY3474 ) ) ) )
= $true )
| ( ( in @ SV669 @ SV179 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1783]) ).
thf(2094,plain,
! [SV670: $i > $i > $o,SV475: $i,SV180: $i] :
( ( ( ~ ! [SY3805: $i] :
( ~ ( in @ SY3805 @ SV180 )
| ~ ! [SY3806: $i] :
~ ~ ( ~ ( in @ SY3806 @ SV475 )
| ~ ( SV670 @ SY3805 @ SY3806 ) ) ) )
= $true )
| ( ( ! [SY3807: $i] :
( ~ ( in @ SY3807 @ ( breln1Set @ SV475 ) )
| ~ ( reflwellordering @ SV475 @ SY3807 )
| ! [SY3808: $i] :
( ~ ( in @ SY3808 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY3809: $i] :
~ ( ~ ( SV670 @ SY3808 @ SY3809 )
| ~ ! [SY3810: $i] :
( ~ ( in @ SY3810 @ SV475 )
| ~ ( SV670 @ SY3808 @ SY3810 )
| ( in @ ( kpair @ SY3809 @ SY3810 ) @ SY3807 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1784]) ).
thf(2095,plain,
! [SV476: $i,SV181: $i,SV671: $i] :
( ( ( ~ ( in @ SV671 @ SV181 ) )
= $true )
| ( ( ! [SY3811: $i] :
( ~ ( in @ SY3811 @ SV476 )
| ( in @ ( setadjoin @ ( setadjoin @ SV671 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV671 @ ( setadjoin @ SY3811 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV181 @ SV476 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1785]) ).
thf(2096,plain,
! [SV477: $i,SV672: $i > $i,SV182: $i] :
( ( ( ~ ! [SY3812: $i] :
( ~ ( in @ SY3812 @ SV182 )
| ( in @ ( SV672 @ SY3812 ) @ SV477 ) ) )
= $true )
| ( ( ! [SY3813: $i] :
( ~ ( in @ SY3813 @ SV182 )
| ( ( ap @ SV182 @ SV477
@ ( lam @ SV182 @ SV477
@ ^ [SY3814: $i] : ( SV672 @ SY3814 ) )
@ SY3813 )
= ( SV672 @ SY3813 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1786]) ).
thf(2097,plain,
! [SV478: $i,SV183: $i,SV673: $i] :
( ( ( ~ ( in @ SV673 @ SV183 ) )
= $true )
| ( ( ~ ~ ( in @ SV673 @ SV478 )
| ~ ( subset @ SV183 @ SV478 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1787]) ).
thf(2098,plain,
! [SV479: $i,SV184: $i,SV674: $i] :
( ( ( ~ ( in @ SV674 @ SV184 ) )
= $true )
| ( ( ~ ~ ( in @ SV674 @ SV479 )
| ( SV184 != SV479 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1788]) ).
thf(2099,plain,
! [SV185: $i,SV480: $i] :
( ( ( in @ SV480 @ ( powerset @ SV185 ) )
= $false )
| ( ( ! [SY3490: $i] :
( ~ ( in @ SY3490 @ ( powerset @ SV185 ) )
| ( in @ ( binintersect @ SV480 @ SY3490 ) @ ( powerset @ SV185 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(2100,plain,
! [SV186: $i,SV481: $i] :
( ( ( in @ SV481 @ ( powerset @ SV186 ) )
= $false )
| ( ( ! [SY3491: $i] :
( ~ ( in @ SY3491 @ ( powerset @ SV186 ) )
| ! [SY3492: $i] :
( ~ ( in @ SY3492 @ SV186 )
| ~ ( in @ SV481 @ ( powerset @ SY3491 ) )
| ~ ( in @ SY3492 @ SV481 )
| ( in @ SY3492 @ SY3491 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1790]) ).
thf(2101,plain,
! [SV482: $i,SV187: $i] :
( ( ( ( binintersect @ SV187 @ SV482 )
= SV187 )
= $false )
| ( ( subset @ SV187 @ SV482 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(2102,plain,
! [SV483: $i > $o,SV188: $i,SV675: $i] :
( ( ( ~ ( in @ SV675 @ SV188 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV675
@ ( dsetconstr @ SV188
@ ^ [SY3494: $i] : ( SV483 @ SY3494 ) ) )
| ( SV483 @ SV675 ) )
| ~ ( ~ ( SV483 @ SV675 )
| ( in @ SV675
@ ( dsetconstr @ SV188
@ ^ [SY3495: $i] : ( SV483 @ SY3495 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1792]) ).
thf(2103,plain,
! [SV484: $i > $o,SV189: $i] :
( ( ( ~ ! [SY3496: $i] :
( ~ ( in @ SY3496 @ SV189 )
| ( SV484 @ SY3496 ) ) )
= $false )
| ( ( ~ ! [SY3497: $i] :
~ ~ ( ~ ( in @ SY3497 @ SV189 )
| ~ ~ ( SV484 @ SY3497 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(2104,plain,
! [SV190: $i,SV485: $i] :
( ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false )
| ( ( ! [SY3498: $o] :
( ~ ! [SY3499: $i] :
( ~ ( in @ SV485 @ SY3499 )
| ~ ( in @ SY3499 @ SV190 )
| SY3498 )
| SY3498 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1794]) ).
thf(2105,plain,
! [SV486: $i,SV191: $i,SV676: $i] :
( ( ( ~ ( in @ SV676 @ ( funcSet @ SV191 @ SV486 ) ) )
= $true )
| ( ( ! [SY3817: $i] :
( ~ ( in @ SY3817 @ SV191 )
| ! [SY3818: $i] :
( ~ ( in @ SY3818 @ SV486 )
| ~ ( in @ ( kpair @ SY3817 @ SY3818 ) @ SV676 )
| ( ( ap @ SV191 @ SV486 @ SV676 @ SY3817 )
= SY3818 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1795]) ).
thf(2106,plain,
! [SV487: $i,SV192: $i,SV677: $i] :
( ( ( ~ ( subset @ SV677 @ SV192 ) )
= $true )
| ( ( ~ ( subset @ SV677 @ SV487 )
| ( subset @ SV677 @ ( binintersect @ SV192 @ SV487 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1796]) ).
thf(2107,plain,
! [SV193: $i,SV488: $i > $i] :
( ( ~ ! [SY3930: $i] :
~ ( ~ ( ~ ( in @ SY3930 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
| ~ ! [SY3506: $i] :
~ ~ ( ~ ( in @ SY3506 @ SV193 )
| ( SY3930
!= ( SV488 @ SY3506 ) ) ) )
| ~ ( ~ ~ ! [SY3507: $i] :
~ ~ ( ~ ( in @ SY3507 @ SV193 )
| ( SY3930
!= ( SV488 @ SY3507 ) ) )
| ( in @ SY3930 @ ( sK4_SY3504 @ SV488 @ SV193 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1797]) ).
thf(2108,plain,
! [SV194: $i,SV489: $i] :
( ( ( in @ SV489 @ ( powerset @ SV194 ) )
= $false )
| ( ( ! [SY3508: $i] :
( ~ ( in @ SY3508 @ SV194 )
| ~ ~ ( in @ SY3508 @ ( setminus @ SV194 @ SV489 ) )
| ( in @ SY3508 @ SV489 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1798]) ).
thf(2109,plain,
! [SV678: $i,SV490: $i,SV195: $i] :
( ( ( ~ ( func @ SV195 @ SV490 @ SV678 ) )
= $true )
| ( ( ( lam @ SV195 @ SV490
@ ^ [SY3819: $i] : ( ap @ SV195 @ SV490 @ SV678 @ SY3819 ) )
= SV678 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(2110,plain,
( ( ! [SY3511: $i] :
( ~ ( in @ SY3511 @ sK1_SX0 )
| ( subset @ SY3511 @ sK1_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1800]) ).
thf(2111,plain,
( ( ~ ! [SY3933: $i] :
( ~ ( in @ SY3933 @ sK5_SY3512 )
| ( subset @ SY3933 @ sK5_SY3512 ) )
| ! [SY3934: $i] :
( ~ ( in @ SY3934 @ ( binintersect @ sK1_SX0 @ sK5_SY3512 ) )
| ( subset @ SY3934 @ ( binintersect @ sK1_SX0 @ sK5_SY3512 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1801]) ).
thf(2112,plain,
! [SV196: $i > $o] :
( ( ( ! [SY2853: $i] :
~ ~ ( ~ ( SV196 @ SY2853 )
| ~ ! [SY2854: $i] :
( ~ ( SV196 @ SY2854 )
| ( SY2853 = SY2854 ) ) ) )
= $true )
| ( ( ~ ! [SY2855: $i] :
~ ~ ( ~ ( SV196 @ SY2855 )
| ~ ! [SY2856: $i] :
( ~ ( SV196 @ SY2856 )
| ( SY2855 = SY2856 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1802]) ).
thf(2113,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ! [SY3515: $i,SY3516: $i] :
( ( SY3515 != SY3516 )
| ~ ( ~ ( ~ ( SV197 @ SY3515 )
| ( SV491 @ SY3516 ) )
| ~ ( ~ ( SV491 @ SY3516 )
| ( SV197 @ SY3515 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(2114,plain,
! [SV198: $i] :
( ( ( ~ ( in @ ( sK6_SY2868 @ SV198 ) @ SV198 ) )
= $false )
| ( ( SV198 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1804]) ).
thf(2115,plain,
! [SV492: $i,SV199: $i,SV679: $i] :
( ( ( ~ ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) ) )
= $true )
| ( ( ~ ! [SY3820: $i] :
~ ~ ( ~ ( in @ SY3820 @ SV199 )
| ~ ~ ! [SY3821: $i] :
~ ~ ( ~ ( in @ SY3821 @ SV492 )
| ( SV679
!= ( kpair @ SY3820 @ SY3821 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1805]) ).
thf(2116,plain,
! [SV200: $i,SV493: $i] :
( ( ( in @ SV493 @ ( powerset @ SV200 ) )
= $false )
| ( ( ! [SY3528: $i] :
( ~ ( in @ SY3528 @ ( powerset @ SV200 ) )
| ! [SY3529: $i] :
( ~ ( in @ SY3529 @ SV200 )
| ~ ~ ( in @ SY3529 @ ( binunion @ SV493 @ SY3528 ) )
| ~ ( in @ SY3529 @ SY3528 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(2117,plain,
! [SV494: $i,SV201: $i] :
( ( ( SV201 = SV494 )
= $false )
| ( ( subset @ SV201 @ SV494 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1807]) ).
thf(2118,plain,
! [SV495: $o,SV202: $i,SV680: $i] :
( ( ( ~ ( in @ SV680 @ SV202 ) )
= $true )
| ( ( ! [SY3822: $i] :
( ~ ( in @ SY3822 @ SV202 )
| ( in @ ( if @ SV202 @ SV495 @ SV680 @ SY3822 ) @ SV202 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1808]) ).
thf(2119,plain,
! [SV202: $i,SV681: $i] :
( ( ( ~ ( in @ SV681 @ SV202 ) )
= $true )
| ( ( ! [SY3823: $i] :
( ~ ( in @ SY3823 @ SV202 )
| ( in @ ( if @ SV202 @ $true @ SV681 @ SY3823 ) @ SV202 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1809]) ).
thf(2120,plain,
! [SV202: $i,SV682: $i] :
( ( ( ~ ( in @ SV682 @ SV202 ) )
= $true )
| ( ( ! [SY3824: $i] :
( ~ ( in @ SY3824 @ SV202 )
| ( in @ ( if @ SV202 @ $false @ SV682 @ SY3824 ) @ SV202 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1810]) ).
thf(2121,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) ) )
= $true )
| ( ( ! [SY3825: $o] :
( ~ ( ~ ( in @ SV683 @ SV203 )
| ~ ~ ( in @ SV683 @ SV496 )
| SY3825 )
| ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SY3825 )
| SY3825 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1811]) ).
thf(2122,plain,
! [SV497: $i,SV684: $i > $i,SV204: $i] :
( ( ( ~ ! [SY3826: $i] :
( ~ ( in @ SY3826 @ SV204 )
| ( in @ ( SV684 @ SY3826 ) @ SV497 ) ) )
= $true )
| ( ( func @ SV204 @ SV497
@ ( lam @ SV204 @ SV497
@ ^ [SY3827: $i] : ( SV684 @ SY3827 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1812]) ).
thf(2123,plain,
! [SV498: $i,SV685: $i,SV205: $i] :
( ( ( ~ ( subset @ SV205 @ SV685 ) )
= $true )
| ( ( subset @ SV205 @ ( setadjoin @ SV498 @ SV685 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1813]) ).
thf(2124,plain,
! [SV499: $o,SV206: $i,SV686: $i] :
( ( ( ~ ( in @ SV686 @ SV206 ) )
= $true )
| ( ( ! [SY3828: $i] :
( ~ ( in @ SY3828 @ SV206 )
| ( in @ ( if @ SV206 @ SV499 @ SV686 @ SY3828 ) @ ( setadjoin @ SV686 @ ( setadjoin @ SY3828 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1814]) ).
thf(2125,plain,
! [SV206: $i,SV687: $i] :
( ( ( ~ ( in @ SV687 @ SV206 ) )
= $true )
| ( ( ! [SY3829: $i] :
( ~ ( in @ SY3829 @ SV206 )
| ( in @ ( if @ SV206 @ $true @ SV687 @ SY3829 ) @ ( setadjoin @ SV687 @ ( setadjoin @ SY3829 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1815]) ).
thf(2126,plain,
! [SV206: $i,SV688: $i] :
( ( ( ~ ( in @ SV688 @ SV206 ) )
= $true )
| ( ( ! [SY3830: $i] :
( ~ ( in @ SY3830 @ SV206 )
| ( in @ ( if @ SV206 @ $false @ SV688 @ SY3830 ) @ ( setadjoin @ SV688 @ ( setadjoin @ SY3830 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(2127,plain,
! [SV500: $i > $o,SV207: $i] :
( ( ( ~ ~ ! [SY3540: $i] :
~ ~ ( ~ ( in @ SY3540 @ SV207 )
| ~ ( SV500 @ SY3540 ) ) )
= $false )
| ( ( ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SV207 )
| ~ ( SV500 @ SY3541 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(2128,plain,
! [SV208: $i,SV501: $i] :
( ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false )
| ( ( ! [SY3542: $i] :
( ~ ( in @ SY3542 @ ( powerset @ SV208 ) )
| ! [SY3543: $o,SY3544: $i] :
( ~ ( in @ SY3544 @ SV208 )
| ~ ( in @ SY3544 @ ( binunion @ SV501 @ SY3542 ) )
| ~ ( ~ ( in @ SY3544 @ SV501 )
| SY3543 )
| ~ ( ~ ( in @ SY3544 @ SY3542 )
| SY3543 )
| SY3543 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1818]) ).
thf(2129,plain,
! [SV689: $i,SV502: $i,SV209: $i] :
( ( ( ~ ( breln @ SV209 @ SV502 @ SV689 ) )
= $true )
| ( ( ! [SY3831: $i > $o] :
( ~ ! [SY3832: $i] :
( ~ ( in @ SY3832 @ SV209 )
| ! [SY3833: $i] :
( ~ ( in @ SY3833 @ SV502 )
| ~ ( in @ ( kpair @ SY3832 @ SY3833 ) @ SV689 )
| ( SY3831 @ ( kpair @ SY3832 @ SY3833 ) ) ) )
| ! [SY3834: $i] :
( ~ ( in @ SY3834 @ SV689 )
| ( SY3831 @ SY3834 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1819]) ).
thf(2130,plain,
! [SV503: $o,SV210: $i,SV690: $i] :
( ( ( ~ ( in @ SV690 @ SV210 ) )
= $true )
| ( ( ! [SY3835: $i] :
( ~ ( in @ SY3835 @ SV210 )
| ~ SV503
| ( in @ SV690
@ ( dsetconstr @ SV210
@ ^ [SY3836: $i] :
( ~ ( ~ SV503
| ( SY3836 != SV690 ) )
| ~ ( ~ ~ SV503
| ( SY3836 != SY3835 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(2131,plain,
! [SV210: $i,SV691: $i] :
( ( ( ~ ( in @ SV691 @ SV210 ) )
= $true )
| ( ( ! [SY3837: $i] :
( ~ ( in @ SY3837 @ SV210 )
| ~ $true
| ( in @ SV691
@ ( dsetconstr @ SV210
@ ^ [SY3838: $i] :
( ~ ( ~ $true
| ( SY3838 != SV691 ) )
| ~ ( ~ ~ $true
| ( SY3838 != SY3837 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(2132,plain,
! [SV210: $i,SV692: $i] :
( ( ( ~ ( in @ SV692 @ SV210 ) )
= $true )
| ( ( ! [SY3839: $i] :
( ~ ( in @ SY3839 @ SV210 )
| ~ $false
| ( in @ SV692
@ ( dsetconstr @ SV210
@ ^ [SY3840: $i] :
( ~ ( ~ $false
| ( SY3840 != SV692 ) )
| ~ ( ~ ~ $false
| ( SY3840 != SY3839 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1822]) ).
thf(2133,plain,
! [SV693: $i,SV504: $i,SV212: $i] :
( ( ( ~ ( subset @ SV212 @ SV504 ) )
= $true )
| ( ( ~ ~ ( in @ SV693 @ SV504 )
| ~ ( in @ SV693 @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1824]) ).
thf(2134,plain,
! [SV750: $i,SV694: $i,SV505: $i,SV213: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV213 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV213 @ ( setadjoin @ SV505 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV694 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV694 @ ( setadjoin @ SV750 @ emptyset ) ) @ emptyset ) ) )
| ( SV213 = SV694 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2135,plain,
! [SV506: $i,SV214: $i,SV695: $i] :
( ( ( ~ ( in @ SV695 @ ( injFuncSet @ SV214 @ SV506 ) ) )
= $true )
| ( ( injective @ SV214 @ SV506 @ SV695 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1826]) ).
thf(2136,plain,
! [SV215: $i,SV507: $i] :
( ( ( in @ SV507 @ SV215 )
= $false )
| ( ( subset @ ( setadjoin @ SV507 @ emptyset ) @ SV215 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1827]) ).
thf(2137,plain,
! [SV508: $i,SV216: $i] :
( ( ( breln1 @ SV216 @ SV508 )
= $false )
| ( ( ! [SY3557: $i] :
( ~ ( breln1 @ SV216 @ SY3557 )
| ! [SY3558: $i] :
( ~ ( in @ SY3558 @ SV216 )
| ! [SY3559: $i] :
( ~ ( in @ SY3559 @ SV216 )
| ~ ( in @ ( kpair @ SY3558 @ SY3559 ) @ ( binunion @ SV508 @ SY3557 ) )
| ! [SY3560: $o] :
( ~ ( ~ ( in @ ( kpair @ SY3558 @ SY3559 ) @ SV508 )
| SY3560 )
| ~ ( ~ ( in @ ( kpair @ SY3558 @ SY3559 ) @ SY3557 )
| SY3560 )
| SY3560 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1828]) ).
thf(2138,plain,
! [SV217: $i,SV509: $i] :
( ( ( in @ SV509 @ ( powerset @ SV217 ) )
= $false )
| ( ( ! [SY3561: $i] :
( ~ ( in @ SY3561 @ ( powerset @ SV217 ) )
| ! [SY3562: $i] :
( ~ ( in @ SY3562 @ SV217 )
| ~ ( in @ SY3562 @ ( setminus @ SV217 @ ( binunion @ SV509 @ SY3561 ) ) )
| ( in @ SY3562 @ ( binintersect @ ( setminus @ SV217 @ SV509 ) @ ( setminus @ SV217 @ SY3561 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1829]) ).
thf(2139,plain,
! [SV510: $i > $i,SV218: $i,SV696: $i] :
( ( ( ~ ( in @ SV696
@ ( image1 @ SV218
@ ^ [SY3564: $i] : ( SV510 @ SY3564 ) ) ) )
= $true )
| ( ( ~ ! [SY3843: $i] :
~ ~ ( ~ ( in @ SY3843 @ SV218 )
| ( SV696
!= ( SV510 @ SY3843 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(2140,plain,
! [SV219: $i] :
( ( ( ( omegaS @ SV219 )
= emptyset )
= $false )
| ( ( in @ SV219 @ omega )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1831]) ).
thf(2141,plain,
! [SV511: $i,SV220: $i,SV697: $i] :
( ( ( ~ ( in @ SV697 @ ( setadjoin @ SV220 @ ( setadjoin @ SV511 @ emptyset ) ) ) )
= $true )
| ( ( ( SV697 = SV220 )
| ( SV697 = SV511 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1832]) ).
thf(2142,plain,
! [SV512: $i,SV221: $i,SV698: $i] :
( ( ( ~ ( in @ SV698 @ ( surjFuncSet @ SV221 @ SV512 ) ) )
= $true )
| ( ( in @ SV698 @ ( funcSet @ SV221 @ SV512 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(2143,plain,
! [SV513: $i,SV222: $i] :
( ( ( subset @ SV222 @ SV513 )
= $false )
| ( ( in @ SV222 @ ( powerset @ SV513 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(2144,plain,
! [SV514: $o,SV223: $i,SV699: $i] :
( ( ( ~ ( in @ SV699 @ SV223 ) )
= $true )
| ( ( ! [SY3844: $i] :
( ~ ( in @ SY3844 @ SV223 )
| ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY3845: $i] :
( ~ ( ~ SV514
| ( SY3845 != SV699 ) )
| ~ ( ~ ~ SV514
| ( SY3845 != SY3844 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(2145,plain,
! [SV223: $i,SV700: $i] :
( ( ( ~ ( in @ SV700 @ SV223 ) )
= $true )
| ( ( ! [SY3846: $i] :
( ~ ( in @ SY3846 @ SV223 )
| ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY3847: $i] :
( ~ ( ~ $true
| ( SY3847 != SV700 ) )
| ~ ( ~ ~ $true
| ( SY3847 != SY3846 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1836]) ).
thf(2146,plain,
! [SV223: $i,SV701: $i] :
( ( ( ~ ( in @ SV701 @ SV223 ) )
= $true )
| ( ( ! [SY3848: $i] :
( ~ ( in @ SY3848 @ SV223 )
| ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY3849: $i] :
( ~ ( ~ $false
| ( SY3849 != SV701 ) )
| ~ ( ~ ~ $false
| ( SY3849 != SY3848 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1837]) ).
thf(2147,plain,
! [SV224: $i,SV515: $i] :
( ( ( in @ SV515 @ ( powerset @ SV224 ) )
= $false )
| ( ( ! [SY3571: $i] :
( ~ ( in @ SY3571 @ ( powerset @ SV224 ) )
| ~ ( subset @ SV515 @ SY3571 )
| ( subset @ ( setminus @ SV224 @ SY3571 ) @ ( setminus @ SV224 @ SV515 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(2148,plain,
! [SV751: $i,SV702: $i,SV516: $i,SV225: $i] :
( ( ( ( kpair @ SV225 @ SV516 )
!= ( kpair @ SV702 @ SV751 ) )
| ( SV516 = SV751 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2149,plain,
! [SV226: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY3851: $i] :
( ~ ( in @ SY3851 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY2945: $i] :
( ~ ( in @ SY2945 @ SY3851 )
| ( in @ SY2945 @ SV226 ) ) )
| ~ ! [SY3853: $i,SY3854: $i] :
( ~ ~ ( ~ ( in @ SY3853 @ SV226 )
| ~ ( in @ SY3854 @ SV226 ) )
| ~ ! [SY3855: $i] :
( ~ ( in @ SY3855 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SY3853 @ SY3855 )
| ( in @ SY3854 @ SY3855 ) )
| ~ ( ~ ( in @ SY3854 @ SY3855 )
| ( in @ SY3853 @ SY3855 ) ) ) )
| ( SY3853 = SY3854 ) ) )
| ~ ! [SY3856: $i,SY3857: $i] :
( ~ ~ ( ~ ( in @ SY3856 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY3857 @ ( sK2_SY2943 @ SV226 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3856 )
| ( in @ SX4 @ SY3857 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3857 )
| ( in @ SX4 @ SY3856 ) ) ) )
| ~ ! [SY3860: $i] :
( ~ ~ ( ~ ! [SY2954: $i] :
( ~ ( in @ SY2954 @ SY3860 )
| ( in @ SY2954 @ SV226 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY3860 ) )
| ~ ! [SY3863: $i] :
~ ~ ! [SY3864: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3863 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY3864 @ SY3860 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY3863 )
| ~ ( in @ SX5 @ SY3860 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY3863 ) )
| ( in @ SY3864 @ SY3866 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1840]) ).
thf(2150,plain,
! [SV703: $i > $i > $o,SV517: $i,SV227: $i,SV752: $i] :
( ( ~ ( in @ SV752 @ SV227 )
| ! [SY3935: $i] :
( ~ ( in @ SY3935 @ SV517 )
| ~ ( in @ ( kpair @ SV752 @ SY3935 )
@ ( dpsetconstr @ SV227 @ SV517
@ ^ [SY3870: $i,SY3871: $i] : ( SV703 @ SY3870 @ SY3871 ) ) )
| ( SV703 @ SV752 @ SY3935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2151,plain,
! [SV228: $i,SV704: $i,SV518: $i] :
( ( ( ~ ( in @ SV518 @ SV704 ) )
= $true )
| ( ( ~ ( in @ SV704 @ SV228 )
| ( in @ SV518 @ ( setunion @ SV228 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1842]) ).
thf(2152,plain,
! [SV229: $i,SV519: $i] :
( ( ( in @ SV519 @ ( powerset @ SV229 ) )
= $false )
| ( ( ! [SY3580: $i] :
( ~ ( in @ SY3580 @ ( powerset @ SV229 ) )
| ! [SY3581: $i] :
( ~ ( in @ SY3581 @ SV229 )
| ~ ~ ( in @ SY3581 @ ( binunion @ SV519 @ SY3580 ) )
| ~ ( in @ SY3581 @ SV519 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1843]) ).
thf(2153,plain,
! [SV230: $i > $i > $o,SV520: $i] :
( ( ( ! [SY3582: $i] :
( ~ ( in @ SY3582 @ SV520 )
| ~ ! [SY2974: $i] :
~ ~ ( ~ ( SV230 @ SY3582 @ SY2974 )
| ~ ! [SY2975: $i] :
( ~ ( SV230 @ SY3582 @ SY2975 )
| ( SY2974 = SY2975 ) ) ) ) )
= $false )
| ( ( ~ ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1844]) ).
thf(2154,plain,
! [SV705: $i,SV521: $i,SV231: $i] :
( ( ( ~ ( func @ SV231 @ SV521 @ SV705 ) )
= $true )
| ( ( ! [SY3872: $i] :
( ~ ( func @ SV231 @ SV521 @ SY3872 )
| ~ ! [SY3873: $i] :
( ~ ( in @ SY3873 @ SV231 )
| ( ( ap @ SV231 @ SV521 @ SV705 @ SY3873 )
= ( ap @ SV231 @ SV521 @ SY3872 @ SY3873 ) ) )
| ( SV705 = SY3872 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1845]) ).
thf(2155,plain,
! [SV522: $o,SV232: $i,SV706: $i] :
( ( ( ~ ( in @ SV706 @ SV232 ) )
= $true )
| ( ( ! [SY3874: $i] :
( ~ ( in @ SY3874 @ SV232 )
| ~ SV522
| ( ( if @ SV232 @ SV522 @ SV706 @ SY3874 )
= SV706 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1846]) ).
thf(2156,plain,
! [SV232: $i,SV707: $i] :
( ( ( ~ ( in @ SV707 @ SV232 ) )
= $true )
| ( ( ! [SY3875: $i] :
( ~ ( in @ SY3875 @ SV232 )
| ~ $true
| ( ( if @ SV232 @ $true @ SV707 @ SY3875 )
= SV707 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1847]) ).
thf(2157,plain,
! [SV232: $i,SV708: $i] :
( ( ( ~ ( in @ SV708 @ SV232 ) )
= $true )
| ( ( ! [SY3876: $i] :
( ~ ( in @ SY3876 @ SV232 )
| ~ $false
| ( ( if @ SV232 @ $false @ SV708 @ SY3876 )
= SV708 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(2158,plain,
! [SV523: $i,SV233: $i] :
( ( ( breln1 @ SV233 @ SV523 )
= $false )
| ( ( ! [SY3594: $i > $o] :
( ~ ! [SY3595: $i] :
( ~ ( in @ SY3595 @ SV233 )
| ! [SY3596: $i] :
( ~ ( in @ SY3596 @ SV233 )
| ~ ( in @ ( kpair @ SY3595 @ SY3596 ) @ SV523 )
| ( SY3594 @ ( kpair @ SY3595 @ SY3596 ) ) ) )
| ! [SY3597: $i] :
( ~ ( in @ SY3597 @ SV523 )
| ( SY3594 @ SY3597 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1849]) ).
thf(2159,plain,
! [SV234: $i,SV524: $i] :
( ( ( ! [SY3598: $i] :
( ~ ( in @ SY3598 @ SV524 )
| ( in @ SY3598 @ SV234 ) ) )
= $false )
| ( ( in @ SV524 @ ( powerset @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(2160,plain,
! [SV235: $i,SV525: $i] :
( ( ( in @ SV525 @ ( setunion @ SV235 ) )
= $false )
| ( ( ~ ! [SY3599: $i] :
~ ~ ( ~ ( in @ SY3599 @ SV235 )
| ~ ( in @ SV525 @ SY3599 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(2161,plain,
! [SV526: $i,SV237: $i,SV709: $i] :
( ( ( ~ ( in @ SV709 @ ( setminus @ SV237 @ SV526 ) ) )
= $true )
| ( ( in @ SV709 @ SV237 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1853]) ).
thf(2162,plain,
! [SV527: $i,SV238: $i] :
( ( ( SV238 = SV527 )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ SV238 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV238 @ ( setadjoin @ SV527 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV238 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(2163,plain,
! [SV528: $i,SV239: $i,SV710: $i] :
( ( ( ~ ( in @ SV710 @ ( binunion @ SV239 @ SV528 ) ) )
= $true )
| ( ( ( in @ SV710 @ SV239 )
| ( in @ SV710 @ SV528 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(2164,plain,
! [SV711: $i,SV529: $i,SV240: $i] :
( ( ( ~ ( func @ SV240 @ SV529 @ SV711 ) )
= $true )
| ( ( ! [SY3877: $i] :
( ~ ( in @ SY3877 @ SV240 )
| ( in @ ( kpair @ SY3877 @ ( ap @ SV240 @ SV529 @ SV711 @ SY3877 ) ) @ SV711 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1856]) ).
thf(2165,plain,
! [SV241: $i,SV530: $i] :
( ( ( in @ SV530 @ ( powerset @ SV241 ) )
= $false )
| ( ( ! [SY3604: $i] :
( ~ ( in @ SY3604 @ ( powerset @ SV241 ) )
| ( in @ ( setminus @ SV241 @ SV530 ) @ ( powerset @ ( setminus @ SV241 @ ( binintersect @ SV530 @ SY3604 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(2166,plain,
! [SV242: $i] :
( ( ( SV242 = emptyset )
= $true )
| ( ( ~ ! [SY3006: $i] :
~ ( in @ SY3006 @ SV242 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1858]) ).
thf(2167,plain,
! [SV243: $i,SV531: $i] :
( ( ( in @ SV531 @ ( powerset @ SV243 ) )
= $false )
| ( ( ! [SY3605: $i] :
( ~ ( in @ SY3605 @ ( powerset @ SV243 ) )
| ! [SY3606: $i] :
( ~ ( in @ SY3606 @ ( powerset @ SV243 ) )
| ( in @ ( binintersect @ SV531 @ SY3605 ) @ ( powerset @ ( binintersect @ ( binunion @ SV531 @ SY3606 ) @ ( binunion @ SY3605 @ SY3606 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(2168,plain,
! [SV244: $i,SV532: $i] :
( ( ( in @ SV532 @ ( powerset @ SV244 ) )
= $false )
| ( ( ! [SY3607: $i] :
( ~ ( in @ SY3607 @ SV244 )
| ~ ( in @ SY3607 @ ( setminus @ SV244 @ ( setminus @ SV244 @ SV532 ) ) )
| ( in @ SY3607 @ SV532 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(2169,plain,
! [SV533: $i > $o,SV245: $i] :
( ( ( ~ ! [SY3608: $i] :
~ ~ ( ~ ( in @ SY3608 @ SV245 )
| ~ ( SV533 @ SY3608 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV245
@ ^ [SY3609: $i] : ( SV533 @ SY3609 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(2170,plain,
! [SV712: $i,SV534: $i,SV246: $i] :
( ( ( ~ ( func @ SV246 @ SV534 @ SV712 ) )
= $true )
| ( ( ! [SY3878: $i] :
( ~ ( in @ SY3878 @ SV246 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV534
@ ^ [SY3879: $i] : ( in @ ( kpair @ SY3878 @ SY3879 ) @ SV712 ) ) )
@ SV534 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1862]) ).
thf(2171,plain,
! [SV535: $i,SV247: $i] :
( ( ( breln1 @ SV247 @ SV535 )
= $false )
| ( ( ! [SY3613: $i] :
( ~ ( in @ SY3613 @ SV247 )
| ! [SY3614: $i] :
( ~ ( in @ SY3614 @ SV247 )
| ~ ( in @ ( kpair @ SY3614 @ SY3613 ) @ ( breln1invset @ SV247 @ SV535 ) )
| ( in @ ( kpair @ SY3613 @ SY3614 ) @ SV535 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1863]) ).
thf(2172,plain,
! [SV536: $i,SV248: $i] :
( ( ( ( binintersect @ SV248 @ SV536 )
= SV536 )
= $false )
| ( ( subset @ SV536 @ SV248 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(2173,plain,
! [SV249: $i] :
( ( ( ~ ( in @ ( sK7_SY3023 @ SV249 ) @ SV249 )
| ( subset @ ( sK7_SY3023 @ SV249 ) @ SV249 ) )
= $false )
| ( ( ! [SY3024: $i] :
( ~ ( in @ SY3024 @ SV249 )
| ( subset @ SY3024 @ SV249 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1865]) ).
thf(2174,plain,
! [SV537: $i,SV250: $i,SV713: $i] :
( ( ( ~ ( in @ SV713 @ ( setadjoin @ SV250 @ ( setadjoin @ SV537 @ emptyset ) ) ) )
= $true )
| ( ( ( SV713 = SV250 )
| ( SV713 = SV537 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1866]) ).
thf(2175,plain,
! [SV251: $i,SV538: $i] :
( ( ( in @ SV538 @ ( powerset @ SV251 ) )
= $false )
| ( ( ! [SY3616: $i] :
( ~ ( in @ SY3616 @ ( powerset @ SV251 ) )
| ! [SY3617: $i] :
( ~ ( in @ SY3617 @ SV251 )
| ~ ~ ( in @ SY3617 @ SV538 )
| ~ ~ ( in @ SY3617 @ SY3616 )
| ~ ( in @ SY3617 @ ( binunion @ SV538 @ SY3616 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(2176,plain,
! [SV539: $o,SV252: $i,SV714: $i] :
( ( ( ~ ( in @ SV714 @ SV252 ) )
= $true )
| ( ( ! [SY3880: $i] :
( ~ ( in @ SY3880 @ SV252 )
| ~ SV539
| ( ( dsetconstr @ SV252
@ ^ [SY3881: $i] :
( ~ ( ~ SV539
| ( SY3881 != SV714 ) )
| ~ ( ~ ~ SV539
| ( SY3881 != SY3880 ) ) ) )
= ( setadjoin @ SV714 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1868]) ).
thf(2177,plain,
! [SV252: $i,SV715: $i] :
( ( ( ~ ( in @ SV715 @ SV252 ) )
= $true )
| ( ( ! [SY3882: $i] :
( ~ ( in @ SY3882 @ SV252 )
| ~ $true
| ( ( dsetconstr @ SV252
@ ^ [SY3883: $i] :
( ~ ( ~ $true
| ( SY3883 != SV715 ) )
| ~ ( ~ ~ $true
| ( SY3883 != SY3882 ) ) ) )
= ( setadjoin @ SV715 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1869]) ).
thf(2178,plain,
! [SV252: $i,SV716: $i] :
( ( ( ~ ( in @ SV716 @ SV252 ) )
= $true )
| ( ( ! [SY3884: $i] :
( ~ ( in @ SY3884 @ SV252 )
| ~ $false
| ( ( dsetconstr @ SV252
@ ^ [SY3885: $i] :
( ~ ( ~ $false
| ( SY3885 != SV716 ) )
| ~ ( ~ ~ $false
| ( SY3885 != SY3884 ) ) ) )
= ( setadjoin @ SV716 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1870]) ).
thf(2179,plain,
! [SV253: $i,SV540: $i] :
( ( ( in @ SV540 @ ( breln1Set @ SV253 ) )
= $false )
| ( ( breln1 @ SV253 @ SV540 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1871]) ).
thf(2180,plain,
! [SV717: $i,SV541: $i,SV254: $i] :
( ( ( ~ ( func @ SV254 @ SV541 @ SV717 ) )
= $true )
| ( ( ! [SY3886: $i] :
( ~ ( in @ SY3886 @ SV254 )
| ( ( ap @ SV254 @ SV541 @ SV717 @ SY3886 )
= ( ap @ SV254 @ SV541 @ SV717 @ SY3886 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1872]) ).
thf(2181,plain,
! [SV542: $i,SV255: $i] :
( ( ( subset @ SV255 @ SV542 )
= $false )
| ( ( subset @ ( powerset @ SV255 ) @ ( powerset @ SV542 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1873]) ).
thf(2182,plain,
! [SV753: $i,SV718: $i,SV543: $i,SV256: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV256 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV256 @ ( setadjoin @ SV543 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV718 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV718 @ ( setadjoin @ SV753 @ emptyset ) ) @ emptyset ) ) )
| ( SV718 != SV753 )
| ( SV543 = SV753 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2183,plain,
! [SV257: $i,SV544: $i] :
( ( ( in @ SV544 @ ( powerset @ SV257 ) )
= $false )
| ( ( subset @ SV544 @ SV257 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1875]) ).
thf(2184,plain,
! [SV258: $o,SV545: $i] :
( ( ( in @ SV545 @ ( prop2set @ SV258 ) )
= $false )
| ( SV258 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(2185,plain,
! [SV546: $i] :
( ( ( in @ SV546 @ ( prop2set @ $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1877]) ).
thf(2186,plain,
! [SV547: $i] :
( ( ( in @ SV547 @ ( prop2set @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(2187,plain,
! [SV719: $i,SV548: $i,SV259: $i] :
( ( ( ~ ( func @ SV259 @ SV548 @ SV719 ) )
= $true )
| ( ( ! [SY3888: $i] :
( ~ ( in @ SY3888 @ SV259 )
| ! [SY3889: $i] :
( ~ ( in @ SY3889 @ SV548 )
| ~ ( in @ ( kpair @ SY3888 @ SY3889 ) @ SV719 )
| ( ( ap @ SV259 @ SV548 @ SV719 @ SY3888 )
= SY3889 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1879]) ).
thf(2188,plain,
! [SV549: $i,SV260: $i] :
( ( ( breln1 @ SV260 @ SV549 )
= $false )
| ( ( ! [SY3628: $i] :
( ~ ( breln1 @ SV260 @ SY3628 )
| ~ ! [SY3629: $i] :
( ~ ( in @ SY3629 @ SV260 )
| ! [SY3630: $i] :
( ~ ( in @ SY3630 @ SV260 )
| ~ ( in @ ( kpair @ SY3629 @ SY3630 ) @ SV549 )
| ( in @ ( kpair @ SY3629 @ SY3630 ) @ SY3628 ) ) )
| ~ ! [SY3631: $i] :
( ~ ( in @ SY3631 @ SV260 )
| ! [SY3632: $i] :
( ~ ( in @ SY3632 @ SV260 )
| ~ ( in @ ( kpair @ SY3631 @ SY3632 ) @ SY3628 )
| ( in @ ( kpair @ SY3631 @ SY3632 ) @ SV549 ) ) )
| ( SV549 = SY3628 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1880]) ).
thf(2189,plain,
! [SV550: $i,SV261: $i] :
( ( ( breln1 @ SV261 @ SV550 )
= $false )
| ( ( breln1 @ SV261 @ ( breln1invset @ SV261 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1881]) ).
thf(2190,plain,
! [SV551: $i > $o,SV262: $i,SV720: $i] :
( ( ( ~ ( in @ SV720
@ ( dsetconstr @ SV262
@ ^ [SY3634: $i] : ( SV551 @ SY3634 ) ) ) )
= $true )
| ( ( SV551 @ SV720 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1882]) ).
thf(2191,plain,
! [SV552: $i,SV263: $i,SV721: $i] :
( ( ( ~ ( in @ SV721 @ SV263 ) )
= $true )
| ( ( ~ ( in @ SV721 @ SV552 )
| ( in @ SV721 @ ( binintersect @ SV263 @ SV552 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1883]) ).
thf(2192,plain,
! [SV553: $i,SV264: $i] :
( ( ( breln1 @ SV264 @ SV553 )
= $false )
| ( ( ! [SY3636: $i] :
( ~ ( breln1 @ SV264 @ SY3636 )
| ! [SY3637: $i] :
( ~ ( in @ SY3637 @ SV264 )
| ! [SY3638: $i] :
( ~ ( in @ SY3638 @ SV264 )
| ~ ( ( in @ ( kpair @ SY3637 @ SY3638 ) @ SV553 )
| ( in @ ( kpair @ SY3637 @ SY3638 ) @ SY3636 ) )
| ( in @ ( kpair @ SY3637 @ SY3638 ) @ ( binunion @ SV553 @ SY3636 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(2193,plain,
! [SV554: $i,SV265: $i,SV722: $i] :
( ( ( ~ ( in @ SV722 @ SV265 ) )
= $true )
| ( ( ! [SY3891: $i] :
( ~ ( in @ SY3891 @ SV554 )
| ( subset @ ( setadjoin @ SV722 @ ( setadjoin @ SY3891 @ emptyset ) ) @ ( binunion @ SV265 @ SV554 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1885]) ).
thf(2194,plain,
! [SV266: $i,SV555: $i] :
( ( ( in @ SV555 @ ( powerset @ SV266 ) )
= $false )
| ( ( ! [SY3641: $i] :
( ~ ( in @ SY3641 @ ( powerset @ SV266 ) )
| ( in @ ( setminus @ SV266 @ SV555 ) @ ( powerset @ ( setminus @ SV266 @ ( binintersect @ SV555 @ SY3641 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(2195,plain,
! [SV556: $i,SV267: $i,SV723: $i] :
( ( ( ~ ( in @ SV723 @ ( injFuncSet @ SV267 @ SV556 ) ) )
= $true )
| ( ( in @ SV723 @ ( funcSet @ SV267 @ SV556 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1887]) ).
thf(2196,plain,
! [SV557: $i,SV268: $i,SV724: $i] :
( ( ( ~ ( in @ SV724 @ ( surjFuncSet @ SV268 @ SV557 ) ) )
= $true )
| ( ( surjective @ SV268 @ SV557 @ SV724 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1888]) ).
thf(2197,plain,
! [SV270: $i,SV558: $i] :
( ( ( in @ SV558 @ ( powerset @ SV270 ) )
= $false )
| ( ( ! [SY3644: $i] :
( ~ ( in @ SY3644 @ ( powerset @ SV270 ) )
| ( ( setminus @ SV270 @ ( binunion @ SV558 @ SY3644 ) )
= ( binintersect @ ( setminus @ SV270 @ SV558 ) @ ( setminus @ SV270 @ SY3644 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1890]) ).
thf(2198,plain,
! [SV559: $i,SV271: $i] :
( ( ( breln1 @ SV271 @ SV559 )
= $false )
| ( ( ! [SY3645: $i > $o] :
( ~ ! [SY3646: $i] :
( ~ ( in @ SY3646 @ SV271 )
| ! [SY3647: $i] :
( ~ ( in @ SY3647 @ SV271 )
| ~ ( in @ ( kpair @ SY3646 @ SY3647 ) @ SV559 )
| ( SY3645 @ ( kpair @ SY3646 @ SY3647 ) ) ) )
| ! [SY3648: $i] :
( ~ ( in @ SY3648 @ SV559 )
| ( SY3645 @ SY3648 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(2199,plain,
! [SV560: $i,SV272: $i,SV725: $i] :
( ( ( ~ ( in @ SV725 @ SV272 ) )
= $true )
| ( ( ~ ~ ( in @ SV725 @ SV560 )
| ( in @ SV725 @ ( symdiff @ SV272 @ SV560 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(2200,plain,
! [SV561: $i,SV273: $i,SV726: $i] :
( ( ( ~ ( in @ SV726 @ SV273 ) )
= $true )
| ( ( ! [SY3892: $i] :
( ~ ( in @ SY3892 @ SV561 )
| ( ( kfst @ ( kpair @ SV726 @ SY3892 ) )
= SV726 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1893]) ).
thf(2201,plain,
! [SV274: $i,SV562: $i] :
( ( ( in @ SV562 @ ( powerset @ SV274 ) )
= $false )
| ( ( ! [SY3652: $i] :
( ~ ( in @ SY3652 @ ( powerset @ SV274 ) )
| ~ ( subset @ ( setminus @ SV274 @ SY3652 ) @ ( setminus @ SV274 @ SV562 ) )
| ( subset @ SV562 @ SY3652 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1894]) ).
thf(2202,plain,
! [SV563: $i > $o,SV275: $i] :
( ( ( ! [SY3653: $i] :
( ~ ( in @ SY3653 @ SV275 )
| ~ ( SV563 @ SY3653 ) ) )
= $false )
| ( ( ~ ~ ! [SY3654: $i] :
~ ~ ( ~ ( in @ SY3654 @ SV275 )
| ~ ( SV563 @ SY3654 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(2203,plain,
! [SV564: $i,SV276: $i] :
( ( ( subset @ SV276 @ SV564 )
= $false )
| ( ( ( setminus @ SV276 @ SV564 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1896]) ).
thf(2204,plain,
! [SV277: $i,SV565: $i] :
( ( ( in @ SV565 @ ( powerset @ SV277 ) )
= $false )
| ( ( ! [SY3655: $i] :
( ~ ( in @ SY3655 @ ( powerset @ SV277 ) )
| ! [SY3656: $i] :
( ~ ( in @ SY3656 @ SV277 )
| ~ ( in @ SY3656 @ ( setminus @ SV277 @ ( binunion @ SV565 @ SY3655 ) ) )
| ( in @ SY3656 @ ( setminus @ SV277 @ SV565 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1897]) ).
thf(2205,plain,
! [SV566: $i,SV278: $i] :
( ( ( ! [SY3657: $i] :
( ~ ( in @ SY3657 @ SV278 )
| ( in @ SY3657 @ SV566 ) ) )
= $false )
| ( ( ~ ! [SY3658: $i] :
( ~ ( in @ SY3658 @ SV566 )
| ( in @ SY3658 @ SV278 ) )
| ( SV278 = SV566 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1898]) ).
thf(2206,plain,
! [SV567: $i,SV279: $i,SV727: $i] :
( ( ( ~ ( in @ SV727 @ ( binintersect @ SV279 @ SV567 ) ) )
= $true )
| ( ( in @ SV727 @ SV279 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1899]) ).
thf(2207,plain,
! [SV568: $i,SV280: $i] :
( ( ( breln1 @ SV280 @ SV568 )
= $false )
| ( ( ! [SY3660: $i] :
( ~ ( breln1 @ SV280 @ SY3660 )
| ! [SY3661: $i] :
( ~ ( in @ SY3661 @ SV280 )
| ! [SY3662: $i] :
( ~ ( in @ SY3662 @ SV280 )
| ~ ( in @ ( kpair @ SY3661 @ SY3662 ) @ ( breln1compset @ SV280 @ SV568 @ SY3660 ) )
| ! [SY3663: $o] :
( ~ ! [SY3664: $i] :
( ~ ( in @ SY3664 @ SV280 )
| ~ ( in @ ( kpair @ SY3661 @ SY3664 ) @ SV568 )
| ~ ( in @ ( kpair @ SY3664 @ SY3662 ) @ SY3660 )
| SY3663 )
| SY3663 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1900]) ).
thf(2208,plain,
! [SV569: $i,SV281: $i] :
( ( ( subset @ SV281 @ SV569 )
= $false )
| ( ( ( binintersect @ SV281 @ SV569 )
= SV281 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1901]) ).
thf(2209,plain,
! [SV570: $i,SV282: $i,SV728: $i] :
( ( ( ~ ~ ( in @ SV728 @ SV282 ) )
= $true )
| ( ( ~ ( in @ SV728 @ SV570 )
| ( in @ SV728 @ ( symdiff @ SV282 @ SV570 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1902]) ).
thf(2210,plain,
! [SV571: $i,SV283: $i,SV754: $i,SV729: $i] :
( ( ~ ( in @ ( kpair @ SV729 @ SV754 ) @ ( cartprod @ SV283 @ SV571 ) )
| ( in @ SV754 @ SV571 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2211,plain,
! [SV572: $i,SV284: $i] :
( ( ( ~ ~ ! [SY3668: $i] :
~ ~ ( ~ ( in @ SY3668 @ SV284 )
| ~ ( in @ SY3668 @ SV572 ) ) )
= $false )
| ( ( ( binintersect @ SV284 @ SV572 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1904]) ).
thf(2212,plain,
! [SV573: $i,SV285: $i,SV730: $i] :
( ( ( ~ ( in @ SV730 @ SV285 ) )
= $true )
| ( ( in @ SV730 @ ( binunion @ SV285 @ SV573 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1905]) ).
thf(2213,plain,
! [SV286: $i,SV574: $i] :
( ( ( in @ SV574 @ SV286 )
= $false )
| ( ( in @ SV574 @ ( powerset @ ( setunion @ SV286 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1906]) ).
thf(2214,plain,
! [SV288: $i > $o] :
( ( ( ! [SY3117: $i] :
~ ~ ( ~ ( SV288 @ SY3117 )
| ~ ! [SY3118: $i] :
( ~ ( SV288 @ SY3118 )
| ( SY3117 = SY3118 ) ) ) )
= $true )
| ( ( ! [SY3119: $i,SY3120: $i] :
( ~ ( SV288 @ SY3119 )
| ~ ( SV288 @ SY3120 )
| ( SY3119 = SY3120 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1908]) ).
thf(2215,plain,
! [SV575: $i > $o,SV289: $i] :
( ( ( ~ ~ ! [SY3670: $i] :
~ ~ ( ~ ( in @ SY3670 @ SV289 )
| ~ ( SV575 @ SY3670 ) ) )
= $false )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV289 )
| ~ ( SV575 @ SY3671 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1909]) ).
thf(2216,plain,
! [SV290: $i,SV576: $i] :
( ( ( in @ SV576 @ ( powerset @ SV290 ) )
= $false )
| ( ( subset @ ( setminus @ SV290 @ ( setminus @ SV290 @ SV576 ) ) @ SV576 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1910]) ).
thf(2217,plain,
! [SV577: $i > $o,SV291: $i,SV731: $i] :
( ( ( ~ ( in @ SV731 @ SV291 ) )
= $true )
| ( ( ~ ( SV577 @ SV731 )
| ( in @ SV731
@ ( dsetconstr @ SV291
@ ^ [SY3673: $i] : ( SV577 @ SY3673 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(2218,plain,
! [SV578: $i,SV292: $i] :
( ( ( breln1 @ SV292 @ SV578 )
= $false )
| ( ( ! [SY3674: $i] :
( ~ ( breln1 @ SV292 @ SY3674 )
| ( breln1 @ SV292 @ ( binunion @ SV578 @ SY3674 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(2219,plain,
! [SV732: $i > $i > $o,SV579: $i,SV293: $i,SV755: $i] :
( ( ~ ( in @ SV755 @ SV293 )
| ! [SY3938: $i] :
( ~ ( in @ SY3938 @ SV579 )
| ~ ( SV732 @ SV755 @ SY3938 )
| ( in @ ( kpair @ SV755 @ SY3938 )
@ ( dpsetconstr @ SV293 @ SV579
@ ^ [SY3897: $i,SY3898: $i] : ( SV732 @ SY3897 @ SY3898 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2220,plain,
! [SV294: $i,SV756: $i] :
( ( ( ~ ( in @ SV756 @ SV294 )
| ( ( setunion @ SV294 )
= SV756 ) )
= $true )
| ( ( singleton @ SV294 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2221,plain,
! [SV580: $i,SV295: $i] :
( ( ( in @ SV295 @ ( setadjoin @ SV580 @ emptyset ) )
= $false )
| ( ( in @ SV580 @ ( setadjoin @ SV295 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1915]) ).
thf(2222,plain,
! [SV581: $i,SV296: $i] :
( ( ( ~ ( subset @ SV296 @ SV581 ) )
= $false )
| ( ( SV296 != SV581 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(2223,plain,
! [SV582: $i,SV297: $i] :
( ( ( breln1 @ SV297 @ SV582 )
= $false )
| ( ( ! [SY3680: $i] :
( ~ ( breln1 @ SV297 @ SY3680 )
| ( ( binunion @ SV582 @ SY3680 )
= ( binunion @ SY3680 @ SV582 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(2224,plain,
! [SV757: $o,SV583: $i,SV298: $i,SV733: $i] :
( ( ~ ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
| ~ ( ~ ( in @ SV733 @ SV298 )
| SV757 )
| ~ ( ~ ( in @ SV733 @ SV583 )
| SV757 )
| SV757 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1918]) ).
thf(2225,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( ~ ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
| ~ ( ~ ( in @ SV733 @ SV298 )
| $true )
| ~ ( ~ ( in @ SV733 @ SV583 )
| $true )
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1918]) ).
thf(2226,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( ~ ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
| ~ ( ~ ( in @ SV733 @ SV298 )
| $false )
| ~ ( ~ ( in @ SV733 @ SV583 )
| $false )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1918]) ).
thf(2227,plain,
! [SV299: $i,SV584: $i] :
( ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false )
| ( ( ! [SY3683: $i] :
( ~ ( in @ SY3683 @ ( powerset @ SV299 ) )
| ~ ! [SY3684: $i] :
( ~ ( in @ SY3684 @ SV299 )
| ~ ( in @ SY3684 @ SV584 )
| ( in @ SY3684 @ SY3683 ) )
| ~ ! [SY3685: $i] :
( ~ ( in @ SY3685 @ SV299 )
| ~ ( in @ SY3685 @ SY3683 )
| ( in @ SY3685 @ SV584 ) )
| ( SV584 = SY3683 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(2228,plain,
! [SV585: $i,SV300: $i] :
( ( ( breln1 @ SV300 @ SV585 )
= $false )
| ( ( ! [SY3686: $i] :
( ~ ( breln1 @ SV300 @ SY3686 )
| ! [SY3687: $i] :
( ~ ( in @ SY3687 @ SV300 )
| ! [SY3688: $i] :
( ~ ( in @ SY3688 @ SV300 )
| ~ ( in @ ( kpair @ SY3687 @ SY3688 ) @ SV585 )
| ( in @ ( kpair @ SY3687 @ SY3688 ) @ ( binunion @ SV585 @ SY3686 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(2229,plain,
! [SV734: $i,SV586: $i,SV301: $i] :
( ( ( ~ ( func @ SV301 @ SV586 @ SV734 ) )
= $true )
| ( ( ! [SY3900: $i] :
( ~ ( func @ SV301 @ SV586 @ SY3900 )
| ~ ! [SY3901: $i] :
( ~ ( in @ SY3901 @ SV301 )
| ( ( ap @ SV301 @ SV586 @ SV734 @ SY3901 )
= ( ap @ SV301 @ SV586 @ SY3900 @ SY3901 ) ) )
| ! [SY3902: $i] :
( ~ ( in @ SY3902 @ SV301 )
| ! [SY3903: $i] :
( ~ ( in @ SY3903 @ SV586 )
| ~ ( in @ ( kpair @ SY3902 @ SY3903 ) @ SY3900 )
| ( in @ ( kpair @ SY3902 @ SY3903 ) @ SV734 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1921]) ).
thf(2230,plain,
! [SV302: $i,SV587: $i] :
( ( ( in @ SV587 @ ( powerset @ SV302 ) )
= $false )
| ( ( ! [SY3694: $i] :
( ~ ( in @ SY3694 @ ( powerset @ SV302 ) )
| ! [SY3695: $i] :
( ~ ( in @ SY3695 @ SV302 )
| ~ ( in @ SY3695 @ ( binunion @ ( setminus @ SV302 @ SV587 ) @ ( setminus @ SV302 @ SY3694 ) ) )
| ( in @ SY3695 @ ( setminus @ SV302 @ ( binintersect @ SV587 @ SY3694 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(2231,plain,
! [SV304: $i,SV588: $i] :
( ( ( in @ SV588 @ ( powerset @ SV304 ) )
= $false )
| ( ( SV588
= ( setminus @ SV304 @ ( setminus @ SV304 @ SV588 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1924]) ).
thf(2232,plain,
! [SV305: $i,SV589: $i] :
( ( ( in @ SV589 @ ( powerset @ SV305 ) )
= $false )
| ( ( ! [SY3696: $i] :
( ~ ( in @ SY3696 @ ( powerset @ SV305 ) )
| ! [SY3697: $i] :
( ~ ( in @ SY3697 @ ( powerset @ SV305 ) )
| ( in @ ( binintersect @ SV589 @ SY3696 ) @ ( powerset @ ( binintersect @ ( binunion @ SV589 @ SY3697 ) @ ( binunion @ SY3696 @ SY3697 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1925]) ).
thf(2233,plain,
! [SV306: $i] :
( ( ( ~ ( in @ ( sK8_SY3165 @ SV306 ) @ SV306 ) )
= $false )
| ( ( SV306 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1926]) ).
thf(2234,plain,
! [SV307: $i,SV590: $i] :
( ( ( in @ SV590 @ ( powerset @ SV307 ) )
= $false )
| ( ( ! [SY3698: $i] :
( ~ ( in @ SY3698 @ ( powerset @ SV307 ) )
| ! [SY3699: $i] :
( ~ ( in @ SY3699 @ SV307 )
| ~ ( in @ SY3699 @ ( binintersect @ ( setminus @ SV307 @ SV590 ) @ ( setminus @ SV307 @ SY3698 ) ) )
| ( in @ SY3699 @ ( setminus @ SV307 @ ( binunion @ SV590 @ SY3698 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1927]) ).
thf(2235,plain,
! [SV308: $i,SV591: $i] :
( ( ( in @ SV591 @ ( powerset @ SV308 ) )
= $false )
| ( ( ! [SY3700: $i] :
( ~ ( in @ SY3700 @ ( powerset @ SV308 ) )
| ~ ! [SY3701: $i] :
( ~ ( in @ SY3701 @ SV308 )
| ~ ( in @ SY3701 @ SV591 )
| ( in @ SY3701 @ SY3700 ) )
| ( in @ SV591 @ ( powerset @ SY3700 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1928]) ).
thf(2236,plain,
! [SV309: $i,SV592: $i] :
( ( ( in @ SV592 @ ( powerset @ SV309 ) )
= $false )
| ( ( ! [SY3702: $i] :
( ~ ( in @ SY3702 @ ( powerset @ SV309 ) )
| ! [SY3703: $i] :
( ~ ( in @ SY3703 @ SV309 )
| ~ ( in @ SY3703 @ ( setminus @ SV309 @ SV592 ) )
| ~ ( in @ SY3703 @ ( setminus @ SV309 @ SY3702 ) )
| ( in @ SY3703 @ ( setminus @ SV309 @ ( binunion @ SV592 @ SY3702 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1929]) ).
thf(2237,plain,
! [SV310: $i,SV593: $i] :
( ( ( in @ SV593 @ ( powerset @ SV310 ) )
= $false )
| ( ( in @ ( setminus @ SV310 @ SV593 ) @ ( powerset @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(2238,plain,
! [SV594: $i,SV311: $i] :
( ( ( SV311 != SV594 )
= $false )
| ( ( ~ ( in @ SV594 @ ( setadjoin @ SV311 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(2239,plain,
! [SV312: $i,SV595: $i,SV735: $i] :
( ( ( ~ ( in @ SV735 @ SV595 ) )
= $true )
| ( ( in @ SV735 @ ( binunion @ SV312 @ SV595 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1932]) ).
thf(2240,plain,
! [SV596: $i,SV313: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ SV313 ) )
= $true )
| ( ( ! [SY3904: $i] :
( ~ ( in @ SY3904 @ SV596 )
| ( in @ ( setadjoin @ SV736 @ ( setadjoin @ SY3904 @ emptyset ) ) @ ( powerset @ ( binunion @ SV313 @ SV596 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1933]) ).
thf(2241,plain,
! [SV597: $i,SV314: $i,SV737: $i] :
( ( ( ~ ( in @ SV737 @ SV314 ) )
= $true )
| ( ( ! [SY3905: $i] :
( ~ ( in @ SY3905 @ SV597 )
| ( ( ksnd @ ( kpair @ SV737 @ SY3905 ) )
= SY3905 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1934]) ).
thf(2242,plain,
! [SV315: $i,SV598: $i] :
( ( ( in @ SV598 @ ( powerset @ SV315 ) )
= $false )
| ( ( ! [SY3709: $i] :
( ~ ( in @ SY3709 @ ( powerset @ SV315 ) )
| ! [SY3710: $i] :
( ~ ( in @ SY3710 @ SV315 )
| ~ ( in @ SY3710 @ ( setminus @ SV315 @ ( binunion @ SV598 @ SY3709 ) ) )
| ~ ( in @ SY3710 @ SV598 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(2243,plain,
! [SV316: $i > $o] :
( ( ( ! [SY3188: $i] :
~ ~ ( ~ ( SV316 @ SY3188 )
| ~ ! [SY3189: $i] :
( ~ ( SV316 @ SY3189 )
| ( SY3188 = SY3189 ) ) ) )
= $true )
| ( ( ~ ! [SY3190: $i] :
~ ! [SY3191: $i] :
~ ( ~ ( ~ ( SV316 @ SY3191 )
| ( SY3191 = SY3190 ) )
| ~ ( ( SY3191 != SY3190 )
| ( SV316 @ SY3191 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1936]) ).
thf(2244,plain,
! [SV317: $i,SV599: $i] :
( ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false )
| ( ( ! [SY3711: $i] :
( ~ ( in @ SY3711 @ ( powerset @ SV317 ) )
| ! [SY3712: $i] :
( ~ ( in @ SY3712 @ ( powerset @ SV317 ) )
| ! [SY3713: $i] :
( ~ ( in @ SY3713 @ ( powerset @ SV317 ) )
| ~ ( subset @ SV599 @ SY3712 )
| ~ ( subset @ SY3711 @ SY3713 )
| ( subset @ ( binintersect @ SV599 @ SY3711 ) @ ( binintersect @ SY3712 @ SY3713 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(2245,plain,
! [SV318: $i,SV600: $i] :
( ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false )
| ( ( ! [SY3714: $i] :
( ~ ( in @ SY3714 @ ( powerset @ SV318 ) )
| ! [SY3715: $i] :
( ~ ( in @ SY3715 @ SV318 )
| ~ ~ ( in @ SY3715 @ SY3714 )
| ~ ( in @ SY3715 @ ( binintersect @ SV600 @ SY3714 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(2246,plain,
! [SV738: $i,SV601: $i,SV319: $i] :
( ( ( ~ ( breln @ SV319 @ SV601 @ SV738 ) )
= $true )
| ( ( ! [SY3906: $i > $o] :
( ~ ! [SY3907: $i] :
( ~ ( in @ SY3907 @ SV319 )
| ! [SY3908: $i] :
( ~ ( in @ SY3908 @ SV601 )
| ~ ( in @ ( kpair @ SY3907 @ SY3908 ) @ SV738 )
| ( SY3906 @ ( kpair @ SY3907 @ SY3908 ) ) ) )
| ! [SY3909: $i] :
( ~ ( in @ SY3909 @ SV738 )
| ( SY3906 @ SY3909 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1939]) ).
thf(2247,plain,
! [SV602: $i,SV320: $i] :
( ( ( ! [SY3721: $i] :
( ~ ( in @ SY3721 @ SV320 )
| ( in @ SY3721 @ SV602 ) ) )
= $false )
| ( ( subset @ SV320 @ SV602 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1940]) ).
thf(2248,plain,
! [SV603: $o,SV321: $i,SV739: $i] :
( ( ( ~ ( in @ SV739 @ SV321 ) )
= $true )
| ( ( ! [SY3910: $i] :
( ~ ( in @ SY3910 @ SV321 )
| ~ ~ SV603
| ( ( if @ SV321 @ SV603 @ SV739 @ SY3910 )
= SY3910 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1941]) ).
thf(2249,plain,
! [SV321: $i,SV740: $i] :
( ( ( ~ ( in @ SV740 @ SV321 ) )
= $true )
| ( ( ! [SY3911: $i] :
( ~ ( in @ SY3911 @ SV321 )
| ~ ~ $true
| ( ( if @ SV321 @ $true @ SV740 @ SY3911 )
= SY3911 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1942]) ).
thf(2250,plain,
! [SV321: $i,SV741: $i] :
( ( ( ~ ( in @ SV741 @ SV321 ) )
= $true )
| ( ( ! [SY3912: $i] :
( ~ ( in @ SY3912 @ SV321 )
| ~ ~ $false
| ( ( if @ SV321 @ $false @ SV741 @ SY3912 )
= SY3912 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1943]) ).
thf(2251,plain,
! [SV322: $i] :
( ( ( ! [SY3210: $i] :
~ ( in @ SY3210 @ SV322 ) )
= $true )
| ( ( ~ ! [SY3211: $i] :
~ ~ ( ~ ( in @ SY3211 @ SV322 )
| ~ ~ ~ ! [SY3212: $i] :
~ ~ ( ~ ( in @ SY3212 @ SY3211 )
| ~ ( in @ SY3212 @ SV322 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1944]) ).
thf(2252,plain,
! [SV604: $i,SV323: $i,SV758: $i,SV742: $i] :
( ( ~ ( in @ ( kpair @ SV742 @ SV758 ) @ ( cartprod @ SV323 @ SV604 ) )
| ( in @ SV742 @ SV323 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2253,plain,
! [SV605: $i,SV324: $i] :
( ( ( ! [SY3726: $i] :
( ~ ( in @ SY3726 @ SV324 )
| ( in @ SY3726 @ SV605 ) ) )
= $false )
| ( ( subset @ SV324 @ SV605 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1946]) ).
thf(2254,plain,
! [SV325: $i,SV606: $i] :
( ( ( in @ SV606 @ ( powerset @ SV325 ) )
= $false )
| ( ( ! [SY3727: $i] :
( ~ ( in @ SY3727 @ ( powerset @ SV325 ) )
| ! [SY3728: $i] :
( ~ ( in @ SY3728 @ ( powerset @ SV325 ) )
| ~ ( subset @ SV606 @ SY3727 )
| ~ ( subset @ SV606 @ SY3728 )
| ( subset @ SV606 @ ( binintersect @ SY3727 @ SY3728 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1947]) ).
thf(2255,plain,
! [SV37: $i] :
( ( ( ! [SY2402: $i] :
~ ~ ( ~ ( in @ SY2402 @ SV37 )
| ~ $true ) )
= $false )
| ( ( SV37 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1949]) ).
thf(2256,plain,
! [SV38: $i,SV743: $i] :
( ( ( ~ ( in @ SV743 @ omega ) )
= $true )
| ( ( ( ( omegaS @ SV38 )
!= ( omegaS @ SV743 ) )
| ( SV38 = SV743 ) )
= $true )
| ( ( in @ SV38 @ omega )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1950]) ).
thf(2257,plain,
! [SV350: $i,SV610: $i > $i,SV39: $i] :
( ( ( ! [SY3733: $i] :
( ~ ( in @ SY3733 @ SV39 )
| ( in @ ( SV610 @ SY3733 ) @ SV350 ) ) )
= $false )
| ( ( func @ SV39 @ SV350
@ ( dpsetconstr @ SV39 @ SV350
@ ^ [SY3734: $i,SY3735: $i] :
( ( SV610 @ SY3734 )
= SY3735 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1951]) ).
thf(2258,plain,
! [SV759: $i,SV40: $i > $o] :
( ( ( ~ ~ ( ~ ( SV40 @ SV759 )
| ~ ! [SY3941: $i] :
( ~ ( SV40 @ SY3941 )
| ( SV759 = SY3941 ) ) ) )
= $true )
| ( ( ~ ! [SY2411: $i] :
~ ( SV40 @ SY2411 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2259,plain,
! [SV351: $i,SV41: $i,SV611: $i] :
( ( ( in @ SV611 @ SV41 )
= $false )
| ( ( ! [SY3736: $i] :
( ~ ( in @ SY3736 @ SV351 )
| ( ( kpair @ SV611 @ SY3736 )
= ( kpair @ SV611 @ SY3736 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1953]) ).
thf(2260,plain,
! [SV760: $i,SV42: $i > $o] :
( ( ( ~ ~ ( ~ ( SV42 @ SV760 )
| ~ ! [SY3942: $i] :
( ~ ( SV42 @ SY3942 )
| ( SV760 = SY3942 ) ) ) )
= $true )
| ( ( SV42
@ ( descr
@ ^ [SY2417: $i] : ( SV42 @ SY2417 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2261,plain,
! [SV44: $i,SV353: $i > $o] :
( ( ( ~ ( in @ ( sK9_SY3238 @ SV353 @ SV44 ) @ SV44 )
| ! [SY3943: $i] :
( ~ ( in @ SY3943 @ SV44 )
| ~ ( SV353 @ ( sK9_SY3238 @ SV353 @ SV44 ) )
| ~ ( SV353 @ SY3943 )
| ( ( sK9_SY3238 @ SV353 @ SV44 )
= SY3943 ) ) )
= $false )
| ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) )
| ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1956]) ).
thf(2262,plain,
! [SV354: $i,SV45: $i,SV612: $i] :
( ( ( in @ SV612 @ ( funcSet @ SV45 @ SV354 ) )
= $false )
| ( ( ! [SY3737: $i] :
( ~ ( in @ SY3737 @ ( funcSet @ SV45 @ SV354 ) )
| ~ ! [SY3738: $i] :
( ~ ( in @ SY3738 @ SV45 )
| ( ( ap @ SV45 @ SV354 @ SV612 @ SY3738 )
= ( ap @ SV45 @ SV354 @ SY3737 @ SY3738 ) ) )
| ( SV612 = SY3737 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1957]) ).
thf(2263,plain,
! [SV355: $i,SV46: $i,SV613: $i] :
( ( ( in @ SV613 @ SV46 )
= $false )
| ( ( in @ ( setadjoin @ SV613 @ emptyset ) @ ( powerset @ ( binunion @ SV46 @ SV355 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2264,plain,
! [SV356: $i,SV47: $i,SV614: $i] :
( ( ( in @ SV614 @ ( funcSet @ SV47 @ SV356 ) )
= $false )
| ( ( ! [SY3739: $i] :
( ~ ( in @ SY3739 @ SV47 )
| ( in @ ( kpair @ SY3739 @ ( ap @ SV47 @ SV356 @ SV614 @ SY3739 ) ) @ SV614 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1959]) ).
thf(2265,plain,
! [SV744: $i,SV615: $i,SV357: $i,SV48: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV48 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV48 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV615 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV615 @ ( setadjoin @ SV744 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV357 = SV744 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1960]) ).
thf(2266,plain,
! [SV358: $i,SV49: $i,SV616: $i] :
( ( ( in @ SV616 @ ( funcSet @ SV49 @ SV358 ) )
= $false )
| ( ( ! [SY3741: $i] :
( ~ ( in @ SY3741 @ SV49 )
| ( in @ ( ap @ SV49 @ SV358 @ SV616 @ SY3741 ) @ SV358 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1961]) ).
thf(2267,plain,
! [SV359: $i,SV50: $i,SV761: $i] :
( ( ( ! [SY3944: $i] :
( ( SV761 != SY3944 )
| ( ( setadjoin @ SV50 @ SV761 )
= ( setadjoin @ SV359 @ SY3944 ) ) ) )
= $true )
| ( ( SV50 = SV359 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2268,plain,
! [SV360: $i,SV51: $i,SV617: $i] :
( ( ( in @ SV617 @ ( funcSet @ SV51 @ SV360 ) )
= $false )
| ( ( func @ SV51 @ SV360 @ SV617 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1963]) ).
thf(2269,plain,
! [SV361: $i,SV52: $i,SV762: $i] :
( ( ( ~ ( in @ SV762 @ ( powerset @ SV52 ) )
| ! [SY3945: $i] :
( ~ ( in @ SY3945 @ ( powerset @ SV52 ) )
| ! [SY3946: $i] :
( ~ ( in @ SY3946 @ SV52 )
| ~ ( in @ SY3946 @ ( binintersect @ SV361 @ SV762 ) )
| ( in @ SY3946 @ ( binunion @ SV762 @ SY3945 ) ) ) ) )
= $true )
| ( ( in @ SV361 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2270,plain,
! [SV363: $i,SV618: $i > $i,SV54: $i] :
( ( ( ! [SY3742: $i] :
( ~ ( in @ SY3742 @ SV54 )
| ( in @ ( SV618 @ SY3742 ) @ SV363 ) ) )
= $false )
| ( ( in
@ ( lam @ SV54 @ SV363
@ ^ [SY3743: $i] : ( SV618 @ SY3743 ) )
@ ( funcSet @ SV54 @ SV363 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(2271,plain,
! [SV364: $i,SV55: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ ( powerset @ SV55 ) )
| ~ ( subset @ SV364 @ ( setminus @ SV55 @ SV763 ) )
| ( subset @ SV763 @ ( setminus @ SV55 @ SV364 ) ) )
= $true )
| ( ( in @ SV364 @ ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2272,plain,
! [SV365: $i,SV56: $i,SV764: $i] :
( ( ( ~ ( in @ SV764 @ ( powerset @ SV56 ) )
| ! [SY3947: $i] :
( ~ ( in @ SY3947 @ ( powerset @ SV56 ) )
| ! [SY3948: $i] :
( ~ ( in @ SY3948 @ ( powerset @ SV56 ) )
| ( ( setminus @ SV56 @ ( binintersect @ ( binunion @ SV365 @ SV764 ) @ ( binunion @ SY3947 @ SY3948 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV56 @ SV365 ) @ ( setminus @ SV56 @ SV764 ) ) @ ( binintersect @ ( setminus @ SV56 @ SY3947 ) @ ( setminus @ SV56 @ SY3948 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV365 @ ( powerset @ SV56 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2273,plain,
! [SV57: $i,SV366: $i] :
( ( ~ ( in @ SV366 @ ( setunion @ SV57 ) )
| ~ ! [SY3265: $i] :
~ ~ ( ~ ( in @ SV366 @ SY3265 )
| ~ ( in @ SY3265 @ SV57 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1969]) ).
thf(2274,plain,
! [SV57: $i,SV366: $i] :
( ( ~ ~ ! [SY3266: $i] :
~ ~ ( ~ ( in @ SV366 @ SY3266 )
| ~ ( in @ SY3266 @ SV57 ) )
| ( in @ SV366 @ ( setunion @ SV57 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1970]) ).
thf(2275,plain,
! [SV765: $i,SV58: $i > $o] :
( ( ( ~ ~ ( ~ ( SV58 @ SV765 )
| ~ ! [SY3949: $i] :
( ~ ( SV58 @ SY3949 )
| ( SV765 = SY3949 ) ) ) )
= $true )
| ( ( ! [SY2464: $i,SY2465: $i] :
( ~ ( SV58 @ SY2464 )
| ~ ( SV58 @ SY2465 )
| ( SY2464 = SY2465 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2276,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ! [SY3950: $i] :
~ ( ~ ( ~ ( SV59 @ SY3950 )
| ( SY3950 = SV766 ) )
| ~ ( ( SY3950 != SV766 )
| ( SV59 @ SY3950 ) ) ) )
= $true )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2277,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ~ ~ ( ~ ( SV60 @ SV767 )
| ~ ! [SY3951: $i] :
( ~ ( SV60 @ SY3951 )
| ( SV767 = SY3951 ) ) ) )
= $true )
| ( ( ~ ! [SY2472: $i] :
~ ~ ( ~ ( SV60 @ SY2472 )
| ~ ! [SY2473: $i] :
( ~ ( SV60 @ SY2473 )
| ( SY2472 = SY2473 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2278,plain,
! [SV367: $i > $o,SV61: $i] :
( ( ( ! [SY3267: $i] :
( ~ ( in @ SY3267 @ SV61 )
| ( SV367 @ SY3267 ) ) )
= $true )
| ( ( ~ ! [SY3268: $i] :
~ ~ ( ~ ( in @ SY3268 @ SV61 )
| ~ ~ ( SV367 @ SY3268 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1974]) ).
thf(2279,plain,
! [SV619: $i,SV369: $i,SV63: $i] :
( ( ( func @ SV63 @ SV369 @ SV619 )
= $false )
| ( ( ! [SY3744: $i] :
( ~ ( in @ SY3744 @ SV63 )
| ( in @ ( ap @ SV63 @ SV369 @ SV619 @ SY3744 ) @ SV369 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1976]) ).
thf(2280,plain,
! [SV370: $i,SV620: $i > $i,SV64: $i] :
( ( ( ! [SY3745: $i] :
( ~ ( in @ SY3745 @ SV64 )
| ( in @ ( SV620 @ SY3745 ) @ SV370 ) ) )
= $false )
| ( ( ( lam @ SV64 @ SV370
@ ^ [SY3746: $i] : ( SV620 @ SY3746 ) )
= ( lam @ SV64 @ SV370
@ ^ [SY3747: $i] : ( SV620 @ SY3747 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1977]) ).
thf(2281,plain,
! [SV65: $i,SV371: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 )
| ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 ) )
| ~ ( ~ ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 )
| ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 ) ) ) )
= $false )
| ( ( SV65 = SV371 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1978]) ).
thf(2282,plain,
! [SV372: $i,SV68: $i,SV768: $i] :
( ( ( ~ ( in @ SV768 @ ( powerset @ SV68 ) )
| ~ ( subset @ SV372 @ ( setminus @ SV68 @ SV768 ) )
| ! [SY3952: $i] :
( ~ ( in @ SY3952 @ SV68 )
| ~ ( in @ SY3952 @ SV768 )
| ( in @ SY3952 @ ( setminus @ SV68 @ SV372 ) ) ) )
= $true )
| ( ( in @ SV372 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2283,plain,
! [SV373: $i,SV69: $i,SV769: $i] :
( ( ( ~ ( in @ SV769 @ ( powerset @ SV69 ) )
| ! [SY3953: $i] :
( ~ ( in @ SY3953 @ SV69 )
| ~ ( in @ SY3953 @ ( setminus @ SV69 @ ( binintersect @ SV373 @ SV769 ) ) )
| ( in @ SY3953 @ ( binunion @ ( setminus @ SV69 @ SV373 ) @ ( setminus @ SV69 @ SV769 ) ) ) ) )
= $true )
| ( ( in @ SV373 @ ( powerset @ SV69 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2284,plain,
! [SV375: $i,SV71: $i,SV770: $i] :
( ( ( ~ ( in @ SV770 @ ( powerset @ SV71 ) )
| ( in @ ( binunion @ SV375 @ SV770 ) @ ( powerset @ SV71 ) ) )
= $true )
| ( ( in @ SV375 @ ( powerset @ SV71 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2285,plain,
! [SV376: $i,SV72: $i,SV621: $i] :
( ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false )
| ( ( ! [SY3748: $o] :
( ~ ( ( SV621 != SV72 )
| SY3748 )
| ~ ( ~ ( in @ SV621 @ SV376 )
| SY3748 )
| SY3748 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1986]) ).
thf(2286,plain,
! [SV377: $i,SV771: $i,SV73: $i] :
( ( ( ~ ( breln1 @ SV73 @ SV771 )
| ( breln1 @ SV73 @ ( breln1compset @ SV73 @ SV377 @ SV771 ) ) )
= $true )
| ( ( breln1 @ SV73 @ SV377 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2287,plain,
! [SV379: $i,SV75: $i,SV772: $i] :
( ( ( ~ ( in @ SV772 @ ( powerset @ SV75 ) )
| ! [SY3954: $i] :
( ~ ( in @ SY3954 @ SV75 )
| ~ ( in @ SY3954 @ ( setminus @ SV75 @ ( binunion @ SV379 @ SV772 ) ) )
| ( in @ SY3954 @ ( setminus @ SV75 @ SV772 ) ) ) )
= $true )
| ( ( in @ SV379 @ ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2288,plain,
! [SV380: $i > $i,SV76: $i,SV622: $i] :
( ( ~ ( ~ ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3287: $i] : ( SV380 @ SY3287 ) ) )
| ~ ! [SY3750: $i] :
~ ~ ( ~ ( in @ SY3750 @ SV76 )
| ( SV622
!= ( SV380 @ SY3750 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1990]) ).
thf(2289,plain,
! [SV380: $i > $i,SV622: $i,SV76: $i] :
( ( ~ ( ~ ~ ! [SY3751: $i] :
~ ~ ( ~ ( in @ SY3751 @ SV76 )
| ( SV622
!= ( SV380 @ SY3751 ) ) )
| ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3290: $i] : ( SV380 @ SY3290 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1990]) ).
thf(2290,plain,
! [SV381: $i > $i,SV623: $i,SV77: $i] :
( ( ( ~ ! [SY3753: $i] :
~ ~ ( ~ ( in @ SY3753 @ SV77 )
| ( SV623
!= ( SV381 @ SY3753 ) ) ) )
= $false )
| ( ( in @ SV623
@ ( image1 @ SV77
@ ^ [SY3293: $i] : ( SV381 @ SY3293 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1991]) ).
thf(2291,plain,
! [SV382: $i,SV773: $i,SV78: $i] :
( ( ( ~ ( breln1 @ SV78 @ SV773 )
| ! [SY3955: $i] :
( ~ ( in @ SY3955 @ SV78 )
| ! [SY3956: $i] :
( ~ ( in @ SY3956 @ SV78 )
| ~ ( in @ ( kpair @ SY3955 @ SY3956 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
| ~ ! [SY3957: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3957 @ SV78 )
| ~ ( in @ ( kpair @ SY3955 @ SY3957 ) @ SV382 ) )
| ~ ( in @ ( kpair @ SY3957 @ SY3956 ) @ SV773 ) ) ) ) )
= $true )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2292,plain,
! [SV383: $i,SV79: $i,SV624: $i] :
( ( ( in @ SV624 @ ( cartprod @ SV79 @ SV383 ) )
= $false )
| ( ( in @ ( kfst @ SV624 ) @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1993]) ).
thf(2293,plain,
! [SV384: $i,SV80: $i,SV625: $i] :
( ( ~ ( ~ ( in @ SV625 @ ( setadjoin @ SV80 @ SV384 ) )
| ( SV625 = SV80 )
| ( in @ SV625 @ SV384 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1994]) ).
thf(2294,plain,
! [SV384: $i,SV80: $i,SV625: $i] :
( ( ~ ( ~ ( ( SV625 = SV80 )
| ( in @ SV625 @ SV384 ) )
| ( in @ SV625 @ ( setadjoin @ SV80 @ SV384 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1994]) ).
thf(2295,plain,
! [SV81: $i,SV385: $i,SV626: $i] :
( ( ( in @ SV626 @ SV385 )
= $false )
| ( ( in @ SV626 @ ( setadjoin @ SV81 @ SV385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1995]) ).
thf(2296,plain,
! [SV386: $i,SV774: $i,SV82: $i] :
( ( ( ~ ( breln1 @ SV82 @ SV774 )
| ! [SY3958: $i] :
( ~ ( in @ SY3958 @ SV82 )
| ! [SY3959: $i] :
( ~ ( in @ SY3959 @ SV82 )
| ~ ( in @ ( kpair @ SY3958 @ SY3959 ) @ ( binunion @ SV386 @ SV774 ) )
| ( in @ ( kpair @ SY3958 @ SY3959 ) @ SV386 )
| ( in @ ( kpair @ SY3958 @ SY3959 ) @ SV774 ) ) ) )
= $true )
| ( ( breln1 @ SV82 @ SV386 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2297,plain,
! [SV388: $i,SV85: $i,SV775: $i] :
( ( ( ~ ( in @ SV775 @ ( powerset @ SV85 ) )
| ( ( setminus @ SV85 @ ( binintersect @ SV388 @ SV775 ) )
= ( binunion @ ( setminus @ SV85 @ SV388 ) @ ( setminus @ SV85 @ SV775 ) ) ) )
= $true )
| ( ( in @ SV388 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2298,plain,
! [SV389: $i,SV86: $i,SV776: $i] :
( ( ( ~ ( in @ SV776 @ ( powerset @ SV86 ) )
| ! [SY3960: $i] :
( ~ ( in @ SY3960 @ SV86 )
| ~ ( subset @ SV389 @ ( setminus @ SV86 @ SV776 ) )
| ~ ( in @ SY3960 @ SV776 )
| ~ ( in @ SY3960 @ SV389 ) ) )
= $true )
| ( ( in @ SV389 @ ( powerset @ SV86 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2299,plain,
! [SV390: $i,SV87: $i,SV777: $i] :
( ( ( ~ ( in @ SV777 @ ( powerset @ SV87 ) )
| ! [SY3961: $i] :
( ~ ( in @ SY3961 @ SV87 )
| ~ ( subset @ SV390 @ SV777 )
| ~ ~ ( in @ SY3961 @ SV777 )
| ~ ( in @ SY3961 @ SV390 ) ) )
= $true )
| ( ( in @ SV390 @ ( powerset @ SV87 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2300,plain,
! [SV391: $i,SV88: $i,SV778: $i] :
( ( ( ~ ( in @ SV778 @ ( powerset @ SV88 ) )
| ( subset @ ( setminus @ SV88 @ SV391 ) @ ( setminus @ SV88 @ ( binintersect @ SV391 @ SV778 ) ) ) )
= $true )
| ( ( in @ SV391 @ ( powerset @ SV88 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2301,plain,
! [SV393: $i,SV90: $i,SV779: $i] :
( ( ( ~ ( in @ SV779 @ ( powerset @ SV90 ) )
| ! [SY3962: $i] :
( ~ ( in @ SY3962 @ ( powerset @ SV90 ) )
| ! [SY3963: $i] :
( ~ ( in @ SY3963 @ SV90 )
| ~ ( in @ SY3963 @ ( binintersect @ SV393 @ SV779 ) )
| ( in @ SY3963 @ ( binintersect @ ( binunion @ SV393 @ SY3962 ) @ ( binunion @ SV779 @ SY3962 ) ) ) ) ) )
= $true )
| ( ( in @ SV393 @ ( powerset @ SV90 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2302,plain,
! [SV394: $i,SV92: $i,SV627: $i] :
( ( ( in @ SV627 @ SV92 )
= $false )
| ( ( ~ ~ ( in @ SV627 @ SV394 )
| ( in @ SV627 @ ( setminus @ SV92 @ SV394 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2303,plain,
! [SV396: $i,SV95: $i,SV628: $i] :
( ( ( in @ SV628 @ ( funcSet @ SV95 @ SV396 ) )
= $false )
| ( ( ! [SY3755: $i] :
( ~ ( in @ SY3755 @ SV95 )
| ( ( ap @ SV95 @ SV396 @ SV628 @ SY3755 )
= ( ap @ SV95 @ SV396 @ SV628 @ SY3755 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2006]) ).
thf(2304,plain,
! [SV397: $i,SV96: $i,SV629: $i] :
( ( ( ~ ( in @ SV629 @ ( setminus @ SV96 @ SV397 ) ) )
= $false )
| ( ( ~ ( in @ SV629 @ SV96 )
| ( in @ SV629 @ SV397 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2007]) ).
thf(2305,plain,
! [SV398: $i,SV97: $i,SV630: $i] :
( ( ( in @ SV630 @ ( cartprod @ SV97 @ SV398 ) )
= $false )
| ( ( iskpair @ SV630 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2008]) ).
thf(2306,plain,
! [SV400: $i,SV99: $i,SV780: $i] :
( ( ( ~ ( in @ SV780 @ ( powerset @ SV99 ) )
| ! [SY3964: $i] :
( ~ ( in @ SY3964 @ SV99 )
| ~ ( in @ SY3964 @ ( setminus @ SV99 @ ( binunion @ SV400 @ SV780 ) ) )
| ( in @ SY3964 @ ( setminus @ SV99 @ SV400 ) ) ) )
= $true )
| ( ( in @ SV400 @ ( powerset @ SV99 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2307,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV781 ) )
= $true )
| ( ( ~ ! [SY2563: $i,SY2564: $i] :
( ~ ( SV100 @ SY2563 )
| ~ ( SV100 @ SY2564 )
| ( SY2563 = SY2564 ) )
| ~ ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2308,plain,
! [SV402: $i,SV102: $i,SV631: $i] :
( ( ( ~ ( in @ SV631 @ ( setminus @ SV102 @ SV402 ) ) )
= $false )
| ( ( ~ ~ ( in @ SV631 @ SV402 )
| ~ ( in @ SV631 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2309,plain,
! [SV403: $i,SV103: $i,SV632: $i] :
( ( ( in @ SV632 @ ( funcSet @ SV103 @ SV403 ) )
= $false )
| ( ( ( lam @ SV103 @ SV403
@ ^ [SY3756: $i] : ( ap @ SV103 @ SV403 @ SV632 @ SY3756 ) )
= SV632 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2014]) ).
thf(2310,plain,
! [SV404: $i > $o,SV104: $i] :
( ( ( ! [SY3323: $i] :
~ ~ ( ~ ( in @ SY3323 @ SV104 )
| ~ ~ ( SV404 @ SY3323 ) ) )
= $true )
| ( ( ~ ! [SY3324: $i] :
( ~ ( in @ SY3324 @ SV104 )
| ( SV404 @ SY3324 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2015]) ).
thf(2311,plain,
! [SV405: $i,SV105: $i] :
( ( ( surjective @ SV105 @ ( powerset @ SV105 ) @ SV405 )
= $false )
| ( ( in @ SV405 @ ( funcSet @ SV105 @ ( powerset @ SV105 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2016]) ).
thf(2312,plain,
! [SV106: $i] :
( ( ( ~ ( in @ emptyset @ SV106 ) )
= $true )
| ( ( ~ ! [SY2577: $i] :
( ~ ~ ( ~ ( in @ SY2577 @ omega )
| ~ ( in @ SY2577 @ SV106 ) )
| ( in @ ( setadjoin @ SY2577 @ SY2577 ) @ SV106 ) ) )
= $true )
| ( ( ! [SY2578: $i] :
( ~ ( in @ SY2578 @ omega )
| ( in @ SY2578 @ SV106 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2017]) ).
thf(2313,plain,
! [SV633: $i,SV406: $i,SV108: $i] :
( ( ( func @ SV108 @ SV406 @ SV633 )
= $false )
| ( ( ! [SY3757: $i] :
( ~ ( in @ SY3757 @ SV108 )
| ( singleton
@ ( dsetconstr @ SV406
@ ^ [SY3758: $i] : ( in @ ( kpair @ SY3757 @ SY3758 ) @ SV633 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2314,plain,
! [SV407: $i,SV109: $i,SV782: $i] :
( ( ( ~ ( in @ SV782 @ ( powerset @ SV109 ) )
| ~ ! [SY3965: $i] :
( ~ ( in @ SY3965 @ SV109 )
| ~ ( in @ SY3965 @ SV407 )
| ( in @ SY3965 @ SV782 ) )
| ( subset @ SV407 @ SV782 ) )
= $true )
| ( ( in @ SV407 @ ( powerset @ SV109 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2315,plain,
! [SV408: $i,SV110: $i,SV783: $i] :
( ( ( ~ ( in @ SV783 @ ( powerset @ SV110 ) )
| ! [SY3966: $i] :
( ~ ( in @ SY3966 @ SV110 )
| ~ ~ ( in @ SY3966 @ SV408 )
| ~ ( in @ SY3966 @ ( binintersect @ SV408 @ SV783 ) ) ) )
= $true )
| ( ( in @ SV408 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2316,plain,
! [SV409: $i,SV111: $i,SV634: $i] :
( ( ( in @ SV634 @ ( cartprod @ SV111 @ SV409 ) )
= $false )
| ( ( in @ ( ksnd @ SV634 ) @ SV409 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2021]) ).
thf(2317,plain,
! [SV410: $i,SV112: $i,SV635: $i] :
( ( ( in @ SV635 @ SV112 )
= $false )
| ( ( ! [SY3759: $i] :
( ~ ( in @ SY3759 @ SV410 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV635 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV635 @ ( setadjoin @ SY3759 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV112 @ SV410 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2022]) ).
thf(2318,plain,
! [SV411: $i,SV113: $i,SV784: $i] :
( ( ( ~ ( in @ SV784 @ ( powerset @ SV113 ) )
| ! [SY3967: $i] :
( ~ ( in @ SY3967 @ SV113 )
| ~ ( in @ SY3967 @ ( setminus @ SV113 @ SV411 ) )
| ( in @ SY3967 @ ( setminus @ SV113 @ ( binintersect @ SV411 @ SV784 ) ) ) ) )
= $true )
| ( ( in @ SV411 @ ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2319,plain,
! [SV412: $i,SV114: $i,SV785: $i] :
( ( ( ~ ( in @ SV785 @ SV114 )
| ~ ( in @ SV785 @ SV412 )
| ~ ( in @ SV785 @ ( setminus @ SV114 @ SV412 ) ) )
= $true )
| ( ( in @ SV412 @ ( powerset @ SV114 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2320,plain,
! [SV636: $i > $i > $o,SV413: $i,SV115: $i,SV786: $i,SV746: $i] :
( ( ~ ( in @ ( kpair @ SV746 @ SV786 )
@ ( dpsetconstr @ SV115 @ SV413
@ ^ [SY3762: $i,SY3763: $i] : ( SV636 @ SY3762 @ SY3763 ) ) )
| ( in @ SV746 @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2321,plain,
! [SV637: $i > $i > $o,SV414: $i,SV116: $i,SV787: $i,SV747: $i] :
( ( ~ ( in @ ( kpair @ SV747 @ SV787 )
@ ( dpsetconstr @ SV116 @ SV414
@ ^ [SY3766: $i,SY3767: $i] : ( SV637 @ SY3766 @ SY3767 ) ) )
| ( in @ SV787 @ SV414 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2322,plain,
! [SV415: $i,SV117: $i,SV638: $i] :
( ( ( in @ SV638 @ ( setminus @ SV117 @ SV415 ) )
= $false )
| ( ( ~ ( in @ SV638 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2323,plain,
! [SV416: $i > $o,SV118: $i,SV639: $i] :
( ( ( in @ SV639 @ SV118 )
= $false )
| ( ( ~ ( SV416 @ SV639 )
| ~ ! [SY3768: $i] :
( ~ ( in @ SY3768 @ SV118 )
| ~ ( SV416 @ SY3768 )
| ( SY3768 = SV639 ) )
| ( ex1 @ SV118
@ ^ [SY3351: $i] : ( SV416 @ SY3351 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2324,plain,
! [SV418: $i,SV120: $i,SV640: $i] :
( ( ( ~ ( in @ SV640 @ SV120 ) )
= $false )
| ( ( ~ ~ ( in @ SV640 @ SV418 )
| ~ ( in @ SV640 @ ( symdiff @ SV120 @ SV418 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2325,plain,
! [SV419: $i,SV641: $i > $i,SV121: $i] :
( ( ( ! [SY3770: $i] :
( ~ ( in @ SY3770 @ SV121 )
| ( in @ ( SV641 @ SY3770 ) @ SV419 ) ) )
= $false )
| ( ( ! [SY3771: $i] :
( ~ ( in @ SY3771 @ SV121 )
| ( ( ap @ SV121 @ SV419
@ ( lam @ SV121 @ SV419
@ ^ [SY3772: $i] : ( SV641 @ SY3772 ) )
@ SY3771 )
= ( SV641 @ SY3771 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2031]) ).
thf(2326,plain,
! [SV788: $i > $o,SV420: $i,SV122: $i] :
( ( ( ! [SY3972: $i > $o] :
( ~ ! [SY3973: $i] :
( ~ ( in @ SY3973 @ SV122 )
| ! [SY3974: $i] :
( ~ ( in @ SY3974 @ SV420 )
| ( SY3973 != SY3974 )
| ~ ( ~ ( ~ ( SV788 @ SY3973 )
| ( SY3972 @ SY3974 ) )
| ~ ( ~ ( SY3972 @ SY3974 )
| ( SV788 @ SY3973 ) ) ) ) )
| ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SX4: $i] : ( SY3972 @ SX4 ) ) ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2327,plain,
! [SV421: $i > $o,SV123: $i,SV789: $i] :
( ( ( ~ ( in @ SV789 @ SV123 )
| ! [SY3977: $i] :
( ~ ( in @ SY3977 @ SV123 )
| ~ ( SV421 @ SV789 )
| ~ ( SV421 @ SY3977 )
| ( SV789 = SY3977 ) ) )
= $true )
| ( ( ex1 @ SV123
@ ^ [SY3363: $i] : ( SV421 @ SY3363 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2328,plain,
! [SV124: $i,SV422: $i] :
( ( ( in @ SV422 @ SV124 )
= $false )
| ( ( in @ SV124 @ SV422 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2034]) ).
thf(2329,plain,
! [SV423: $i,SV790: $i,SV125: $i] :
( ( ( ~ ( breln1 @ SV125 @ SV790 )
| ! [SY3978: $i] :
( ~ ( in @ SY3978 @ SV125 )
| ! [SY3979: $i] :
( ~ ( in @ SY3979 @ SV125 )
| ~ ( in @ ( kpair @ SY3978 @ SY3979 ) @ SV790 )
| ( in @ ( kpair @ SY3978 @ SY3979 ) @ ( binunion @ SV423 @ SV790 ) ) ) ) )
= $true )
| ( ( breln1 @ SV125 @ SV423 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2330,plain,
! [SV424: $o,SV126: $i,SV642: $i] :
( ( ( in @ SV642 @ SV126 )
= $false )
| ( ( ! [SY3773: $i] :
( ~ ( in @ SY3773 @ SV126 )
| ~ ~ SV424
| ( in @ SY3773
@ ( dsetconstr @ SV126
@ ^ [SY3774: $i] :
( ~ ( ~ SV424
| ( SY3774 != SV642 ) )
| ~ ( ~ ~ SV424
| ( SY3774 != SY3773 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2331,plain,
! [SV126: $i,SV643: $i] :
( ( ( in @ SV643 @ SV126 )
= $false )
| ( ( ! [SY3775: $i] :
( ~ ( in @ SY3775 @ SV126 )
| ~ ~ $true
| ( in @ SY3775
@ ( dsetconstr @ SV126
@ ^ [SY3776: $i] :
( ~ ( ~ $true
| ( SY3776 != SV643 ) )
| ~ ( ~ ~ $true
| ( SY3776 != SY3775 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2037]) ).
thf(2332,plain,
! [SV126: $i,SV644: $i] :
( ( ( in @ SV644 @ SV126 )
= $false )
| ( ( ! [SY3777: $i] :
( ~ ( in @ SY3777 @ SV126 )
| ~ ~ $false
| ( in @ SY3777
@ ( dsetconstr @ SV126
@ ^ [SY3778: $i] :
( ~ ( ~ $false
| ( SY3778 != SV644 ) )
| ~ ( ~ ~ $false
| ( SY3778 != SY3777 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2038]) ).
thf(2333,plain,
! [SV425: $i,SV127: $i,SV645: $i] :
( ( ( in @ SV645 @ ( setadjoin @ SV127 @ SV425 ) )
= $false )
| ( ( ( SV645 = SV127 )
| ( in @ SV645 @ SV425 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2039]) ).
thf(2334,plain,
! [SV426: $i,SV128: $i,SV646: $i] :
( ( ( in @ SV646 @ SV128 )
= $false )
| ( ( ~ ( in @ SV646 @ SV426 )
| ~ ( in @ SV646 @ ( symdiff @ SV128 @ SV426 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2040]) ).
thf(2335,plain,
! [SV129: $i,SV791: $i] :
( ( ( ~ ( in @ SV791 @ SV129 ) )
= $true )
| ( ( SV129 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2336,plain,
! [SV130: $i,SV427: $i] :
( ( ~ ( in @ SV427 @ ( powerset @ SV130 ) )
| ! [SY3374: $i] :
( ~ ( in @ SY3374 @ SV427 )
| ( in @ SY3374 @ SV130 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2042]) ).
thf(2337,plain,
! [SV130: $i,SV427: $i] :
( ( ~ ! [SY3375: $i] :
( ~ ( in @ SY3375 @ SV427 )
| ( in @ SY3375 @ SV130 ) )
| ( in @ SV427 @ ( powerset @ SV130 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2043]) ).
thf(2338,plain,
! [SV428: $i,SV792: $i,SV131: $i] :
( ( ( ~ ( breln1 @ SV131 @ SV792 )
| ! [SY3980: $i] :
( ~ ( in @ SY3980 @ SV131 )
| ! [SY3981: $i] :
( ~ ( in @ SY3981 @ SV131 )
| ! [SY3982: $i] :
( ~ ( in @ SY3982 @ SV131 )
| ~ ( in @ ( kpair @ SY3980 @ SY3982 ) @ SV428 )
| ~ ( in @ ( kpair @ SY3982 @ SY3981 ) @ SV792 )
| ( in @ ( kpair @ SY3980 @ SY3981 ) @ ( breln1compset @ SV131 @ SV428 @ SV792 ) ) ) ) ) )
= $true )
| ( ( breln1 @ SV131 @ SV428 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2339,plain,
! [SV429: $i,SV132: $i,SV793: $i] :
( ( ( ~ ( in @ SV793 @ ( powerset @ SV132 ) )
| ( in @ ( setminus @ SV132 @ ( binunion @ SV429 @ SV793 ) ) @ ( powerset @ ( setminus @ SV132 @ SV429 ) ) ) )
= $true )
| ( ( in @ SV429 @ ( powerset @ SV132 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2340,plain,
! [SV430: $i,SV133: $i,SV647: $i] :
( ( ( in @ ( setadjoin @ SV647 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV133 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV133 @ ( setadjoin @ SV430 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV133 = SV647 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2046]) ).
thf(2341,plain,
! [SV648: $i,SV431: $i,SV134: $i] :
( ( ( ( setadjoin @ SV134 @ ( setadjoin @ SV431 @ emptyset ) )
= ( setadjoin @ SV648 @ emptyset ) )
= $false )
| ( ( SV134 = SV431 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2342,plain,
! [SV432: $i,SV794: $i,SV135: $i] :
( ( ( ~ ( breln1 @ SV135 @ SV794 )
| ~ ! [SY3983: $i] :
( ~ ( in @ SY3983 @ SV135 )
| ! [SY3984: $i] :
( ~ ( in @ SY3984 @ SV135 )
| ~ ( in @ ( kpair @ SY3983 @ SY3984 ) @ SV432 )
| ( in @ ( kpair @ SY3983 @ SY3984 ) @ SV794 ) ) )
| ( subset @ SV432 @ SV794 ) )
= $true )
| ( ( breln1 @ SV135 @ SV432 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2343,plain,
! [SV136: $i] :
( ( ( ! [SY2669: $i] :
~ ~ ( ~ ( in @ SY2669 @ SV136 )
| ( ( binintersect @ SY2669 @ SV136 )
!= emptyset ) ) )
= $false )
| ( ( SV136 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2344,plain,
! [SV433: $i,SV137: $i,SV649: $i] :
( ( ( in @ SV649 @ ( cartprod @ SV137 @ SV433 ) )
= $false )
| ( ( ( kpair @ ( kfst @ SV649 ) @ ( ksnd @ SV649 ) )
= SV649 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2050]) ).
thf(2345,plain,
! [SV434: $i,SV138: $i,SV795: $i] :
( ( ( ! [SY3985: $i] :
( ( SV795 != SY3985 )
| ~ ( ~ ( ~ ( in @ SV795 @ SV138 )
| ( in @ SY3985 @ SV434 ) )
| ~ ( ~ ( in @ SY3985 @ SV434 )
| ( in @ SV795 @ SV138 ) ) ) ) )
= $true )
| ( ( SV138 = SV434 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2346,plain,
! [SV435: $i,SV139: $i,SV796: $i] :
( ( ( ~ ( in @ SV796 @ ( powerset @ SV139 ) )
| ! [SY3986: $i] :
( ~ ( in @ SY3986 @ ( powerset @ SV139 ) )
| ~ ( subset @ SV435 @ SY3986 )
| ( subset @ ( binintersect @ SV435 @ SV796 ) @ SY3986 ) ) )
= $true )
| ( ( in @ SV435 @ ( powerset @ SV139 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2347,plain,
! [SV650: $i,SV436: $i,SV140: $i] :
( ( ( breln @ SV140 @ SV436 @ SV650 )
= $false )
| ( ( ! [SY3779: $i] :
( ~ ( breln @ SV140 @ SV436 @ SY3779 )
| ~ ! [SY3780: $i] :
( ~ ( in @ SY3780 @ SV140 )
| ! [SY3781: $i] :
( ~ ( in @ SY3781 @ SV436 )
| ~ ( in @ ( kpair @ SY3780 @ SY3781 ) @ SV650 )
| ( in @ ( kpair @ SY3780 @ SY3781 ) @ SY3779 ) ) )
| ~ ! [SY3782: $i] :
( ~ ( in @ SY3782 @ SV140 )
| ! [SY3783: $i] :
( ~ ( in @ SY3783 @ SV436 )
| ~ ( in @ ( kpair @ SY3782 @ SY3783 ) @ SY3779 )
| ( in @ ( kpair @ SY3782 @ SY3783 ) @ SV650 ) ) )
| ( SV650 = SY3779 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2053]) ).
thf(2348,plain,
! [SV437: $i,SV141: $i,SV651: $i] :
( ( ( in @ SV651 @ SV141 )
= $false )
| ( ( ! [SY3784: $i] :
( ~ ( in @ SY3784 @ SV437 )
| ( in @ ( kpair @ SV651 @ SY3784 ) @ ( cartprod @ SV141 @ SV437 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2054]) ).
thf(2349,plain,
! [SV438: $i,SV142: $i,SV652: $i] :
( ( ( in @ SV652 @ SV142 )
= $false )
| ( ( ! [SY3785: $i] :
( ~ ( in @ SY3785 @ SV438 )
| ( in @ ( kpair @ SV652 @ SY3785 ) @ ( powerset @ ( powerset @ ( binunion @ SV142 @ SV438 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2055]) ).
thf(2350,plain,
! [SV439: $i,SV143: $i,SV653: $i] :
( ( ( in @ SV653 @ ( binintersect @ SV143 @ SV439 ) )
= $false )
| ( ( in @ SV653 @ SV439 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2351,plain,
! [SV440: $i,SV654: $i > $i,SV144: $i] :
( ( ( ! [SY3786: $i] :
( ~ ( in @ SY3786 @ SV144 )
| ( in @ ( SV654 @ SY3786 ) @ SV440 ) ) )
= $false )
| ( ( ! [SY3787: $i] :
( ~ ( in @ SY3787 @ ( funcSet @ SV440 @ SV144 ) )
| ~ ! [SY3788: $i] :
( ~ ( in @ SY3788 @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SY3787 @ ( SV654 @ SY3788 ) )
= SY3788 ) )
| ( surjective @ SV440 @ SV144 @ SY3787 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2057]) ).
thf(2352,plain,
! [SV441: $i,SV145: $i,SV797: $i] :
( ( ( ~ ( in @ SV797 @ SV145 )
| ~ ( in @ SV797 @ SV441 )
| ( in @ SV797 @ ( setminus @ SV145 @ ( setminus @ SV145 @ SV441 ) ) ) )
= $true )
| ( ( in @ SV441 @ ( powerset @ SV145 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2353,plain,
! [SV146: $i,SV442: $i > $o] :
( ( ( ~ ( in @ ( sK11_SY3407 @ SV442 @ SV146 ) @ SV146 )
| ! [SY3987: $i] :
( ~ ( in @ SY3987 @ SV146 )
| ~ ( SV442 @ ( sK11_SY3407 @ SV442 @ SV146 ) )
| ~ ( SV442 @ SY3987 )
| ( ( sK11_SY3407 @ SV442 @ SV146 )
= SY3987 ) ) )
= $false )
| ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) )
| ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2059]) ).
thf(2354,plain,
! [SV443: $i,SV147: $i,SV798: $i] :
( ( ( ~ ( in @ SV798 @ ( powerset @ SV147 ) )
| ! [SY3988: $i] :
( ~ ( in @ SY3988 @ SV147 )
| ~ ( in @ SY3988 @ ( setminus @ SV147 @ SV443 ) )
| ~ ( in @ SY3988 @ ( binintersect @ SV443 @ SV798 ) ) ) )
= $true )
| ( ( in @ SV443 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2355,plain,
! [SV444: $i,SV148: $i,SV799: $i] :
( ( ( ~ ( in @ SV799 @ ( powerset @ SV148 ) )
| ! [SY3989: $i] :
( ~ ( in @ SY3989 @ ( powerset @ SV148 ) )
| ! [SY3990: $i] :
( ~ ( in @ SY3990 @ SV148 )
| ~ ( in @ SY3990 @ ( binintersect @ SV444 @ SV799 ) )
| ( in @ SY3990 @ ( binunion @ SV444 @ SY3989 ) ) ) ) )
= $true )
| ( ( in @ SV444 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2356,plain,
! [SV445: $i > $o,SV149: $i] :
( ( ( ! [SY3417: $i] :
~ ~ ( ~ ( in @ SY3417 @ SV149 )
| ~ ( SV445 @ SY3417 ) ) )
= $false )
| ( ( ex1 @ SV149
@ ^ [SY3416: $i] : ( SV445 @ SY3416 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2062]) ).
thf(2357,plain,
! [SV446: $i,SV800: $i,SV150: $i] :
( ( ( ~ ( breln1 @ SV150 @ SV800 )
| ! [SY3991: $i] :
( ~ ( breln1 @ SV150 @ SY3991 )
| ( ( breln1compset @ SV150 @ ( binunion @ SV446 @ SV800 ) @ SY3991 )
= ( binunion @ ( breln1compset @ SV150 @ SV446 @ SY3991 ) @ ( breln1compset @ SV150 @ SV800 @ SY3991 ) ) ) ) )
= $true )
| ( ( breln1 @ SV150 @ SV446 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2358,plain,
! [SV655: $i > $i > $o,SV447: $i,SV151: $i,SV801: $i,SV748: $i] :
( ( ~ ( in @ ( kpair @ SV748 @ SV801 )
@ ( dpsetconstr @ SV151 @ SV447
@ ^ [SY3791: $i,SY3792: $i] : ( SV655 @ SY3791 @ SY3792 ) ) )
| ( SV655 @ SV748 @ SV801 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2359,plain,
! [SV152: $i > $o,SV448: $i > $o] :
( ( ( ! [SY3994: $i] :
( ( ( sK12_SY3425 @ SV448 @ SV152 )
!= SY3994 )
| ~ ( ~ ( ~ ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
| ( SV448 @ SY3994 ) )
| ~ ( ~ ( SV448 @ SY3994 )
| ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2065]) ).
thf(2360,plain,
! [SV153: $i,SV449: $i] :
( ( ( ~ ( subset @ SV449 @ SV153 ) )
= $true )
| ( ( SV153 = SV449 )
= $true )
| ( ( subset @ SV153 @ SV449 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2066]) ).
thf(2361,plain,
! [SV656: $i,SV450: $i,SV154: $i] :
( ( ( func @ SV154 @ SV450 @ SV656 )
= $false )
| ( ( in @ SV656 @ ( funcSet @ SV154 @ SV450 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2067]) ).
thf(2362,plain,
! [SV451: $o,SV155: $i,SV657: $i] :
( ( ( in @ SV657 @ SV155 )
= $false )
| ( ( ! [SY3793: $i] :
( ~ ( in @ SY3793 @ SV155 )
| ~ ~ SV451
| ( ( dsetconstr @ SV155
@ ^ [SY3794: $i] :
( ~ ( ~ SV451
| ( SY3794 != SV657 ) )
| ~ ( ~ ~ SV451
| ( SY3794 != SY3793 ) ) ) )
= ( setadjoin @ SY3793 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2363,plain,
! [SV155: $i,SV658: $i] :
( ( ( in @ SV658 @ SV155 )
= $false )
| ( ( ! [SY3795: $i] :
( ~ ( in @ SY3795 @ SV155 )
| ~ ~ $true
| ( ( dsetconstr @ SV155
@ ^ [SY3796: $i] :
( ~ ( ~ $true
| ( SY3796 != SV658 ) )
| ~ ( ~ ~ $true
| ( SY3796 != SY3795 ) ) ) )
= ( setadjoin @ SY3795 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2069]) ).
thf(2364,plain,
! [SV155: $i,SV659: $i] :
( ( ( in @ SV659 @ SV155 )
= $false )
| ( ( ! [SY3797: $i] :
( ~ ( in @ SY3797 @ SV155 )
| ~ ~ $false
| ( ( dsetconstr @ SV155
@ ^ [SY3798: $i] :
( ~ ( ~ $false
| ( SY3798 != SV659 ) )
| ~ ( ~ ~ $false
| ( SY3798 != SY3797 ) ) ) )
= ( setadjoin @ SY3797 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2365,plain,
! [SV660: $i,SV156: $i,SV452: $i] :
( ( ( in @ SV452 @ ( powerset @ SV156 ) )
= $false )
| ( ( ~ ( in @ SV660 @ SV452 )
| ( in @ SV660 @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2071]) ).
thf(2366,plain,
! [SV453: $i,SV157: $i,SV802: $i] :
( ( ( ~ ( in @ SV802 @ SV157 )
| ! [SY3995: $i] :
( ~ ( in @ SY3995 @ SV157 )
| ~ ( in @ ( kpair @ SV802 @ SY3995 ) @ SV453 )
| ( in @ ( kpair @ SY3995 @ SV802 ) @ ( breln1invset @ SV157 @ SV453 ) ) ) )
= $true )
| ( ( breln1 @ SV157 @ SV453 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2367,plain,
! [SV661: $i,SV454: $i,SV158: $i] :
( ( ( subset @ SV158 @ SV454 )
= $false )
| ( ( ~ ( subset @ SV454 @ SV661 )
| ( subset @ SV158 @ SV661 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2073]) ).
thf(2368,plain,
! [SV455: $i > $o,SV159: $i,SV662: $i] :
( ( ( in @ SV662 @ SV159 )
= $false )
| ( ( ~ ( SV455 @ SV662 )
| ( ( dsetconstr @ SV159
@ ^ [SY3442: $i] : ( SV455 @ SY3442 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2074]) ).
thf(2369,plain,
! [SV663: $i,SV456: $i,SV160: $i] :
( ( ( subset @ SV160 @ SV456 )
= $false )
| ( ( ~ ( in @ SV663 @ SV160 )
| ( in @ SV663 @ SV456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2075]) ).
thf(2370,plain,
! [SV458: $i,SV162: $i,SV803: $i] :
( ( ( ~ ( in @ SV803 @ ( powerset @ SV162 ) )
| ( in @ ( setminus @ SV162 @ ( binunion @ SV458 @ SV803 ) ) @ ( powerset @ ( setminus @ SV162 @ SV458 ) ) ) )
= $true )
| ( ( in @ SV458 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2371,plain,
! [SV459: $i,SV163: $i,SV804: $i] :
( ( ( ~ ( in @ SV804 @ ( powerset @ SV163 ) )
| ! [SY3996: $i] :
( ~ ( in @ SY3996 @ ( powerset @ SV163 ) )
| ~ ( subset @ SV804 @ SY3996 )
| ( subset @ ( binintersect @ SV459 @ SV804 ) @ SY3996 ) ) )
= $true )
| ( ( in @ SV459 @ ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2372,plain,
! [SV460: $i,SV164: $i,SV664: $i] :
( ( ( ~ ( in @ SV664 @ SV164 ) )
= $false )
| ( ( ~ ( in @ SV664 @ ( setminus @ SV164 @ SV460 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2079]) ).
thf(2373,plain,
! [SV166: $i,SV462: $i,SV665: $i] :
( ( ( in @ SV665 @ SV462 )
= $false )
| ( ( ~ ( in @ SV665 @ ( setminus @ SV166 @ SV462 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2081]) ).
thf(2374,plain,
! [SV463: $i,SV167: $i,SV805: $i] :
( ( ( ! [SY3997: $i] :
( ( SV805 != SY3997 )
| ~ ( in @ SV805 @ SV167 )
| ( in @ SY3997 @ SV463 ) ) )
= $true )
| ( ( SV167 = SV463 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2375,plain,
! [SV666: $i,SV464: $i,SV168: $i] :
( ( ( breln @ SV168 @ SV464 @ SV666 )
= $false )
| ( ( ! [SY3800: $i] :
( ~ ( breln @ SV168 @ SV464 @ SY3800 )
| ~ ! [SY3801: $i] :
( ~ ( in @ SY3801 @ SV168 )
| ! [SY3802: $i] :
( ~ ( in @ SY3802 @ SV464 )
| ~ ( in @ ( kpair @ SY3801 @ SY3802 ) @ SV666 )
| ( in @ ( kpair @ SY3801 @ SY3802 ) @ SY3800 ) ) )
| ( subset @ SV666 @ SY3800 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2083]) ).
thf(2376,plain,
! [SV465: $i,SV806: $i,SV169: $i] :
( ( ( ~ ( breln1 @ SV169 @ SV806 )
| ! [SY3998: $i] :
( ~ ( breln1 @ SV169 @ SY3998 )
| ( ( breln1compset @ SV169 @ ( binunion @ SV465 @ SV806 ) @ SY3998 )
= ( binunion @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SY3998 ) @ ( breln1invset @ SV169 @ SV806 ) ) ) @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SY3998 ) @ ( breln1invset @ SV169 @ SV465 ) ) ) ) ) ) )
= $true )
| ( ( breln1 @ SV169 @ SV465 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2377,plain,
! [SV466: $i,SV171: $i,SV807: $i] :
( ( ( ~ ( in @ SV807 @ ( powerset @ SV171 ) )
| ! [SY3999: $i] :
( ~ ( in @ SY3999 @ ( binintersect @ SV466 @ SV807 ) )
| ( in @ SY3999 @ SV171 ) ) )
= $true )
| ( ( in @ SV466 @ ( powerset @ SV171 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2378,plain,
! [SV468: $i,SV173: $i,SV808: $i] :
( ( ( ~ ( in @ SV808 @ ( powerset @ SV173 ) )
| ~ ( subset @ SV468 @ ( setminus @ SV173 @ SV808 ) )
| ( subset @ SV808 @ ( setminus @ SV173 @ SV468 ) ) )
= $true )
| ( ( in @ SV468 @ ( powerset @ SV173 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2379,plain,
! [SV749: $i,SV667: $i,SV469: $i,SV174: $i] :
( ( ( ( kpair @ SV174 @ SV469 )
!= ( kpair @ SV667 @ SV749 ) )
= $true )
| ( ( SV174 = SV667 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2088]) ).
thf(2380,plain,
! [SV175: $i,SV470: $i > $i] :
( ( ~ ( ~ ! [SY3923: $i] :
~ ( ~ ( ~ ( in @ SY3923 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
| ~ ! [SY3464: $i] :
~ ~ ( ~ ( in @ SY3464 @ SV175 )
| ( SY3923
!= ( SV470 @ SY3464 ) ) ) )
| ~ ( ~ ~ ! [SY3465: $i] :
~ ~ ( ~ ( in @ SY3465 @ SV175 )
| ( SY3923
!= ( SV470 @ SY3465 ) ) )
| ( in @ SY3923 @ ( sK3_SY3462 @ SV470 @ SV175 ) ) ) )
| ~ ! [SY3926: $i] :
( ~ ! [SY3467: $i] :
~ ( ~ ( ~ ( in @ SY3467 @ SY3926 )
| ~ ! [SY3468: $i] :
~ ~ ( ~ ( in @ SY3468 @ SV175 )
| ( SY3467
!= ( SV470 @ SY3468 ) ) ) )
| ~ ( ~ ~ ! [SY3469: $i] :
~ ~ ( ~ ( in @ SY3469 @ SV175 )
| ( SY3467
!= ( SV470 @ SY3469 ) ) )
| ( in @ SY3467 @ SY3926 ) ) )
| ( ( sK3_SY3462 @ SV470 @ SV175 )
= SY3926 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2089]) ).
thf(2381,plain,
! [SV471: $i,SV176: $i,SV809: $i] :
( ( ( ~ ( in @ SV809 @ ( powerset @ SV176 ) )
| ( in @ ( setminus @ SV471 @ SV809 ) @ ( powerset @ SV176 ) ) )
= $true )
| ( ( in @ SV471 @ ( powerset @ SV176 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2382,plain,
! [SV472: $i,SV177: $i,SV668: $i] :
( ( ( in @ SV668 @ ( funcSet @ SV177 @ SV472 ) )
= $false )
| ( ( ~ ( injective @ SV177 @ SV472 @ SV668 )
| ( in @ SV668 @ ( injFuncSet @ SV177 @ SV472 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2091]) ).
thf(2383,plain,
! [SV473: $i,SV810: $i,SV178: $i] :
( ( ( ~ ( breln1 @ SV178 @ SV810 )
| ( ( breln1invset @ SV178 @ ( breln1compset @ SV178 @ SV473 @ SV810 ) )
= ( breln1compset @ SV178 @ ( breln1invset @ SV178 @ SV810 ) @ ( breln1invset @ SV178 @ SV473 ) ) ) )
= $true )
| ( ( breln1 @ SV178 @ SV473 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2384,plain,
! [SV474: $i > $o,SV179: $i,SV669: $i] :
( ( ( in @ SV669
@ ( dsetconstr @ SV179
@ ^ [SY3474: $i] : ( SV474 @ SY3474 ) ) )
= $false )
| ( ( in @ SV669 @ SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2093]) ).
thf(2385,plain,
! [SV670: $i > $i > $o,SV475: $i,SV180: $i] :
( ( ( ! [SY3805: $i] :
( ~ ( in @ SY3805 @ SV180 )
| ~ ! [SY3806: $i] :
~ ~ ( ~ ( in @ SY3806 @ SV475 )
| ~ ( SV670 @ SY3805 @ SY3806 ) ) ) )
= $false )
| ( ( ! [SY3807: $i] :
( ~ ( in @ SY3807 @ ( breln1Set @ SV475 ) )
| ~ ( reflwellordering @ SV475 @ SY3807 )
| ! [SY3808: $i] :
( ~ ( in @ SY3808 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY3809: $i] :
~ ( ~ ( SV670 @ SY3808 @ SY3809 )
| ~ ! [SY3810: $i] :
( ~ ( in @ SY3810 @ SV475 )
| ~ ( SV670 @ SY3808 @ SY3810 )
| ( in @ ( kpair @ SY3809 @ SY3810 ) @ SY3807 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2094]) ).
thf(2386,plain,
! [SV476: $i,SV181: $i,SV671: $i] :
( ( ( in @ SV671 @ SV181 )
= $false )
| ( ( ! [SY3811: $i] :
( ~ ( in @ SY3811 @ SV476 )
| ( in @ ( setadjoin @ ( setadjoin @ SV671 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV671 @ ( setadjoin @ SY3811 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV181 @ SV476 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2095]) ).
thf(2387,plain,
! [SV477: $i,SV672: $i > $i,SV182: $i] :
( ( ( ! [SY3812: $i] :
( ~ ( in @ SY3812 @ SV182 )
| ( in @ ( SV672 @ SY3812 ) @ SV477 ) ) )
= $false )
| ( ( ! [SY3813: $i] :
( ~ ( in @ SY3813 @ SV182 )
| ( ( ap @ SV182 @ SV477
@ ( lam @ SV182 @ SV477
@ ^ [SY3814: $i] : ( SV672 @ SY3814 ) )
@ SY3813 )
= ( SV672 @ SY3813 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2096]) ).
thf(2388,plain,
! [SV478: $i,SV183: $i,SV673: $i] :
( ( ( in @ SV673 @ SV183 )
= $false )
| ( ( ~ ~ ( in @ SV673 @ SV478 )
| ~ ( subset @ SV183 @ SV478 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2389,plain,
! [SV479: $i,SV184: $i,SV674: $i] :
( ( ( in @ SV674 @ SV184 )
= $false )
| ( ( ~ ~ ( in @ SV674 @ SV479 )
| ( SV184 != SV479 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2098]) ).
thf(2390,plain,
! [SV480: $i,SV185: $i,SV811: $i] :
( ( ( ~ ( in @ SV811 @ ( powerset @ SV185 ) )
| ( in @ ( binintersect @ SV480 @ SV811 ) @ ( powerset @ SV185 ) ) )
= $true )
| ( ( in @ SV480 @ ( powerset @ SV185 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2391,plain,
! [SV481: $i,SV186: $i,SV812: $i] :
( ( ( ~ ( in @ SV812 @ ( powerset @ SV186 ) )
| ! [SY4000: $i] :
( ~ ( in @ SY4000 @ SV186 )
| ~ ( in @ SV481 @ ( powerset @ SV812 ) )
| ~ ( in @ SY4000 @ SV481 )
| ( in @ SY4000 @ SV812 ) ) )
= $true )
| ( ( in @ SV481 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2392,plain,
! [SV483: $i > $o,SV188: $i,SV675: $i] :
( ( ( in @ SV675 @ SV188 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV675
@ ( dsetconstr @ SV188
@ ^ [SY3494: $i] : ( SV483 @ SY3494 ) ) )
| ( SV483 @ SV675 ) )
| ~ ( ~ ( SV483 @ SV675 )
| ( in @ SV675
@ ( dsetconstr @ SV188
@ ^ [SY3495: $i] : ( SV483 @ SY3495 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2393,plain,
! [SV484: $i > $o,SV189: $i] :
( ( ( ! [SY3496: $i] :
( ~ ( in @ SY3496 @ SV189 )
| ( SV484 @ SY3496 ) ) )
= $true )
| ( ( ~ ! [SY3497: $i] :
~ ~ ( ~ ( in @ SY3497 @ SV189 )
| ~ ~ ( SV484 @ SY3497 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2103]) ).
thf(2394,plain,
! [SV813: $o,SV190: $i,SV485: $i] :
( ( ( ~ ! [SY4001: $i] :
( ~ ( in @ SV485 @ SY4001 )
| ~ ( in @ SY4001 @ SV190 )
| SV813 )
| SV813 )
= $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2104]) ).
thf(2395,plain,
! [SV190: $i,SV485: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV485 @ SX0 )
| ~ ( in @ SX0 @ SV190 )
| $true )
| $true )
= $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2104]) ).
thf(2396,plain,
! [SV190: $i,SV485: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV485 @ SX0 )
| ~ ( in @ SX0 @ SV190 )
| $false )
| $false )
= $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2104]) ).
thf(2397,plain,
! [SV486: $i,SV191: $i,SV676: $i] :
( ( ( in @ SV676 @ ( funcSet @ SV191 @ SV486 ) )
= $false )
| ( ( ! [SY3817: $i] :
( ~ ( in @ SY3817 @ SV191 )
| ! [SY3818: $i] :
( ~ ( in @ SY3818 @ SV486 )
| ~ ( in @ ( kpair @ SY3817 @ SY3818 ) @ SV676 )
| ( ( ap @ SV191 @ SV486 @ SV676 @ SY3817 )
= SY3818 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2105]) ).
thf(2398,plain,
! [SV487: $i,SV192: $i,SV677: $i] :
( ( ( subset @ SV677 @ SV192 )
= $false )
| ( ( ~ ( subset @ SV677 @ SV487 )
| ( subset @ SV677 @ ( binintersect @ SV192 @ SV487 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2106]) ).
thf(2399,plain,
! [SV193: $i,SV488: $i > $i] :
( ( ! [SY3930: $i] :
~ ( ~ ( ~ ( in @ SY3930 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
| ~ ! [SY3506: $i] :
~ ~ ( ~ ( in @ SY3506 @ SV193 )
| ( SY3930
!= ( SV488 @ SY3506 ) ) ) )
| ~ ( ~ ~ ! [SY3507: $i] :
~ ~ ( ~ ( in @ SY3507 @ SV193 )
| ( SY3930
!= ( SV488 @ SY3507 ) ) )
| ( in @ SY3930 @ ( sK4_SY3504 @ SV488 @ SV193 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2107]) ).
thf(2400,plain,
! [SV489: $i,SV194: $i,SV814: $i] :
( ( ( ~ ( in @ SV814 @ SV194 )
| ~ ~ ( in @ SV814 @ ( setminus @ SV194 @ SV489 ) )
| ( in @ SV814 @ SV489 ) )
= $true )
| ( ( in @ SV489 @ ( powerset @ SV194 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2108]) ).
thf(2401,plain,
! [SV678: $i,SV490: $i,SV195: $i] :
( ( ( func @ SV195 @ SV490 @ SV678 )
= $false )
| ( ( ( lam @ SV195 @ SV490
@ ^ [SY3819: $i] : ( ap @ SV195 @ SV490 @ SV678 @ SY3819 ) )
= SV678 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2109]) ).
thf(2402,plain,
! [SV815: $i] :
( ( ~ ( in @ SV815 @ sK1_SX0 )
| ( subset @ SV815 @ sK1_SX0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2403,plain,
( ( ~ ! [SY3933: $i] :
( ~ ( in @ SY3933 @ sK5_SY3512 )
| ( subset @ SY3933 @ sK5_SY3512 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2111]) ).
thf(2404,plain,
( ( ! [SY3934: $i] :
( ~ ( in @ SY3934 @ ( binintersect @ sK1_SX0 @ sK5_SY3512 ) )
| ( subset @ SY3934 @ ( binintersect @ sK1_SX0 @ sK5_SY3512 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2111]) ).
thf(2405,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ~ ~ ( ~ ( SV196 @ SV816 )
| ~ ! [SY4002: $i] :
( ~ ( SV196 @ SY4002 )
| ( SV816 = SY4002 ) ) ) )
= $true )
| ( ( ~ ! [SY2855: $i] :
~ ~ ( ~ ( SV196 @ SY2855 )
| ~ ! [SY2856: $i] :
( ~ ( SV196 @ SY2856 )
| ( SY2855 = SY2856 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2406,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ! [SY4003: $i] :
( ( ( sK13_SY3515 @ SV491 @ SV197 )
!= SY4003 )
| ~ ( ~ ( ~ ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
| ( SV491 @ SY4003 ) )
| ~ ( ~ ( SV491 @ SY4003 )
| ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2113]) ).
thf(2407,plain,
! [SV198: $i] :
( ( ( in @ ( sK6_SY2868 @ SV198 ) @ SV198 )
= $true )
| ( ( SV198 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2114]) ).
thf(2408,plain,
! [SV492: $i,SV199: $i,SV679: $i] :
( ( ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) )
= $false )
| ( ( ~ ! [SY3820: $i] :
~ ~ ( ~ ( in @ SY3820 @ SV199 )
| ~ ~ ! [SY3821: $i] :
~ ~ ( ~ ( in @ SY3821 @ SV492 )
| ( SV679
!= ( kpair @ SY3820 @ SY3821 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2409,plain,
! [SV493: $i,SV200: $i,SV817: $i] :
( ( ( ~ ( in @ SV817 @ ( powerset @ SV200 ) )
| ! [SY4004: $i] :
( ~ ( in @ SY4004 @ SV200 )
| ~ ~ ( in @ SY4004 @ ( binunion @ SV493 @ SV817 ) )
| ~ ( in @ SY4004 @ SV817 ) ) )
= $true )
| ( ( in @ SV493 @ ( powerset @ SV200 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2410,plain,
! [SV495: $o,SV202: $i,SV680: $i] :
( ( ( in @ SV680 @ SV202 )
= $false )
| ( ( ! [SY3822: $i] :
( ~ ( in @ SY3822 @ SV202 )
| ( in @ ( if @ SV202 @ SV495 @ SV680 @ SY3822 ) @ SV202 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2411,plain,
! [SV202: $i,SV681: $i] :
( ( ( in @ SV681 @ SV202 )
= $false )
| ( ( ! [SY3823: $i] :
( ~ ( in @ SY3823 @ SV202 )
| ( in @ ( if @ SV202 @ $true @ SV681 @ SY3823 ) @ SV202 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2412,plain,
! [SV202: $i,SV682: $i] :
( ( ( in @ SV682 @ SV202 )
= $false )
| ( ( ! [SY3824: $i] :
( ~ ( in @ SY3824 @ SV202 )
| ( in @ ( if @ SV202 @ $false @ SV682 @ SY3824 ) @ SV202 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2413,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false )
| ( ( ! [SY3825: $o] :
( ~ ( ~ ( in @ SV683 @ SV203 )
| ~ ~ ( in @ SV683 @ SV496 )
| SY3825 )
| ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SY3825 )
| SY3825 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2414,plain,
! [SV497: $i,SV684: $i > $i,SV204: $i] :
( ( ( ! [SY3826: $i] :
( ~ ( in @ SY3826 @ SV204 )
| ( in @ ( SV684 @ SY3826 ) @ SV497 ) ) )
= $false )
| ( ( func @ SV204 @ SV497
@ ( lam @ SV204 @ SV497
@ ^ [SY3827: $i] : ( SV684 @ SY3827 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2415,plain,
! [SV498: $i,SV685: $i,SV205: $i] :
( ( ( subset @ SV205 @ SV685 )
= $false )
| ( ( subset @ SV205 @ ( setadjoin @ SV498 @ SV685 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2416,plain,
! [SV499: $o,SV206: $i,SV686: $i] :
( ( ( in @ SV686 @ SV206 )
= $false )
| ( ( ! [SY3828: $i] :
( ~ ( in @ SY3828 @ SV206 )
| ( in @ ( if @ SV206 @ SV499 @ SV686 @ SY3828 ) @ ( setadjoin @ SV686 @ ( setadjoin @ SY3828 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2124]) ).
thf(2417,plain,
! [SV206: $i,SV687: $i] :
( ( ( in @ SV687 @ SV206 )
= $false )
| ( ( ! [SY3829: $i] :
( ~ ( in @ SY3829 @ SV206 )
| ( in @ ( if @ SV206 @ $true @ SV687 @ SY3829 ) @ ( setadjoin @ SV687 @ ( setadjoin @ SY3829 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2418,plain,
! [SV206: $i,SV688: $i] :
( ( ( in @ SV688 @ SV206 )
= $false )
| ( ( ! [SY3830: $i] :
( ~ ( in @ SY3830 @ SV206 )
| ( in @ ( if @ SV206 @ $false @ SV688 @ SY3830 ) @ ( setadjoin @ SV688 @ ( setadjoin @ SY3830 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2419,plain,
! [SV500: $i > $o,SV207: $i] :
( ( ( ~ ! [SY3540: $i] :
~ ~ ( ~ ( in @ SY3540 @ SV207 )
| ~ ( SV500 @ SY3540 ) ) )
= $true )
| ( ( ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SV207 )
| ~ ( SV500 @ SY3541 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2127]) ).
thf(2420,plain,
! [SV501: $i,SV208: $i,SV818: $i] :
( ( ( ~ ( in @ SV818 @ ( powerset @ SV208 ) )
| ! [SY4005: $o,SY4006: $i] :
( ~ ( in @ SY4006 @ SV208 )
| ~ ( in @ SY4006 @ ( binunion @ SV501 @ SV818 ) )
| ~ ( ~ ( in @ SY4006 @ SV501 )
| SY4005 )
| ~ ( ~ ( in @ SY4006 @ SV818 )
| SY4005 )
| SY4005 ) )
= $true )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2421,plain,
! [SV689: $i,SV502: $i,SV209: $i] :
( ( ( breln @ SV209 @ SV502 @ SV689 )
= $false )
| ( ( ! [SY3831: $i > $o] :
( ~ ! [SY3832: $i] :
( ~ ( in @ SY3832 @ SV209 )
| ! [SY3833: $i] :
( ~ ( in @ SY3833 @ SV502 )
| ~ ( in @ ( kpair @ SY3832 @ SY3833 ) @ SV689 )
| ( SY3831 @ ( kpair @ SY3832 @ SY3833 ) ) ) )
| ! [SY3834: $i] :
( ~ ( in @ SY3834 @ SV689 )
| ( SY3831 @ SY3834 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2422,plain,
! [SV503: $o,SV210: $i,SV690: $i] :
( ( ( in @ SV690 @ SV210 )
= $false )
| ( ( ! [SY3835: $i] :
( ~ ( in @ SY3835 @ SV210 )
| ~ SV503
| ( in @ SV690
@ ( dsetconstr @ SV210
@ ^ [SY3836: $i] :
( ~ ( ~ SV503
| ( SY3836 != SV690 ) )
| ~ ( ~ ~ SV503
| ( SY3836 != SY3835 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2423,plain,
! [SV210: $i,SV691: $i] :
( ( ( in @ SV691 @ SV210 )
= $false )
| ( ( ! [SY3837: $i] :
( ~ ( in @ SY3837 @ SV210 )
| ~ $true
| ( in @ SV691
@ ( dsetconstr @ SV210
@ ^ [SY3838: $i] :
( ~ ( ~ $true
| ( SY3838 != SV691 ) )
| ~ ( ~ ~ $true
| ( SY3838 != SY3837 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2131]) ).
thf(2424,plain,
! [SV210: $i,SV692: $i] :
( ( ( in @ SV692 @ SV210 )
= $false )
| ( ( ! [SY3839: $i] :
( ~ ( in @ SY3839 @ SV210 )
| ~ $false
| ( in @ SV692
@ ( dsetconstr @ SV210
@ ^ [SY3840: $i] :
( ~ ( ~ $false
| ( SY3840 != SV692 ) )
| ~ ( ~ ~ $false
| ( SY3840 != SY3839 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2425,plain,
! [SV693: $i,SV504: $i,SV212: $i] :
( ( ( subset @ SV212 @ SV504 )
= $false )
| ( ( ~ ~ ( in @ SV693 @ SV504 )
| ~ ( in @ SV693 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2426,plain,
! [SV750: $i,SV694: $i,SV505: $i,SV213: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV213 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV213 @ ( setadjoin @ SV505 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV694 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV694 @ ( setadjoin @ SV750 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV213 = SV694 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2134]) ).
thf(2427,plain,
! [SV506: $i,SV214: $i,SV695: $i] :
( ( ( in @ SV695 @ ( injFuncSet @ SV214 @ SV506 ) )
= $false )
| ( ( injective @ SV214 @ SV506 @ SV695 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2428,plain,
! [SV508: $i,SV819: $i,SV216: $i] :
( ( ( ~ ( breln1 @ SV216 @ SV819 )
| ! [SY4007: $i] :
( ~ ( in @ SY4007 @ SV216 )
| ! [SY4008: $i] :
( ~ ( in @ SY4008 @ SV216 )
| ~ ( in @ ( kpair @ SY4007 @ SY4008 ) @ ( binunion @ SV508 @ SV819 ) )
| ! [SY4009: $o] :
( ~ ( ~ ( in @ ( kpair @ SY4007 @ SY4008 ) @ SV508 )
| SY4009 )
| ~ ( ~ ( in @ ( kpair @ SY4007 @ SY4008 ) @ SV819 )
| SY4009 )
| SY4009 ) ) ) )
= $true )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2429,plain,
! [SV509: $i,SV217: $i,SV820: $i] :
( ( ( ~ ( in @ SV820 @ ( powerset @ SV217 ) )
| ! [SY4010: $i] :
( ~ ( in @ SY4010 @ SV217 )
| ~ ( in @ SY4010 @ ( setminus @ SV217 @ ( binunion @ SV509 @ SV820 ) ) )
| ( in @ SY4010 @ ( binintersect @ ( setminus @ SV217 @ SV509 ) @ ( setminus @ SV217 @ SV820 ) ) ) ) )
= $true )
| ( ( in @ SV509 @ ( powerset @ SV217 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2138]) ).
thf(2430,plain,
! [SV510: $i > $i,SV218: $i,SV696: $i] :
( ( ( in @ SV696
@ ( image1 @ SV218
@ ^ [SY3564: $i] : ( SV510 @ SY3564 ) ) )
= $false )
| ( ( ~ ! [SY3843: $i] :
~ ~ ( ~ ( in @ SY3843 @ SV218 )
| ( SV696
!= ( SV510 @ SY3843 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2431,plain,
! [SV511: $i,SV220: $i,SV697: $i] :
( ( ( in @ SV697 @ ( setadjoin @ SV220 @ ( setadjoin @ SV511 @ emptyset ) ) )
= $false )
| ( ( ( SV697 = SV220 )
| ( SV697 = SV511 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2432,plain,
! [SV512: $i,SV221: $i,SV698: $i] :
( ( ( in @ SV698 @ ( surjFuncSet @ SV221 @ SV512 ) )
= $false )
| ( ( in @ SV698 @ ( funcSet @ SV221 @ SV512 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2433,plain,
! [SV514: $o,SV223: $i,SV699: $i] :
( ( ( in @ SV699 @ SV223 )
= $false )
| ( ( ! [SY3844: $i] :
( ~ ( in @ SY3844 @ SV223 )
| ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY3845: $i] :
( ~ ( ~ SV514
| ( SY3845 != SV699 ) )
| ~ ( ~ ~ SV514
| ( SY3845 != SY3844 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2144]) ).
thf(2434,plain,
! [SV223: $i,SV700: $i] :
( ( ( in @ SV700 @ SV223 )
= $false )
| ( ( ! [SY3846: $i] :
( ~ ( in @ SY3846 @ SV223 )
| ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY3847: $i] :
( ~ ( ~ $true
| ( SY3847 != SV700 ) )
| ~ ( ~ ~ $true
| ( SY3847 != SY3846 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2435,plain,
! [SV223: $i,SV701: $i] :
( ( ( in @ SV701 @ SV223 )
= $false )
| ( ( ! [SY3848: $i] :
( ~ ( in @ SY3848 @ SV223 )
| ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY3849: $i] :
( ~ ( ~ $false
| ( SY3849 != SV701 ) )
| ~ ( ~ ~ $false
| ( SY3849 != SY3848 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2146]) ).
thf(2436,plain,
! [SV515: $i,SV224: $i,SV821: $i] :
( ( ( ~ ( in @ SV821 @ ( powerset @ SV224 ) )
| ~ ( subset @ SV515 @ SV821 )
| ( subset @ ( setminus @ SV224 @ SV821 ) @ ( setminus @ SV224 @ SV515 ) ) )
= $true )
| ( ( in @ SV515 @ ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2437,plain,
! [SV751: $i,SV702: $i,SV516: $i,SV225: $i] :
( ( ( ( kpair @ SV225 @ SV516 )
!= ( kpair @ SV702 @ SV751 ) )
= $true )
| ( ( SV516 = SV751 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2148]) ).
thf(2438,plain,
! [SV226: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY3851: $i] :
( ~ ( in @ SY3851 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY2945: $i] :
( ~ ( in @ SY2945 @ SY3851 )
| ( in @ SY2945 @ SV226 ) ) )
| ~ ! [SY3853: $i,SY3854: $i] :
( ~ ~ ( ~ ( in @ SY3853 @ SV226 )
| ~ ( in @ SY3854 @ SV226 ) )
| ~ ! [SY3855: $i] :
( ~ ( in @ SY3855 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SY3853 @ SY3855 )
| ( in @ SY3854 @ SY3855 ) )
| ~ ( ~ ( in @ SY3854 @ SY3855 )
| ( in @ SY3853 @ SY3855 ) ) ) )
| ( SY3853 = SY3854 ) ) )
| ~ ! [SY3856: $i,SY3857: $i] :
( ~ ~ ( ~ ( in @ SY3856 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY3857 @ ( sK2_SY2943 @ SV226 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3856 )
| ( in @ SX4 @ SY3857 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3857 )
| ( in @ SX4 @ SY3856 ) ) ) )
| ~ ! [SY3860: $i] :
( ~ ~ ( ~ ! [SY2954: $i] :
( ~ ( in @ SY2954 @ SY3860 )
| ( in @ SY2954 @ SV226 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY3860 ) )
| ~ ! [SY3863: $i] :
~ ~ ! [SY3864: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3863 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY3864 @ SY3860 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY3863 )
| ~ ( in @ SX5 @ SY3860 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY3863 ) )
| ( in @ SY3864 @ SY3866 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2149]) ).
thf(2439,plain,
! [SV703: $i > $i > $o,SV517: $i,SV227: $i,SV752: $i] :
( ( ( ~ ( in @ SV752 @ SV227 ) )
= $true )
| ( ( ! [SY3935: $i] :
( ~ ( in @ SY3935 @ SV517 )
| ~ ( in @ ( kpair @ SV752 @ SY3935 )
@ ( dpsetconstr @ SV227 @ SV517
@ ^ [SY3870: $i,SY3871: $i] : ( SV703 @ SY3870 @ SY3871 ) ) )
| ( SV703 @ SV752 @ SY3935 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2150]) ).
thf(2440,plain,
! [SV228: $i,SV704: $i,SV518: $i] :
( ( ( in @ SV518 @ SV704 )
= $false )
| ( ( ~ ( in @ SV704 @ SV228 )
| ( in @ SV518 @ ( setunion @ SV228 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2151]) ).
thf(2441,plain,
! [SV519: $i,SV229: $i,SV822: $i] :
( ( ( ~ ( in @ SV822 @ ( powerset @ SV229 ) )
| ! [SY4011: $i] :
( ~ ( in @ SY4011 @ SV229 )
| ~ ~ ( in @ SY4011 @ ( binunion @ SV519 @ SV822 ) )
| ~ ( in @ SY4011 @ SV519 ) ) )
= $true )
| ( ( in @ SV519 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2442,plain,
! [SV520: $i,SV230: $i > $i > $o] :
( ( ( ~ ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
| ~ ! [SY4012: $i] :
~ ~ ( ~ ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SY4012 )
| ~ ! [SY4013: $i] :
( ~ ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SY4013 )
| ( SY4012 = SY4013 ) ) ) )
= $false )
| ( ( ~ ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2153]) ).
thf(2443,plain,
! [SV705: $i,SV521: $i,SV231: $i] :
( ( ( func @ SV231 @ SV521 @ SV705 )
= $false )
| ( ( ! [SY3872: $i] :
( ~ ( func @ SV231 @ SV521 @ SY3872 )
| ~ ! [SY3873: $i] :
( ~ ( in @ SY3873 @ SV231 )
| ( ( ap @ SV231 @ SV521 @ SV705 @ SY3873 )
= ( ap @ SV231 @ SV521 @ SY3872 @ SY3873 ) ) )
| ( SV705 = SY3872 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2154]) ).
thf(2444,plain,
! [SV522: $o,SV232: $i,SV706: $i] :
( ( ( in @ SV706 @ SV232 )
= $false )
| ( ( ! [SY3874: $i] :
( ~ ( in @ SY3874 @ SV232 )
| ~ SV522
| ( ( if @ SV232 @ SV522 @ SV706 @ SY3874 )
= SV706 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2155]) ).
thf(2445,plain,
! [SV232: $i,SV707: $i] :
( ( ( in @ SV707 @ SV232 )
= $false )
| ( ( ! [SY3875: $i] :
( ~ ( in @ SY3875 @ SV232 )
| ~ $true
| ( ( if @ SV232 @ $true @ SV707 @ SY3875 )
= SV707 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2446,plain,
! [SV232: $i,SV708: $i] :
( ( ( in @ SV708 @ SV232 )
= $false )
| ( ( ! [SY3876: $i] :
( ~ ( in @ SY3876 @ SV232 )
| ~ $false
| ( ( if @ SV232 @ $false @ SV708 @ SY3876 )
= SV708 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2447,plain,
! [SV823: $i > $o,SV523: $i,SV233: $i] :
( ( ( ~ ! [SY4014: $i] :
( ~ ( in @ SY4014 @ SV233 )
| ! [SY4015: $i] :
( ~ ( in @ SY4015 @ SV233 )
| ~ ( in @ ( kpair @ SY4014 @ SY4015 ) @ SV523 )
| ( SV823 @ ( kpair @ SY4014 @ SY4015 ) ) ) )
| ! [SY4016: $i] :
( ~ ( in @ SY4016 @ SV523 )
| ( SV823 @ SY4016 ) ) )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2448,plain,
! [SV524: $i,SV234: $i] :
( ( ( ~ ( in @ ( sK15_SY3598 @ SV234 @ SV524 ) @ SV524 )
| ( in @ ( sK15_SY3598 @ SV234 @ SV524 ) @ SV234 ) )
= $false )
| ( ( in @ SV524 @ ( powerset @ SV234 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2159]) ).
thf(2449,plain,
! [SV525: $i,SV235: $i] :
( ( ( ! [SY3599: $i] :
~ ~ ( ~ ( in @ SY3599 @ SV235 )
| ~ ( in @ SV525 @ SY3599 ) ) )
= $false )
| ( ( in @ SV525 @ ( setunion @ SV235 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2160]) ).
thf(2450,plain,
! [SV526: $i,SV237: $i,SV709: $i] :
( ( ( in @ SV709 @ ( setminus @ SV237 @ SV526 ) )
= $false )
| ( ( in @ SV709 @ SV237 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2451,plain,
! [SV528: $i,SV239: $i,SV710: $i] :
( ( ( in @ SV710 @ ( binunion @ SV239 @ SV528 ) )
= $false )
| ( ( ( in @ SV710 @ SV239 )
| ( in @ SV710 @ SV528 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2452,plain,
! [SV711: $i,SV529: $i,SV240: $i] :
( ( ( func @ SV240 @ SV529 @ SV711 )
= $false )
| ( ( ! [SY3877: $i] :
( ~ ( in @ SY3877 @ SV240 )
| ( in @ ( kpair @ SY3877 @ ( ap @ SV240 @ SV529 @ SV711 @ SY3877 ) ) @ SV711 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2164]) ).
thf(2453,plain,
! [SV530: $i,SV241: $i,SV824: $i] :
( ( ( ~ ( in @ SV824 @ ( powerset @ SV241 ) )
| ( in @ ( setminus @ SV241 @ SV530 ) @ ( powerset @ ( setminus @ SV241 @ ( binintersect @ SV530 @ SV824 ) ) ) ) )
= $true )
| ( ( in @ SV530 @ ( powerset @ SV241 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(2454,plain,
! [SV242: $i] :
( ( ( ! [SY3006: $i] :
~ ( in @ SY3006 @ SV242 ) )
= $false )
| ( ( SV242 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2166]) ).
thf(2455,plain,
! [SV531: $i,SV243: $i,SV825: $i] :
( ( ( ~ ( in @ SV825 @ ( powerset @ SV243 ) )
| ! [SY4017: $i] :
( ~ ( in @ SY4017 @ ( powerset @ SV243 ) )
| ( in @ ( binintersect @ SV531 @ SV825 ) @ ( powerset @ ( binintersect @ ( binunion @ SV531 @ SY4017 ) @ ( binunion @ SV825 @ SY4017 ) ) ) ) ) )
= $true )
| ( ( in @ SV531 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2456,plain,
! [SV532: $i,SV244: $i,SV826: $i] :
( ( ( ~ ( in @ SV826 @ SV244 )
| ~ ( in @ SV826 @ ( setminus @ SV244 @ ( setminus @ SV244 @ SV532 ) ) )
| ( in @ SV826 @ SV532 ) )
= $true )
| ( ( in @ SV532 @ ( powerset @ SV244 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2457,plain,
! [SV533: $i > $o,SV245: $i] :
( ( ( ! [SY3608: $i] :
~ ~ ( ~ ( in @ SY3608 @ SV245 )
| ~ ( SV533 @ SY3608 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV245
@ ^ [SY3609: $i] : ( SV533 @ SY3609 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2169]) ).
thf(2458,plain,
! [SV712: $i,SV534: $i,SV246: $i] :
( ( ( func @ SV246 @ SV534 @ SV712 )
= $false )
| ( ( ! [SY3878: $i] :
( ~ ( in @ SY3878 @ SV246 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV534
@ ^ [SY3879: $i] : ( in @ ( kpair @ SY3878 @ SY3879 ) @ SV712 ) ) )
@ SV534 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2170]) ).
thf(2459,plain,
! [SV535: $i,SV247: $i,SV827: $i] :
( ( ( ~ ( in @ SV827 @ SV247 )
| ! [SY4018: $i] :
( ~ ( in @ SY4018 @ SV247 )
| ~ ( in @ ( kpair @ SY4018 @ SV827 ) @ ( breln1invset @ SV247 @ SV535 ) )
| ( in @ ( kpair @ SV827 @ SY4018 ) @ SV535 ) ) )
= $true )
| ( ( breln1 @ SV247 @ SV535 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(2460,plain,
! [SV249: $i] :
( ( ( ~ ( in @ ( sK7_SY3023 @ SV249 ) @ SV249 ) )
= $false )
| ( ( ! [SY3024: $i] :
( ~ ( in @ SY3024 @ SV249 )
| ( subset @ SY3024 @ SV249 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2173]) ).
thf(2461,plain,
! [SV249: $i] :
( ( ( subset @ ( sK7_SY3023 @ SV249 ) @ SV249 )
= $false )
| ( ( ! [SY3024: $i] :
( ~ ( in @ SY3024 @ SV249 )
| ( subset @ SY3024 @ SV249 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2173]) ).
thf(2462,plain,
! [SV537: $i,SV250: $i,SV713: $i] :
( ( ( in @ SV713 @ ( setadjoin @ SV250 @ ( setadjoin @ SV537 @ emptyset ) ) )
= $false )
| ( ( ( SV713 = SV250 )
| ( SV713 = SV537 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2463,plain,
! [SV538: $i,SV251: $i,SV828: $i] :
( ( ( ~ ( in @ SV828 @ ( powerset @ SV251 ) )
| ! [SY4019: $i] :
( ~ ( in @ SY4019 @ SV251 )
| ~ ~ ( in @ SY4019 @ SV538 )
| ~ ~ ( in @ SY4019 @ SV828 )
| ~ ( in @ SY4019 @ ( binunion @ SV538 @ SV828 ) ) ) )
= $true )
| ( ( in @ SV538 @ ( powerset @ SV251 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2464,plain,
! [SV539: $o,SV252: $i,SV714: $i] :
( ( ( in @ SV714 @ SV252 )
= $false )
| ( ( ! [SY3880: $i] :
( ~ ( in @ SY3880 @ SV252 )
| ~ SV539
| ( ( dsetconstr @ SV252
@ ^ [SY3881: $i] :
( ~ ( ~ SV539
| ( SY3881 != SV714 ) )
| ~ ( ~ ~ SV539
| ( SY3881 != SY3880 ) ) ) )
= ( setadjoin @ SV714 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2176]) ).
thf(2465,plain,
! [SV252: $i,SV715: $i] :
( ( ( in @ SV715 @ SV252 )
= $false )
| ( ( ! [SY3882: $i] :
( ~ ( in @ SY3882 @ SV252 )
| ~ $true
| ( ( dsetconstr @ SV252
@ ^ [SY3883: $i] :
( ~ ( ~ $true
| ( SY3883 != SV715 ) )
| ~ ( ~ ~ $true
| ( SY3883 != SY3882 ) ) ) )
= ( setadjoin @ SV715 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2177]) ).
thf(2466,plain,
! [SV252: $i,SV716: $i] :
( ( ( in @ SV716 @ SV252 )
= $false )
| ( ( ! [SY3884: $i] :
( ~ ( in @ SY3884 @ SV252 )
| ~ $false
| ( ( dsetconstr @ SV252
@ ^ [SY3885: $i] :
( ~ ( ~ $false
| ( SY3885 != SV716 ) )
| ~ ( ~ ~ $false
| ( SY3885 != SY3884 ) ) ) )
= ( setadjoin @ SV716 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2178]) ).
thf(2467,plain,
! [SV717: $i,SV541: $i,SV254: $i] :
( ( ( func @ SV254 @ SV541 @ SV717 )
= $false )
| ( ( ! [SY3886: $i] :
( ~ ( in @ SY3886 @ SV254 )
| ( ( ap @ SV254 @ SV541 @ SV717 @ SY3886 )
= ( ap @ SV254 @ SV541 @ SV717 @ SY3886 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2180]) ).
thf(2468,plain,
! [SV753: $i,SV718: $i,SV543: $i,SV256: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV256 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV256 @ ( setadjoin @ SV543 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV718 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV718 @ ( setadjoin @ SV753 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( ( SV718 != SV753 )
| ( SV543 = SV753 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2182]) ).
thf(2469,plain,
! [SV719: $i,SV548: $i,SV259: $i] :
( ( ( func @ SV259 @ SV548 @ SV719 )
= $false )
| ( ( ! [SY3888: $i] :
( ~ ( in @ SY3888 @ SV259 )
| ! [SY3889: $i] :
( ~ ( in @ SY3889 @ SV548 )
| ~ ( in @ ( kpair @ SY3888 @ SY3889 ) @ SV719 )
| ( ( ap @ SV259 @ SV548 @ SV719 @ SY3888 )
= SY3889 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2470,plain,
! [SV549: $i,SV829: $i,SV260: $i] :
( ( ( ~ ( breln1 @ SV260 @ SV829 )
| ~ ! [SY4020: $i] :
( ~ ( in @ SY4020 @ SV260 )
| ! [SY4021: $i] :
( ~ ( in @ SY4021 @ SV260 )
| ~ ( in @ ( kpair @ SY4020 @ SY4021 ) @ SV549 )
| ( in @ ( kpair @ SY4020 @ SY4021 ) @ SV829 ) ) )
| ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) )
| ( SV549 = SV829 ) )
= $true )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2471,plain,
! [SV551: $i > $o,SV262: $i,SV720: $i] :
( ( ( in @ SV720
@ ( dsetconstr @ SV262
@ ^ [SY3634: $i] : ( SV551 @ SY3634 ) ) )
= $false )
| ( ( SV551 @ SV720 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2472,plain,
! [SV552: $i,SV263: $i,SV721: $i] :
( ( ( in @ SV721 @ SV263 )
= $false )
| ( ( ~ ( in @ SV721 @ SV552 )
| ( in @ SV721 @ ( binintersect @ SV263 @ SV552 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2473,plain,
! [SV553: $i,SV830: $i,SV264: $i] :
( ( ( ~ ( breln1 @ SV264 @ SV830 )
| ! [SY4024: $i] :
( ~ ( in @ SY4024 @ SV264 )
| ! [SY4025: $i] :
( ~ ( in @ SY4025 @ SV264 )
| ~ ( ( in @ ( kpair @ SY4024 @ SY4025 ) @ SV553 )
| ( in @ ( kpair @ SY4024 @ SY4025 ) @ SV830 ) )
| ( in @ ( kpair @ SY4024 @ SY4025 ) @ ( binunion @ SV553 @ SV830 ) ) ) ) )
= $true )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2474,plain,
! [SV554: $i,SV265: $i,SV722: $i] :
( ( ( in @ SV722 @ SV265 )
= $false )
| ( ( ! [SY3891: $i] :
( ~ ( in @ SY3891 @ SV554 )
| ( subset @ ( setadjoin @ SV722 @ ( setadjoin @ SY3891 @ emptyset ) ) @ ( binunion @ SV265 @ SV554 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2193]) ).
thf(2475,plain,
! [SV555: $i,SV266: $i,SV831: $i] :
( ( ( ~ ( in @ SV831 @ ( powerset @ SV266 ) )
| ( in @ ( setminus @ SV266 @ SV555 ) @ ( powerset @ ( setminus @ SV266 @ ( binintersect @ SV555 @ SV831 ) ) ) ) )
= $true )
| ( ( in @ SV555 @ ( powerset @ SV266 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2476,plain,
! [SV556: $i,SV267: $i,SV723: $i] :
( ( ( in @ SV723 @ ( injFuncSet @ SV267 @ SV556 ) )
= $false )
| ( ( in @ SV723 @ ( funcSet @ SV267 @ SV556 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2195]) ).
thf(2477,plain,
! [SV557: $i,SV268: $i,SV724: $i] :
( ( ( in @ SV724 @ ( surjFuncSet @ SV268 @ SV557 ) )
= $false )
| ( ( surjective @ SV268 @ SV557 @ SV724 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2196]) ).
thf(2478,plain,
! [SV558: $i,SV270: $i,SV832: $i] :
( ( ( ~ ( in @ SV832 @ ( powerset @ SV270 ) )
| ( ( setminus @ SV270 @ ( binunion @ SV558 @ SV832 ) )
= ( binintersect @ ( setminus @ SV270 @ SV558 ) @ ( setminus @ SV270 @ SV832 ) ) ) )
= $true )
| ( ( in @ SV558 @ ( powerset @ SV270 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2479,plain,
! [SV833: $i > $o,SV559: $i,SV271: $i] :
( ( ( ~ ! [SY4026: $i] :
( ~ ( in @ SY4026 @ SV271 )
| ! [SY4027: $i] :
( ~ ( in @ SY4027 @ SV271 )
| ~ ( in @ ( kpair @ SY4026 @ SY4027 ) @ SV559 )
| ( SV833 @ ( kpair @ SY4026 @ SY4027 ) ) ) )
| ! [SY4028: $i] :
( ~ ( in @ SY4028 @ SV559 )
| ( SV833 @ SY4028 ) ) )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2480,plain,
! [SV560: $i,SV272: $i,SV725: $i] :
( ( ( in @ SV725 @ SV272 )
= $false )
| ( ( ~ ~ ( in @ SV725 @ SV560 )
| ( in @ SV725 @ ( symdiff @ SV272 @ SV560 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2199]) ).
thf(2481,plain,
! [SV561: $i,SV273: $i,SV726: $i] :
( ( ( in @ SV726 @ SV273 )
= $false )
| ( ( ! [SY3892: $i] :
( ~ ( in @ SY3892 @ SV561 )
| ( ( kfst @ ( kpair @ SV726 @ SY3892 ) )
= SV726 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2200]) ).
thf(2482,plain,
! [SV562: $i,SV274: $i,SV834: $i] :
( ( ( ~ ( in @ SV834 @ ( powerset @ SV274 ) )
| ~ ( subset @ ( setminus @ SV274 @ SV834 ) @ ( setminus @ SV274 @ SV562 ) )
| ( subset @ SV562 @ SV834 ) )
= $true )
| ( ( in @ SV562 @ ( powerset @ SV274 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(2483,plain,
! [SV275: $i,SV563: $i > $o] :
( ( ( ~ ( in @ ( sK16_SY3653 @ SV563 @ SV275 ) @ SV275 )
| ~ ( SV563 @ ( sK16_SY3653 @ SV563 @ SV275 ) ) )
= $false )
| ( ( ~ ~ ! [SY3654: $i] :
~ ~ ( ~ ( in @ SY3654 @ SV275 )
| ~ ( SV563 @ SY3654 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2202]) ).
thf(2484,plain,
! [SV565: $i,SV277: $i,SV835: $i] :
( ( ( ~ ( in @ SV835 @ ( powerset @ SV277 ) )
| ! [SY4029: $i] :
( ~ ( in @ SY4029 @ SV277 )
| ~ ( in @ SY4029 @ ( setminus @ SV277 @ ( binunion @ SV565 @ SV835 ) ) )
| ( in @ SY4029 @ ( setminus @ SV277 @ SV565 ) ) ) )
= $true )
| ( ( in @ SV565 @ ( powerset @ SV277 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2485,plain,
! [SV278: $i,SV566: $i] :
( ( ( ~ ( in @ ( sK17_SY3657 @ SV566 @ SV278 ) @ SV278 )
| ( in @ ( sK17_SY3657 @ SV566 @ SV278 ) @ SV566 ) )
= $false )
| ( ( ~ ! [SY3658: $i] :
( ~ ( in @ SY3658 @ SV566 )
| ( in @ SY3658 @ SV278 ) )
| ( SV278 = SV566 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2205]) ).
thf(2486,plain,
! [SV567: $i,SV279: $i,SV727: $i] :
( ( ( in @ SV727 @ ( binintersect @ SV279 @ SV567 ) )
= $false )
| ( ( in @ SV727 @ SV279 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2206]) ).
thf(2487,plain,
! [SV568: $i,SV836: $i,SV280: $i] :
( ( ( ~ ( breln1 @ SV280 @ SV836 )
| ! [SY4030: $i] :
( ~ ( in @ SY4030 @ SV280 )
| ! [SY4031: $i] :
( ~ ( in @ SY4031 @ SV280 )
| ~ ( in @ ( kpair @ SY4030 @ SY4031 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
| ! [SY4032: $o] :
( ~ ! [SY4033: $i] :
( ~ ( in @ SY4033 @ SV280 )
| ~ ( in @ ( kpair @ SY4030 @ SY4033 ) @ SV568 )
| ~ ( in @ ( kpair @ SY4033 @ SY4031 ) @ SV836 )
| SY4032 )
| SY4032 ) ) ) )
= $true )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2488,plain,
! [SV570: $i,SV282: $i,SV728: $i] :
( ( ( ~ ( in @ SV728 @ SV282 ) )
= $false )
| ( ( ~ ( in @ SV728 @ SV570 )
| ( in @ SV728 @ ( symdiff @ SV282 @ SV570 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2489,plain,
! [SV571: $i,SV283: $i,SV754: $i,SV729: $i] :
( ( ( ~ ( in @ ( kpair @ SV729 @ SV754 ) @ ( cartprod @ SV283 @ SV571 ) ) )
= $true )
| ( ( in @ SV754 @ SV571 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2210]) ).
thf(2490,plain,
! [SV572: $i,SV284: $i] :
( ( ( ~ ! [SY3668: $i] :
~ ~ ( ~ ( in @ SY3668 @ SV284 )
| ~ ( in @ SY3668 @ SV572 ) ) )
= $true )
| ( ( ( binintersect @ SV284 @ SV572 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2211]) ).
thf(2491,plain,
! [SV573: $i,SV285: $i,SV730: $i] :
( ( ( in @ SV730 @ SV285 )
= $false )
| ( ( in @ SV730 @ ( binunion @ SV285 @ SV573 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2212]) ).
thf(2492,plain,
! [SV837: $i,SV288: $i > $o] :
( ( ( ~ ~ ( ~ ( SV288 @ SV837 )
| ~ ! [SY4034: $i] :
( ~ ( SV288 @ SY4034 )
| ( SV837 = SY4034 ) ) ) )
= $true )
| ( ( ! [SY3119: $i,SY3120: $i] :
( ~ ( SV288 @ SY3119 )
| ~ ( SV288 @ SY3120 )
| ( SY3119 = SY3120 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2493,plain,
! [SV575: $i > $o,SV289: $i] :
( ( ( ~ ! [SY3670: $i] :
~ ~ ( ~ ( in @ SY3670 @ SV289 )
| ~ ( SV575 @ SY3670 ) ) )
= $true )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV289 )
| ~ ( SV575 @ SY3671 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2215]) ).
thf(2494,plain,
! [SV577: $i > $o,SV291: $i,SV731: $i] :
( ( ( in @ SV731 @ SV291 )
= $false )
| ( ( ~ ( SV577 @ SV731 )
| ( in @ SV731
@ ( dsetconstr @ SV291
@ ^ [SY3673: $i] : ( SV577 @ SY3673 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2217]) ).
thf(2495,plain,
! [SV578: $i,SV838: $i,SV292: $i] :
( ( ( ~ ( breln1 @ SV292 @ SV838 )
| ( breln1 @ SV292 @ ( binunion @ SV578 @ SV838 ) ) )
= $true )
| ( ( breln1 @ SV292 @ SV578 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2496,plain,
! [SV732: $i > $i > $o,SV579: $i,SV293: $i,SV755: $i] :
( ( ( ~ ( in @ SV755 @ SV293 ) )
= $true )
| ( ( ! [SY3938: $i] :
( ~ ( in @ SY3938 @ SV579 )
| ~ ( SV732 @ SV755 @ SY3938 )
| ( in @ ( kpair @ SV755 @ SY3938 )
@ ( dpsetconstr @ SV293 @ SV579
@ ^ [SY3897: $i,SY3898: $i] : ( SV732 @ SY3897 @ SY3898 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2219]) ).
thf(2497,plain,
! [SV294: $i,SV756: $i] :
( ( ( ~ ( in @ SV756 @ SV294 ) )
= $true )
| ( ( ( setunion @ SV294 )
= SV756 )
= $true )
| ( ( singleton @ SV294 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2220]) ).
thf(2498,plain,
! [SV581: $i,SV296: $i] :
( ( ( subset @ SV296 @ SV581 )
= $true )
| ( ( SV296 != SV581 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2222]) ).
thf(2499,plain,
! [SV582: $i,SV839: $i,SV297: $i] :
( ( ( ~ ( breln1 @ SV297 @ SV839 )
| ( ( binunion @ SV582 @ SV839 )
= ( binunion @ SV839 @ SV582 ) ) )
= $true )
| ( ( breln1 @ SV297 @ SV582 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2223]) ).
thf(2500,plain,
! [SV757: $o,SV583: $i,SV298: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV733 @ SV298 )
| SV757 )
| ~ ( ~ ( in @ SV733 @ SV583 )
| SV757 )
| SV757 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2224]) ).
thf(2501,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV733 @ SV298 )
| $true )
| ~ ( ~ ( in @ SV733 @ SV583 )
| $true )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2225]) ).
thf(2502,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV733 @ SV298 )
| $false )
| ~ ( ~ ( in @ SV733 @ SV583 )
| $false )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2226]) ).
thf(2503,plain,
! [SV584: $i,SV299: $i,SV840: $i] :
( ( ( ~ ( in @ SV840 @ ( powerset @ SV299 ) )
| ~ ! [SY4035: $i] :
( ~ ( in @ SY4035 @ SV299 )
| ~ ( in @ SY4035 @ SV584 )
| ( in @ SY4035 @ SV840 ) )
| ~ ! [SY4036: $i] :
( ~ ( in @ SY4036 @ SV299 )
| ~ ( in @ SY4036 @ SV840 )
| ( in @ SY4036 @ SV584 ) )
| ( SV584 = SV840 ) )
= $true )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2504,plain,
! [SV585: $i,SV841: $i,SV300: $i] :
( ( ( ~ ( breln1 @ SV300 @ SV841 )
| ! [SY4037: $i] :
( ~ ( in @ SY4037 @ SV300 )
| ! [SY4038: $i] :
( ~ ( in @ SY4038 @ SV300 )
| ~ ( in @ ( kpair @ SY4037 @ SY4038 ) @ SV585 )
| ( in @ ( kpair @ SY4037 @ SY4038 ) @ ( binunion @ SV585 @ SV841 ) ) ) ) )
= $true )
| ( ( breln1 @ SV300 @ SV585 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2505,plain,
! [SV734: $i,SV586: $i,SV301: $i] :
( ( ( func @ SV301 @ SV586 @ SV734 )
= $false )
| ( ( ! [SY3900: $i] :
( ~ ( func @ SV301 @ SV586 @ SY3900 )
| ~ ! [SY3901: $i] :
( ~ ( in @ SY3901 @ SV301 )
| ( ( ap @ SV301 @ SV586 @ SV734 @ SY3901 )
= ( ap @ SV301 @ SV586 @ SY3900 @ SY3901 ) ) )
| ! [SY3902: $i] :
( ~ ( in @ SY3902 @ SV301 )
| ! [SY3903: $i] :
( ~ ( in @ SY3903 @ SV586 )
| ~ ( in @ ( kpair @ SY3902 @ SY3903 ) @ SY3900 )
| ( in @ ( kpair @ SY3902 @ SY3903 ) @ SV734 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2229]) ).
thf(2506,plain,
! [SV587: $i,SV302: $i,SV842: $i] :
( ( ( ~ ( in @ SV842 @ ( powerset @ SV302 ) )
| ! [SY4039: $i] :
( ~ ( in @ SY4039 @ SV302 )
| ~ ( in @ SY4039 @ ( binunion @ ( setminus @ SV302 @ SV587 ) @ ( setminus @ SV302 @ SV842 ) ) )
| ( in @ SY4039 @ ( setminus @ SV302 @ ( binintersect @ SV587 @ SV842 ) ) ) ) )
= $true )
| ( ( in @ SV587 @ ( powerset @ SV302 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2507,plain,
! [SV589: $i,SV305: $i,SV843: $i] :
( ( ( ~ ( in @ SV843 @ ( powerset @ SV305 ) )
| ! [SY4040: $i] :
( ~ ( in @ SY4040 @ ( powerset @ SV305 ) )
| ( in @ ( binintersect @ SV589 @ SV843 ) @ ( powerset @ ( binintersect @ ( binunion @ SV589 @ SY4040 ) @ ( binunion @ SV843 @ SY4040 ) ) ) ) ) )
= $true )
| ( ( in @ SV589 @ ( powerset @ SV305 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2508,plain,
! [SV306: $i] :
( ( ( in @ ( sK8_SY3165 @ SV306 ) @ SV306 )
= $true )
| ( ( SV306 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2233]) ).
thf(2509,plain,
! [SV590: $i,SV307: $i,SV844: $i] :
( ( ( ~ ( in @ SV844 @ ( powerset @ SV307 ) )
| ! [SY4041: $i] :
( ~ ( in @ SY4041 @ SV307 )
| ~ ( in @ SY4041 @ ( binintersect @ ( setminus @ SV307 @ SV590 ) @ ( setminus @ SV307 @ SV844 ) ) )
| ( in @ SY4041 @ ( setminus @ SV307 @ ( binunion @ SV590 @ SV844 ) ) ) ) )
= $true )
| ( ( in @ SV590 @ ( powerset @ SV307 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(2510,plain,
! [SV591: $i,SV308: $i,SV845: $i] :
( ( ( ~ ( in @ SV845 @ ( powerset @ SV308 ) )
| ~ ! [SY4042: $i] :
( ~ ( in @ SY4042 @ SV308 )
| ~ ( in @ SY4042 @ SV591 )
| ( in @ SY4042 @ SV845 ) )
| ( in @ SV591 @ ( powerset @ SV845 ) ) )
= $true )
| ( ( in @ SV591 @ ( powerset @ SV308 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2511,plain,
! [SV592: $i,SV309: $i,SV846: $i] :
( ( ( ~ ( in @ SV846 @ ( powerset @ SV309 ) )
| ! [SY4043: $i] :
( ~ ( in @ SY4043 @ SV309 )
| ~ ( in @ SY4043 @ ( setminus @ SV309 @ SV592 ) )
| ~ ( in @ SY4043 @ ( setminus @ SV309 @ SV846 ) )
| ( in @ SY4043 @ ( setminus @ SV309 @ ( binunion @ SV592 @ SV846 ) ) ) ) )
= $true )
| ( ( in @ SV592 @ ( powerset @ SV309 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2512,plain,
! [SV594: $i,SV311: $i] :
( ( ( SV311 = SV594 )
= $true )
| ( ( ~ ( in @ SV594 @ ( setadjoin @ SV311 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2238]) ).
thf(2513,plain,
! [SV312: $i,SV595: $i,SV735: $i] :
( ( ( in @ SV735 @ SV595 )
= $false )
| ( ( in @ SV735 @ ( binunion @ SV312 @ SV595 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2239]) ).
thf(2514,plain,
! [SV596: $i,SV313: $i,SV736: $i] :
( ( ( in @ SV736 @ SV313 )
= $false )
| ( ( ! [SY3904: $i] :
( ~ ( in @ SY3904 @ SV596 )
| ( in @ ( setadjoin @ SV736 @ ( setadjoin @ SY3904 @ emptyset ) ) @ ( powerset @ ( binunion @ SV313 @ SV596 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2240]) ).
thf(2515,plain,
! [SV597: $i,SV314: $i,SV737: $i] :
( ( ( in @ SV737 @ SV314 )
= $false )
| ( ( ! [SY3905: $i] :
( ~ ( in @ SY3905 @ SV597 )
| ( ( ksnd @ ( kpair @ SV737 @ SY3905 ) )
= SY3905 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2241]) ).
thf(2516,plain,
! [SV598: $i,SV315: $i,SV847: $i] :
( ( ( ~ ( in @ SV847 @ ( powerset @ SV315 ) )
| ! [SY4044: $i] :
( ~ ( in @ SY4044 @ SV315 )
| ~ ( in @ SY4044 @ ( setminus @ SV315 @ ( binunion @ SV598 @ SV847 ) ) )
| ~ ( in @ SY4044 @ SV598 ) ) )
= $true )
| ( ( in @ SV598 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(2517,plain,
! [SV848: $i,SV316: $i > $o] :
( ( ( ~ ~ ( ~ ( SV316 @ SV848 )
| ~ ! [SY4045: $i] :
( ~ ( SV316 @ SY4045 )
| ( SV848 = SY4045 ) ) ) )
= $true )
| ( ( ~ ! [SY3190: $i] :
~ ! [SY3191: $i] :
~ ( ~ ( ~ ( SV316 @ SY3191 )
| ( SY3191 = SY3190 ) )
| ~ ( ( SY3191 != SY3190 )
| ( SV316 @ SY3191 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2518,plain,
! [SV599: $i,SV317: $i,SV849: $i] :
( ( ( ~ ( in @ SV849 @ ( powerset @ SV317 ) )
| ! [SY4046: $i] :
( ~ ( in @ SY4046 @ ( powerset @ SV317 ) )
| ! [SY4047: $i] :
( ~ ( in @ SY4047 @ ( powerset @ SV317 ) )
| ~ ( subset @ SV599 @ SY4046 )
| ~ ( subset @ SV849 @ SY4047 )
| ( subset @ ( binintersect @ SV599 @ SV849 ) @ ( binintersect @ SY4046 @ SY4047 ) ) ) ) )
= $true )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2519,plain,
! [SV600: $i,SV318: $i,SV850: $i] :
( ( ( ~ ( in @ SV850 @ ( powerset @ SV318 ) )
| ! [SY4048: $i] :
( ~ ( in @ SY4048 @ SV318 )
| ~ ~ ( in @ SY4048 @ SV850 )
| ~ ( in @ SY4048 @ ( binintersect @ SV600 @ SV850 ) ) ) )
= $true )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2520,plain,
! [SV738: $i,SV601: $i,SV319: $i] :
( ( ( breln @ SV319 @ SV601 @ SV738 )
= $false )
| ( ( ! [SY3906: $i > $o] :
( ~ ! [SY3907: $i] :
( ~ ( in @ SY3907 @ SV319 )
| ! [SY3908: $i] :
( ~ ( in @ SY3908 @ SV601 )
| ~ ( in @ ( kpair @ SY3907 @ SY3908 ) @ SV738 )
| ( SY3906 @ ( kpair @ SY3907 @ SY3908 ) ) ) )
| ! [SY3909: $i] :
( ~ ( in @ SY3909 @ SV738 )
| ( SY3906 @ SY3909 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2246]) ).
thf(2521,plain,
! [SV320: $i,SV602: $i] :
( ( ( ~ ( in @ ( sK18_SY3721 @ SV602 @ SV320 ) @ SV320 )
| ( in @ ( sK18_SY3721 @ SV602 @ SV320 ) @ SV602 ) )
= $false )
| ( ( subset @ SV320 @ SV602 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2247]) ).
thf(2522,plain,
! [SV603: $o,SV321: $i,SV739: $i] :
( ( ( in @ SV739 @ SV321 )
= $false )
| ( ( ! [SY3910: $i] :
( ~ ( in @ SY3910 @ SV321 )
| ~ ~ SV603
| ( ( if @ SV321 @ SV603 @ SV739 @ SY3910 )
= SY3910 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2248]) ).
thf(2523,plain,
! [SV321: $i,SV740: $i] :
( ( ( in @ SV740 @ SV321 )
= $false )
| ( ( ! [SY3911: $i] :
( ~ ( in @ SY3911 @ SV321 )
| ~ ~ $true
| ( ( if @ SV321 @ $true @ SV740 @ SY3911 )
= SY3911 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2524,plain,
! [SV321: $i,SV741: $i] :
( ( ( in @ SV741 @ SV321 )
= $false )
| ( ( ! [SY3912: $i] :
( ~ ( in @ SY3912 @ SV321 )
| ~ ~ $false
| ( ( if @ SV321 @ $false @ SV741 @ SY3912 )
= SY3912 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2250]) ).
thf(2525,plain,
! [SV322: $i,SV851: $i] :
( ( ( ~ ( in @ SV851 @ SV322 ) )
= $true )
| ( ( ~ ! [SY3211: $i] :
~ ~ ( ~ ( in @ SY3211 @ SV322 )
| ~ ~ ~ ! [SY3212: $i] :
~ ~ ( ~ ( in @ SY3212 @ SY3211 )
| ~ ( in @ SY3212 @ SV322 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2526,plain,
! [SV604: $i,SV323: $i,SV758: $i,SV742: $i] :
( ( ( ~ ( in @ ( kpair @ SV742 @ SV758 ) @ ( cartprod @ SV323 @ SV604 ) ) )
= $true )
| ( ( in @ SV742 @ SV323 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2252]) ).
thf(2527,plain,
! [SV324: $i,SV605: $i] :
( ( ( ~ ( in @ ( sK19_SY3726 @ SV605 @ SV324 ) @ SV324 )
| ( in @ ( sK19_SY3726 @ SV605 @ SV324 ) @ SV605 ) )
= $false )
| ( ( subset @ SV324 @ SV605 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2253]) ).
thf(2528,plain,
! [SV606: $i,SV325: $i,SV852: $i] :
( ( ( ~ ( in @ SV852 @ ( powerset @ SV325 ) )
| ! [SY4049: $i] :
( ~ ( in @ SY4049 @ ( powerset @ SV325 ) )
| ~ ( subset @ SV606 @ SV852 )
| ~ ( subset @ SV606 @ SY4049 )
| ( subset @ SV606 @ ( binintersect @ SV852 @ SY4049 ) ) ) )
= $true )
| ( ( in @ SV606 @ ( powerset @ SV325 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2529,plain,
! [SV37: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY2402 @ SV37 ) @ SV37 )
| ~ $true ) )
= $false )
| ( ( SV37 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2255]) ).
thf(2530,plain,
! [SV38: $i,SV743: $i] :
( ( ( in @ SV743 @ omega )
= $false )
| ( ( ( ( omegaS @ SV38 )
!= ( omegaS @ SV743 ) )
| ( SV38 = SV743 ) )
= $true )
| ( ( in @ SV38 @ omega )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2256]) ).
thf(2531,plain,
! [SV39: $i,SV610: $i > $i,SV350: $i] :
( ( ( ~ ( in @ ( sK21_SY3733 @ SV350 @ SV610 @ SV39 ) @ SV39 )
| ( in @ ( SV610 @ ( sK21_SY3733 @ SV350 @ SV610 @ SV39 ) ) @ SV350 ) )
= $false )
| ( ( func @ SV39 @ SV350
@ ( dpsetconstr @ SV39 @ SV350
@ ^ [SY3734: $i,SY3735: $i] :
( ( SV610 @ SY3734 )
= SY3735 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2257]) ).
thf(2532,plain,
! [SV759: $i,SV40: $i > $o] :
( ( ( ~ ( ~ ( SV40 @ SV759 )
| ~ ! [SY3941: $i] :
( ~ ( SV40 @ SY3941 )
| ( SV759 = SY3941 ) ) ) )
= $false )
| ( ( ~ ! [SY2411: $i] :
~ ( SV40 @ SY2411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2258]) ).
thf(2533,plain,
! [SV41: $i,SV611: $i,SV351: $i,SV853: $i] :
( ( ( ~ ( in @ SV853 @ SV351 )
| ( ( kpair @ SV611 @ SV853 )
= ( kpair @ SV611 @ SV853 ) ) )
= $true )
| ( ( in @ SV611 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2534,plain,
! [SV760: $i,SV42: $i > $o] :
( ( ( ~ ( ~ ( SV42 @ SV760 )
| ~ ! [SY3942: $i] :
( ~ ( SV42 @ SY3942 )
| ( SV760 = SY3942 ) ) ) )
= $false )
| ( ( SV42
@ ( descr
@ ^ [SY2417: $i] : ( SV42 @ SY2417 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2260]) ).
thf(2535,plain,
! [SV44: $i,SV353: $i > $o] :
( ( ( ~ ( in @ ( sK9_SY3238 @ SV353 @ SV44 ) @ SV44 ) )
= $false )
| ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) )
| ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2261]) ).
thf(2536,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ( ! [SY3943: $i] :
( ~ ( in @ SY3943 @ SV44 )
| ~ ( SV353 @ ( sK9_SY3238 @ SV353 @ SV44 ) )
| ~ ( SV353 @ SY3943 )
| ( ( sK9_SY3238 @ SV353 @ SV44 )
= SY3943 ) ) )
= $false )
| ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) )
| ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2261]) ).
thf(2537,plain,
! [SV612: $i,SV354: $i,SV45: $i,SV854: $i] :
( ( ( ~ ( in @ SV854 @ ( funcSet @ SV45 @ SV354 ) )
| ~ ! [SY4050: $i] :
( ~ ( in @ SY4050 @ SV45 )
| ( ( ap @ SV45 @ SV354 @ SV612 @ SY4050 )
= ( ap @ SV45 @ SV354 @ SV854 @ SY4050 ) ) )
| ( SV612 = SV854 ) )
= $true )
| ( ( in @ SV612 @ ( funcSet @ SV45 @ SV354 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(2538,plain,
! [SV614: $i,SV356: $i,SV47: $i,SV855: $i] :
( ( ( ~ ( in @ SV855 @ SV47 )
| ( in @ ( kpair @ SV855 @ ( ap @ SV47 @ SV356 @ SV614 @ SV855 ) ) @ SV614 ) )
= $true )
| ( ( in @ SV614 @ ( funcSet @ SV47 @ SV356 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(2539,plain,
! [SV744: $i,SV615: $i,SV357: $i,SV48: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV48 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV48 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV615 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV615 @ ( setadjoin @ SV744 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV357 = SV744 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2265]) ).
thf(2540,plain,
! [SV616: $i,SV358: $i,SV49: $i,SV856: $i] :
( ( ( ~ ( in @ SV856 @ SV49 )
| ( in @ ( ap @ SV49 @ SV358 @ SV616 @ SV856 ) @ SV358 ) )
= $true )
| ( ( in @ SV616 @ ( funcSet @ SV49 @ SV358 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(2541,plain,
! [SV359: $i,SV50: $i,SV857: $i,SV761: $i] :
( ( ( ( SV761 != SV857 )
| ( ( setadjoin @ SV50 @ SV761 )
= ( setadjoin @ SV359 @ SV857 ) ) )
= $true )
| ( ( SV50 = SV359 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2542,plain,
! [SV361: $i,SV52: $i,SV762: $i] :
( ( ( ~ ( in @ SV762 @ ( powerset @ SV52 ) ) )
= $true )
| ( ( ! [SY3945: $i] :
( ~ ( in @ SY3945 @ ( powerset @ SV52 ) )
| ! [SY3946: $i] :
( ~ ( in @ SY3946 @ SV52 )
| ~ ( in @ SY3946 @ ( binintersect @ SV361 @ SV762 ) )
| ( in @ SY3946 @ ( binunion @ SV762 @ SY3945 ) ) ) ) )
= $true )
| ( ( in @ SV361 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2269]) ).
thf(2543,plain,
! [SV54: $i,SV618: $i > $i,SV363: $i] :
( ( ( ~ ( in @ ( sK22_SY3742 @ SV363 @ SV618 @ SV54 ) @ SV54 )
| ( in @ ( SV618 @ ( sK22_SY3742 @ SV363 @ SV618 @ SV54 ) ) @ SV363 ) )
= $false )
| ( ( in
@ ( lam @ SV54 @ SV363
@ ^ [SY3743: $i] : ( SV618 @ SY3743 ) )
@ ( funcSet @ SV54 @ SV363 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2270]) ).
thf(2544,plain,
! [SV364: $i,SV55: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ ( powerset @ SV55 ) ) )
= $true )
| ( ( ~ ( subset @ SV364 @ ( setminus @ SV55 @ SV763 ) )
| ( subset @ SV763 @ ( setminus @ SV55 @ SV364 ) ) )
= $true )
| ( ( in @ SV364 @ ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2545,plain,
! [SV365: $i,SV56: $i,SV764: $i] :
( ( ( ~ ( in @ SV764 @ ( powerset @ SV56 ) ) )
= $true )
| ( ( ! [SY3947: $i] :
( ~ ( in @ SY3947 @ ( powerset @ SV56 ) )
| ! [SY3948: $i] :
( ~ ( in @ SY3948 @ ( powerset @ SV56 ) )
| ( ( setminus @ SV56 @ ( binintersect @ ( binunion @ SV365 @ SV764 ) @ ( binunion @ SY3947 @ SY3948 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV56 @ SV365 ) @ ( setminus @ SV56 @ SV764 ) ) @ ( binintersect @ ( setminus @ SV56 @ SY3947 ) @ ( setminus @ SV56 @ SY3948 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV365 @ ( powerset @ SV56 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2272]) ).
thf(2546,plain,
! [SV57: $i,SV366: $i] :
( ( ( ~ ( in @ SV366 @ ( setunion @ SV57 ) ) )
= $true )
| ( ( ~ ! [SY3265: $i] :
~ ~ ( ~ ( in @ SV366 @ SY3265 )
| ~ ( in @ SY3265 @ SV57 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2273]) ).
thf(2547,plain,
! [SV57: $i,SV366: $i] :
( ( ( ~ ~ ! [SY3266: $i] :
~ ~ ( ~ ( in @ SV366 @ SY3266 )
| ~ ( in @ SY3266 @ SV57 ) ) )
= $true )
| ( ( in @ SV366 @ ( setunion @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2274]) ).
thf(2548,plain,
! [SV765: $i,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ SV765 )
| ~ ! [SY3949: $i] :
( ~ ( SV58 @ SY3949 )
| ( SV765 = SY3949 ) ) ) )
= $false )
| ( ( ! [SY2464: $i,SY2465: $i] :
( ~ ( SV58 @ SY2464 )
| ~ ( SV58 @ SY2465 )
| ( SY2464 = SY2465 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2549,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ! [SY3950: $i] :
~ ( ~ ( ~ ( SV59 @ SY3950 )
| ( SY3950 = SV766 ) )
| ~ ( ( SY3950 != SV766 )
| ( SV59 @ SY3950 ) ) ) )
= $false )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2276]) ).
thf(2550,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ~ ( ~ ( SV60 @ SV767 )
| ~ ! [SY3951: $i] :
( ~ ( SV60 @ SY3951 )
| ( SV767 = SY3951 ) ) ) )
= $false )
| ( ( ~ ! [SY2472: $i] :
~ ~ ( ~ ( SV60 @ SY2472 )
| ~ ! [SY2473: $i] :
( ~ ( SV60 @ SY2473 )
| ( SY2472 = SY2473 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2551,plain,
! [SV367: $i > $o,SV61: $i,SV858: $i] :
( ( ( ~ ( in @ SV858 @ SV61 )
| ( SV367 @ SV858 ) )
= $true )
| ( ( ~ ! [SY3268: $i] :
~ ~ ( ~ ( in @ SY3268 @ SV61 )
| ~ ~ ( SV367 @ SY3268 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(2552,plain,
! [SV619: $i,SV369: $i,SV63: $i,SV859: $i] :
( ( ( ~ ( in @ SV859 @ SV63 )
| ( in @ ( ap @ SV63 @ SV369 @ SV619 @ SV859 ) @ SV369 ) )
= $true )
| ( ( func @ SV63 @ SV369 @ SV619 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2553,plain,
! [SV64: $i,SV620: $i > $i,SV370: $i] :
( ( ( ~ ( in @ ( sK23_SY3745 @ SV370 @ SV620 @ SV64 ) @ SV64 )
| ( in @ ( SV620 @ ( sK23_SY3745 @ SV370 @ SV620 @ SV64 ) ) @ SV370 ) )
= $false )
| ( ( ( lam @ SV64 @ SV370
@ ^ [SY3746: $i] : ( SV620 @ SY3746 ) )
= ( lam @ SV64 @ SV370
@ ^ [SY3747: $i] : ( SV620 @ SY3747 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2280]) ).
thf(2554,plain,
! [SV65: $i,SV371: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 )
| ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 ) )
| ~ ( ~ ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 )
| ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 ) ) )
= $true )
| ( ( SV65 = SV371 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2281]) ).
thf(2555,plain,
! [SV372: $i,SV68: $i,SV768: $i] :
( ( ( ~ ( in @ SV768 @ ( powerset @ SV68 ) ) )
= $true )
| ( ( ~ ( subset @ SV372 @ ( setminus @ SV68 @ SV768 ) )
| ! [SY3952: $i] :
( ~ ( in @ SY3952 @ SV68 )
| ~ ( in @ SY3952 @ SV768 )
| ( in @ SY3952 @ ( setminus @ SV68 @ SV372 ) ) ) )
= $true )
| ( ( in @ SV372 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2282]) ).
thf(2556,plain,
! [SV373: $i,SV69: $i,SV769: $i] :
( ( ( ~ ( in @ SV769 @ ( powerset @ SV69 ) ) )
= $true )
| ( ( ! [SY3953: $i] :
( ~ ( in @ SY3953 @ SV69 )
| ~ ( in @ SY3953 @ ( setminus @ SV69 @ ( binintersect @ SV373 @ SV769 ) ) )
| ( in @ SY3953 @ ( binunion @ ( setminus @ SV69 @ SV373 ) @ ( setminus @ SV69 @ SV769 ) ) ) ) )
= $true )
| ( ( in @ SV373 @ ( powerset @ SV69 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2283]) ).
thf(2557,plain,
! [SV375: $i,SV71: $i,SV770: $i] :
( ( ( ~ ( in @ SV770 @ ( powerset @ SV71 ) ) )
= $true )
| ( ( in @ ( binunion @ SV375 @ SV770 ) @ ( powerset @ SV71 ) )
= $true )
| ( ( in @ SV375 @ ( powerset @ SV71 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2284]) ).
thf(2558,plain,
! [SV376: $i,SV860: $o,SV72: $i,SV621: $i] :
( ( ( ~ ( ( SV621 != SV72 )
| SV860 )
| ~ ( ~ ( in @ SV621 @ SV376 )
| SV860 )
| SV860 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2285]) ).
thf(2559,plain,
! [SV376: $i,SV72: $i,SV621: $i] :
( ( ( ~ ( ( SV621 != SV72 )
| $true )
| ~ ( ~ ( in @ SV621 @ SV376 )
| $true )
| $true )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2285]) ).
thf(2560,plain,
! [SV376: $i,SV72: $i,SV621: $i] :
( ( ( ~ ( ( SV621 != SV72 )
| $false )
| ~ ( ~ ( in @ SV621 @ SV376 )
| $false )
| $false )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2285]) ).
thf(2561,plain,
! [SV377: $i,SV771: $i,SV73: $i] :
( ( ( ~ ( breln1 @ SV73 @ SV771 ) )
= $true )
| ( ( breln1 @ SV73 @ ( breln1compset @ SV73 @ SV377 @ SV771 ) )
= $true )
| ( ( breln1 @ SV73 @ SV377 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2562,plain,
! [SV379: $i,SV75: $i,SV772: $i] :
( ( ( ~ ( in @ SV772 @ ( powerset @ SV75 ) ) )
= $true )
| ( ( ! [SY3954: $i] :
( ~ ( in @ SY3954 @ SV75 )
| ~ ( in @ SY3954 @ ( setminus @ SV75 @ ( binunion @ SV379 @ SV772 ) ) )
| ( in @ SY3954 @ ( setminus @ SV75 @ SV772 ) ) ) )
= $true )
| ( ( in @ SV379 @ ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2287]) ).
thf(2563,plain,
! [SV380: $i > $i,SV76: $i,SV622: $i] :
( ( ~ ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3287: $i] : ( SV380 @ SY3287 ) ) )
| ~ ! [SY3750: $i] :
~ ~ ( ~ ( in @ SY3750 @ SV76 )
| ( SV622
!= ( SV380 @ SY3750 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2288]) ).
thf(2564,plain,
! [SV380: $i > $i,SV622: $i,SV76: $i] :
( ( ~ ~ ! [SY3751: $i] :
~ ~ ( ~ ( in @ SY3751 @ SV76 )
| ( SV622
!= ( SV380 @ SY3751 ) ) )
| ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3290: $i] : ( SV380 @ SY3290 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2289]) ).
thf(2565,plain,
! [SV381: $i > $i,SV623: $i,SV77: $i] :
( ( ( ! [SY3753: $i] :
~ ~ ( ~ ( in @ SY3753 @ SV77 )
| ( SV623
!= ( SV381 @ SY3753 ) ) ) )
= $true )
| ( ( in @ SV623
@ ( image1 @ SV77
@ ^ [SY3293: $i] : ( SV381 @ SY3293 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2290]) ).
thf(2566,plain,
! [SV382: $i,SV773: $i,SV78: $i] :
( ( ( ~ ( breln1 @ SV78 @ SV773 ) )
= $true )
| ( ( ! [SY3955: $i] :
( ~ ( in @ SY3955 @ SV78 )
| ! [SY3956: $i] :
( ~ ( in @ SY3956 @ SV78 )
| ~ ( in @ ( kpair @ SY3955 @ SY3956 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
| ~ ! [SY3957: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3957 @ SV78 )
| ~ ( in @ ( kpair @ SY3955 @ SY3957 ) @ SV382 ) )
| ~ ( in @ ( kpair @ SY3957 @ SY3956 ) @ SV773 ) ) ) ) )
= $true )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2291]) ).
thf(2567,plain,
! [SV384: $i,SV80: $i,SV625: $i] :
( ( ~ ( in @ SV625 @ ( setadjoin @ SV80 @ SV384 ) )
| ( SV625 = SV80 )
| ( in @ SV625 @ SV384 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2293]) ).
thf(2568,plain,
! [SV384: $i,SV80: $i,SV625: $i] :
( ( ~ ( ( SV625 = SV80 )
| ( in @ SV625 @ SV384 ) )
| ( in @ SV625 @ ( setadjoin @ SV80 @ SV384 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2294]) ).
thf(2569,plain,
! [SV386: $i,SV774: $i,SV82: $i] :
( ( ( ~ ( breln1 @ SV82 @ SV774 ) )
= $true )
| ( ( ! [SY3958: $i] :
( ~ ( in @ SY3958 @ SV82 )
| ! [SY3959: $i] :
( ~ ( in @ SY3959 @ SV82 )
| ~ ( in @ ( kpair @ SY3958 @ SY3959 ) @ ( binunion @ SV386 @ SV774 ) )
| ( in @ ( kpair @ SY3958 @ SY3959 ) @ SV386 )
| ( in @ ( kpair @ SY3958 @ SY3959 ) @ SV774 ) ) ) )
= $true )
| ( ( breln1 @ SV82 @ SV386 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2296]) ).
thf(2570,plain,
! [SV388: $i,SV85: $i,SV775: $i] :
( ( ( ~ ( in @ SV775 @ ( powerset @ SV85 ) ) )
= $true )
| ( ( ( setminus @ SV85 @ ( binintersect @ SV388 @ SV775 ) )
= ( binunion @ ( setminus @ SV85 @ SV388 ) @ ( setminus @ SV85 @ SV775 ) ) )
= $true )
| ( ( in @ SV388 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2297]) ).
thf(2571,plain,
! [SV389: $i,SV86: $i,SV776: $i] :
( ( ( ~ ( in @ SV776 @ ( powerset @ SV86 ) ) )
= $true )
| ( ( ! [SY3960: $i] :
( ~ ( in @ SY3960 @ SV86 )
| ~ ( subset @ SV389 @ ( setminus @ SV86 @ SV776 ) )
| ~ ( in @ SY3960 @ SV776 )
| ~ ( in @ SY3960 @ SV389 ) ) )
= $true )
| ( ( in @ SV389 @ ( powerset @ SV86 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2298]) ).
thf(2572,plain,
! [SV390: $i,SV87: $i,SV777: $i] :
( ( ( ~ ( in @ SV777 @ ( powerset @ SV87 ) ) )
= $true )
| ( ( ! [SY3961: $i] :
( ~ ( in @ SY3961 @ SV87 )
| ~ ( subset @ SV390 @ SV777 )
| ~ ~ ( in @ SY3961 @ SV777 )
| ~ ( in @ SY3961 @ SV390 ) ) )
= $true )
| ( ( in @ SV390 @ ( powerset @ SV87 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2299]) ).
thf(2573,plain,
! [SV391: $i,SV88: $i,SV778: $i] :
( ( ( ~ ( in @ SV778 @ ( powerset @ SV88 ) ) )
= $true )
| ( ( subset @ ( setminus @ SV88 @ SV391 ) @ ( setminus @ SV88 @ ( binintersect @ SV391 @ SV778 ) ) )
= $true )
| ( ( in @ SV391 @ ( powerset @ SV88 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2300]) ).
thf(2574,plain,
! [SV393: $i,SV90: $i,SV779: $i] :
( ( ( ~ ( in @ SV779 @ ( powerset @ SV90 ) ) )
= $true )
| ( ( ! [SY3962: $i] :
( ~ ( in @ SY3962 @ ( powerset @ SV90 ) )
| ! [SY3963: $i] :
( ~ ( in @ SY3963 @ SV90 )
| ~ ( in @ SY3963 @ ( binintersect @ SV393 @ SV779 ) )
| ( in @ SY3963 @ ( binintersect @ ( binunion @ SV393 @ SY3962 ) @ ( binunion @ SV779 @ SY3962 ) ) ) ) ) )
= $true )
| ( ( in @ SV393 @ ( powerset @ SV90 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2301]) ).
thf(2575,plain,
! [SV92: $i,SV394: $i,SV627: $i] :
( ( ( ~ ~ ( in @ SV627 @ SV394 ) )
= $true )
| ( ( in @ SV627 @ ( setminus @ SV92 @ SV394 ) )
= $true )
| ( ( in @ SV627 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2302]) ).
thf(2576,plain,
! [SV628: $i,SV396: $i,SV95: $i,SV861: $i] :
( ( ( ~ ( in @ SV861 @ SV95 )
| ( ( ap @ SV95 @ SV396 @ SV628 @ SV861 )
= ( ap @ SV95 @ SV396 @ SV628 @ SV861 ) ) )
= $true )
| ( ( in @ SV628 @ ( funcSet @ SV95 @ SV396 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2577,plain,
! [SV397: $i,SV96: $i,SV629: $i] :
( ( ( in @ SV629 @ ( setminus @ SV96 @ SV397 ) )
= $true )
| ( ( ~ ( in @ SV629 @ SV96 )
| ( in @ SV629 @ SV397 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2304]) ).
thf(2578,plain,
! [SV400: $i,SV99: $i,SV780: $i] :
( ( ( ~ ( in @ SV780 @ ( powerset @ SV99 ) ) )
= $true )
| ( ( ! [SY3964: $i] :
( ~ ( in @ SY3964 @ SV99 )
| ~ ( in @ SY3964 @ ( setminus @ SV99 @ ( binunion @ SV400 @ SV780 ) ) )
| ( in @ SY3964 @ ( setminus @ SV99 @ SV400 ) ) ) )
= $true )
| ( ( in @ SV400 @ ( powerset @ SV99 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2306]) ).
thf(2579,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( SV100 @ SV781 )
= $false )
| ( ( ~ ! [SY2563: $i,SY2564: $i] :
( ~ ( SV100 @ SY2563 )
| ~ ( SV100 @ SY2564 )
| ( SY2563 = SY2564 ) )
| ~ ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2307]) ).
thf(2580,plain,
! [SV402: $i,SV102: $i,SV631: $i] :
( ( ( in @ SV631 @ ( setminus @ SV102 @ SV402 ) )
= $true )
| ( ( ~ ~ ( in @ SV631 @ SV402 )
| ~ ( in @ SV631 @ SV102 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2308]) ).
thf(2581,plain,
! [SV404: $i > $o,SV104: $i,SV862: $i] :
( ( ( ~ ~ ( ~ ( in @ SV862 @ SV104 )
| ~ ~ ( SV404 @ SV862 ) ) )
= $true )
| ( ( ~ ! [SY3324: $i] :
( ~ ( in @ SY3324 @ SV104 )
| ( SV404 @ SY3324 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2582,plain,
! [SV106: $i] :
( ( ( in @ emptyset @ SV106 )
= $false )
| ( ( ~ ! [SY2577: $i] :
( ~ ~ ( ~ ( in @ SY2577 @ omega )
| ~ ( in @ SY2577 @ SV106 ) )
| ( in @ ( setadjoin @ SY2577 @ SY2577 ) @ SV106 ) ) )
= $true )
| ( ( ! [SY2578: $i] :
( ~ ( in @ SY2578 @ omega )
| ( in @ SY2578 @ SV106 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2583,plain,
! [SV633: $i,SV406: $i,SV108: $i,SV863: $i] :
( ( ( ~ ( in @ SV863 @ SV108 )
| ( singleton
@ ( dsetconstr @ SV406
@ ^ [SY4051: $i] : ( in @ ( kpair @ SV863 @ SY4051 ) @ SV633 ) ) ) )
= $true )
| ( ( func @ SV108 @ SV406 @ SV633 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2584,plain,
! [SV407: $i,SV109: $i,SV782: $i] :
( ( ( ~ ( in @ SV782 @ ( powerset @ SV109 ) ) )
= $true )
| ( ( ~ ! [SY3965: $i] :
( ~ ( in @ SY3965 @ SV109 )
| ~ ( in @ SY3965 @ SV407 )
| ( in @ SY3965 @ SV782 ) )
| ( subset @ SV407 @ SV782 ) )
= $true )
| ( ( in @ SV407 @ ( powerset @ SV109 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2314]) ).
thf(2585,plain,
! [SV408: $i,SV110: $i,SV783: $i] :
( ( ( ~ ( in @ SV783 @ ( powerset @ SV110 ) ) )
= $true )
| ( ( ! [SY3966: $i] :
( ~ ( in @ SY3966 @ SV110 )
| ~ ~ ( in @ SY3966 @ SV408 )
| ~ ( in @ SY3966 @ ( binintersect @ SV408 @ SV783 ) ) ) )
= $true )
| ( ( in @ SV408 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2315]) ).
thf(2586,plain,
! [SV112: $i,SV635: $i,SV410: $i,SV864: $i] :
( ( ( ~ ( in @ SV864 @ SV410 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV635 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV635 @ ( setadjoin @ SV864 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV112 @ SV410 ) ) ) )
= $true )
| ( ( in @ SV635 @ SV112 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(2587,plain,
! [SV411: $i,SV113: $i,SV784: $i] :
( ( ( ~ ( in @ SV784 @ ( powerset @ SV113 ) ) )
= $true )
| ( ( ! [SY3967: $i] :
( ~ ( in @ SY3967 @ SV113 )
| ~ ( in @ SY3967 @ ( setminus @ SV113 @ SV411 ) )
| ( in @ SY3967 @ ( setminus @ SV113 @ ( binintersect @ SV411 @ SV784 ) ) ) ) )
= $true )
| ( ( in @ SV411 @ ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2318]) ).
thf(2588,plain,
! [SV412: $i,SV114: $i,SV785: $i] :
( ( ( ~ ( in @ SV785 @ SV114 ) )
= $true )
| ( ( ~ ( in @ SV785 @ SV412 )
| ~ ( in @ SV785 @ ( setminus @ SV114 @ SV412 ) ) )
= $true )
| ( ( in @ SV412 @ ( powerset @ SV114 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2319]) ).
thf(2589,plain,
! [SV636: $i > $i > $o,SV413: $i,SV115: $i,SV786: $i,SV746: $i] :
( ( ( ~ ( in @ ( kpair @ SV746 @ SV786 )
@ ( dpsetconstr @ SV115 @ SV413
@ ^ [SY3762: $i,SY3763: $i] : ( SV636 @ SY3762 @ SY3763 ) ) ) )
= $true )
| ( ( in @ SV746 @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2320]) ).
thf(2590,plain,
! [SV637: $i > $i > $o,SV414: $i,SV116: $i,SV787: $i,SV747: $i] :
( ( ( ~ ( in @ ( kpair @ SV747 @ SV787 )
@ ( dpsetconstr @ SV116 @ SV414
@ ^ [SY3766: $i,SY3767: $i] : ( SV637 @ SY3766 @ SY3767 ) ) ) )
= $true )
| ( ( in @ SV787 @ SV414 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2321]) ).
thf(2591,plain,
! [SV117: $i,SV415: $i,SV638: $i] :
( ( ( in @ SV638 @ SV415 )
= $false )
| ( ( in @ SV638 @ ( setminus @ SV117 @ SV415 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2592,plain,
! [SV118: $i,SV639: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV639 ) )
= $true )
| ( ( ~ ! [SY3768: $i] :
( ~ ( in @ SY3768 @ SV118 )
| ~ ( SV416 @ SY3768 )
| ( SY3768 = SV639 ) )
| ( ex1 @ SV118
@ ^ [SY3351: $i] : ( SV416 @ SY3351 ) ) )
= $true )
| ( ( in @ SV639 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2323]) ).
thf(2593,plain,
! [SV418: $i,SV120: $i,SV640: $i] :
( ( ( in @ SV640 @ SV120 )
= $true )
| ( ( ~ ~ ( in @ SV640 @ SV418 )
| ~ ( in @ SV640 @ ( symdiff @ SV120 @ SV418 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2324]) ).
thf(2594,plain,
! [SV121: $i,SV641: $i > $i,SV419: $i] :
( ( ( ~ ( in @ ( sK24_SY3770 @ SV419 @ SV641 @ SV121 ) @ SV121 )
| ( in @ ( SV641 @ ( sK24_SY3770 @ SV419 @ SV641 @ SV121 ) ) @ SV419 ) )
= $false )
| ( ( ! [SY3771: $i] :
( ~ ( in @ SY3771 @ SV121 )
| ( ( ap @ SV121 @ SV419
@ ( lam @ SV121 @ SV419
@ ^ [SY3772: $i] : ( SV641 @ SY3772 ) )
@ SY3771 )
= ( SV641 @ SY3771 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2325]) ).
thf(2595,plain,
! [SV865: $i > $o,SV788: $i > $o,SV420: $i,SV122: $i] :
( ( ( ~ ! [SY4052: $i] :
( ~ ( in @ SY4052 @ SV122 )
| ! [SY4053: $i] :
( ~ ( in @ SY4053 @ SV420 )
| ( SY4052 != SY4053 )
| ~ ( ~ ( ~ ( SV788 @ SY4052 )
| ( SV865 @ SY4053 ) )
| ~ ( ~ ( SV865 @ SY4053 )
| ( SV788 @ SY4052 ) ) ) ) )
| ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(2596,plain,
! [SV421: $i > $o,SV123: $i,SV789: $i] :
( ( ( ~ ( in @ SV789 @ SV123 ) )
= $true )
| ( ( ! [SY3977: $i] :
( ~ ( in @ SY3977 @ SV123 )
| ~ ( SV421 @ SV789 )
| ~ ( SV421 @ SY3977 )
| ( SV789 = SY3977 ) ) )
= $true )
| ( ( ex1 @ SV123
@ ^ [SY3363: $i] : ( SV421 @ SY3363 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2327]) ).
thf(2597,plain,
! [SV423: $i,SV790: $i,SV125: $i] :
( ( ( ~ ( breln1 @ SV125 @ SV790 ) )
= $true )
| ( ( ! [SY3978: $i] :
( ~ ( in @ SY3978 @ SV125 )
| ! [SY3979: $i] :
( ~ ( in @ SY3979 @ SV125 )
| ~ ( in @ ( kpair @ SY3978 @ SY3979 ) @ SV790 )
| ( in @ ( kpair @ SY3978 @ SY3979 ) @ ( binunion @ SV423 @ SV790 ) ) ) ) )
= $true )
| ( ( breln1 @ SV125 @ SV423 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2329]) ).
thf(2598,plain,
! [SV642: $i,SV424: $o,SV126: $i,SV866: $i] :
( ( ( ~ ( in @ SV866 @ SV126 )
| ~ ~ SV424
| ( in @ SV866
@ ( dsetconstr @ SV126
@ ^ [SY4056: $i] :
( ~ ( ~ SV424
| ( SY4056 != SV642 ) )
| ~ ( ~ ~ SV424
| ( SY4056 != SV866 ) ) ) ) ) )
= $true )
| ( ( in @ SV642 @ SV126 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(2599,plain,
! [SV643: $i,SV126: $i,SV867: $i] :
( ( ( ~ ( in @ SV867 @ SV126 )
| ~ ~ $true
| ( in @ SV867
@ ( dsetconstr @ SV126
@ ^ [SY4057: $i] :
( ~ ( ~ $true
| ( SY4057 != SV643 ) )
| ~ ( ~ ~ $true
| ( SY4057 != SV867 ) ) ) ) ) )
= $true )
| ( ( in @ SV643 @ SV126 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(2600,plain,
! [SV644: $i,SV126: $i,SV868: $i] :
( ( ( ~ ( in @ SV868 @ SV126 )
| ~ ~ $false
| ( in @ SV868
@ ( dsetconstr @ SV126
@ ^ [SY4058: $i] :
( ~ ( ~ $false
| ( SY4058 != SV644 ) )
| ~ ( ~ ~ $false
| ( SY4058 != SV868 ) ) ) ) ) )
= $true )
| ( ( in @ SV644 @ SV126 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(2601,plain,
! [SV425: $i,SV127: $i,SV645: $i] :
( ( ( SV645 = SV127 )
= $true )
| ( ( in @ SV645 @ SV425 )
= $true )
| ( ( in @ SV645 @ ( setadjoin @ SV127 @ SV425 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2333]) ).
thf(2602,plain,
! [SV128: $i,SV426: $i,SV646: $i] :
( ( ( ~ ( in @ SV646 @ SV426 ) )
= $true )
| ( ( ~ ( in @ SV646 @ ( symdiff @ SV128 @ SV426 ) ) )
= $true )
| ( ( in @ SV646 @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2334]) ).
thf(2603,plain,
! [SV129: $i,SV791: $i] :
( ( ( in @ SV791 @ SV129 )
= $false )
| ( ( SV129 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2335]) ).
thf(2604,plain,
! [SV130: $i,SV427: $i] :
( ( ( ~ ( in @ SV427 @ ( powerset @ SV130 ) ) )
= $true )
| ( ( ! [SY3374: $i] :
( ~ ( in @ SY3374 @ SV427 )
| ( in @ SY3374 @ SV130 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2336]) ).
thf(2605,plain,
! [SV130: $i,SV427: $i] :
( ( ( ~ ! [SY3375: $i] :
( ~ ( in @ SY3375 @ SV427 )
| ( in @ SY3375 @ SV130 ) ) )
= $true )
| ( ( in @ SV427 @ ( powerset @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2337]) ).
thf(2606,plain,
! [SV428: $i,SV792: $i,SV131: $i] :
( ( ( ~ ( breln1 @ SV131 @ SV792 ) )
= $true )
| ( ( ! [SY3980: $i] :
( ~ ( in @ SY3980 @ SV131 )
| ! [SY3981: $i] :
( ~ ( in @ SY3981 @ SV131 )
| ! [SY3982: $i] :
( ~ ( in @ SY3982 @ SV131 )
| ~ ( in @ ( kpair @ SY3980 @ SY3982 ) @ SV428 )
| ~ ( in @ ( kpair @ SY3982 @ SY3981 ) @ SV792 )
| ( in @ ( kpair @ SY3980 @ SY3981 ) @ ( breln1compset @ SV131 @ SV428 @ SV792 ) ) ) ) ) )
= $true )
| ( ( breln1 @ SV131 @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2338]) ).
thf(2607,plain,
! [SV429: $i,SV132: $i,SV793: $i] :
( ( ( ~ ( in @ SV793 @ ( powerset @ SV132 ) ) )
= $true )
| ( ( in @ ( setminus @ SV132 @ ( binunion @ SV429 @ SV793 ) ) @ ( powerset @ ( setminus @ SV132 @ SV429 ) ) )
= $true )
| ( ( in @ SV429 @ ( powerset @ SV132 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2339]) ).
thf(2608,plain,
! [SV432: $i,SV794: $i,SV135: $i] :
( ( ( ~ ( breln1 @ SV135 @ SV794 ) )
= $true )
| ( ( ~ ! [SY3983: $i] :
( ~ ( in @ SY3983 @ SV135 )
| ! [SY3984: $i] :
( ~ ( in @ SY3984 @ SV135 )
| ~ ( in @ ( kpair @ SY3983 @ SY3984 ) @ SV432 )
| ( in @ ( kpair @ SY3983 @ SY3984 ) @ SV794 ) ) )
| ( subset @ SV432 @ SV794 ) )
= $true )
| ( ( breln1 @ SV135 @ SV432 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2342]) ).
thf(2609,plain,
! [SV136: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK25_SY2669 @ SV136 ) @ SV136 )
| ( ( binintersect @ ( sK25_SY2669 @ SV136 ) @ SV136 )
!= emptyset ) ) )
= $false )
| ( ( SV136 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2343]) ).
thf(2610,plain,
! [SV434: $i,SV138: $i,SV869: $i,SV795: $i] :
( ( ( ( SV795 != SV869 )
| ~ ( ~ ( ~ ( in @ SV795 @ SV138 )
| ( in @ SV869 @ SV434 ) )
| ~ ( ~ ( in @ SV869 @ SV434 )
| ( in @ SV795 @ SV138 ) ) ) )
= $true )
| ( ( SV138 = SV434 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2345]) ).
thf(2611,plain,
! [SV435: $i,SV139: $i,SV796: $i] :
( ( ( ~ ( in @ SV796 @ ( powerset @ SV139 ) ) )
= $true )
| ( ( ! [SY3986: $i] :
( ~ ( in @ SY3986 @ ( powerset @ SV139 ) )
| ~ ( subset @ SV435 @ SY3986 )
| ( subset @ ( binintersect @ SV435 @ SV796 ) @ SY3986 ) ) )
= $true )
| ( ( in @ SV435 @ ( powerset @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2346]) ).
thf(2612,plain,
! [SV650: $i,SV870: $i,SV436: $i,SV140: $i] :
( ( ( ~ ( breln @ SV140 @ SV436 @ SV870 )
| ~ ! [SY4059: $i] :
( ~ ( in @ SY4059 @ SV140 )
| ! [SY4060: $i] :
( ~ ( in @ SY4060 @ SV436 )
| ~ ( in @ ( kpair @ SY4059 @ SY4060 ) @ SV650 )
| ( in @ ( kpair @ SY4059 @ SY4060 ) @ SV870 ) ) )
| ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) )
| ( SV650 = SV870 ) )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2347]) ).
thf(2613,plain,
! [SV141: $i,SV651: $i,SV437: $i,SV871: $i] :
( ( ( ~ ( in @ SV871 @ SV437 )
| ( in @ ( kpair @ SV651 @ SV871 ) @ ( cartprod @ SV141 @ SV437 ) ) )
= $true )
| ( ( in @ SV651 @ SV141 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(2614,plain,
! [SV142: $i,SV652: $i,SV438: $i,SV872: $i] :
( ( ( ~ ( in @ SV872 @ SV438 )
| ( in @ ( kpair @ SV652 @ SV872 ) @ ( powerset @ ( powerset @ ( binunion @ SV142 @ SV438 ) ) ) ) )
= $true )
| ( ( in @ SV652 @ SV142 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(2615,plain,
! [SV144: $i,SV654: $i > $i,SV440: $i] :
( ( ( ~ ( in @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) @ SV144 )
| ( in @ ( SV654 @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) ) @ SV440 ) )
= $false )
| ( ( ! [SY3787: $i] :
( ~ ( in @ SY3787 @ ( funcSet @ SV440 @ SV144 ) )
| ~ ! [SY3788: $i] :
( ~ ( in @ SY3788 @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SY3787 @ ( SV654 @ SY3788 ) )
= SY3788 ) )
| ( surjective @ SV440 @ SV144 @ SY3787 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2351]) ).
thf(2616,plain,
! [SV441: $i,SV145: $i,SV797: $i] :
( ( ( ~ ( in @ SV797 @ SV145 ) )
= $true )
| ( ( ~ ( in @ SV797 @ SV441 )
| ( in @ SV797 @ ( setminus @ SV145 @ ( setminus @ SV145 @ SV441 ) ) ) )
= $true )
| ( ( in @ SV441 @ ( powerset @ SV145 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2352]) ).
thf(2617,plain,
! [SV146: $i,SV442: $i > $o] :
( ( ( ~ ( in @ ( sK11_SY3407 @ SV442 @ SV146 ) @ SV146 ) )
= $false )
| ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) )
| ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2353]) ).
thf(2618,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ( ! [SY3987: $i] :
( ~ ( in @ SY3987 @ SV146 )
| ~ ( SV442 @ ( sK11_SY3407 @ SV442 @ SV146 ) )
| ~ ( SV442 @ SY3987 )
| ( ( sK11_SY3407 @ SV442 @ SV146 )
= SY3987 ) ) )
= $false )
| ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) )
| ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2353]) ).
thf(2619,plain,
! [SV443: $i,SV147: $i,SV798: $i] :
( ( ( ~ ( in @ SV798 @ ( powerset @ SV147 ) ) )
= $true )
| ( ( ! [SY3988: $i] :
( ~ ( in @ SY3988 @ SV147 )
| ~ ( in @ SY3988 @ ( setminus @ SV147 @ SV443 ) )
| ~ ( in @ SY3988 @ ( binintersect @ SV443 @ SV798 ) ) ) )
= $true )
| ( ( in @ SV443 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2354]) ).
thf(2620,plain,
! [SV444: $i,SV148: $i,SV799: $i] :
( ( ( ~ ( in @ SV799 @ ( powerset @ SV148 ) ) )
= $true )
| ( ( ! [SY3989: $i] :
( ~ ( in @ SY3989 @ ( powerset @ SV148 ) )
| ! [SY3990: $i] :
( ~ ( in @ SY3990 @ SV148 )
| ~ ( in @ SY3990 @ ( binintersect @ SV444 @ SV799 ) )
| ( in @ SY3990 @ ( binunion @ SV444 @ SY3989 ) ) ) ) )
= $true )
| ( ( in @ SV444 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2355]) ).
thf(2621,plain,
! [SV149: $i,SV445: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK27_SY3417 @ SV445 @ SV149 ) @ SV149 )
| ~ ( SV445 @ ( sK27_SY3417 @ SV445 @ SV149 ) ) ) )
= $false )
| ( ( ex1 @ SV149
@ ^ [SY3416: $i] : ( SV445 @ SY3416 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2356]) ).
thf(2622,plain,
! [SV446: $i,SV800: $i,SV150: $i] :
( ( ( ~ ( breln1 @ SV150 @ SV800 ) )
= $true )
| ( ( ! [SY3991: $i] :
( ~ ( breln1 @ SV150 @ SY3991 )
| ( ( breln1compset @ SV150 @ ( binunion @ SV446 @ SV800 ) @ SY3991 )
= ( binunion @ ( breln1compset @ SV150 @ SV446 @ SY3991 ) @ ( breln1compset @ SV150 @ SV800 @ SY3991 ) ) ) ) )
= $true )
| ( ( breln1 @ SV150 @ SV446 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2357]) ).
thf(2623,plain,
! [SV655: $i > $i > $o,SV447: $i,SV151: $i,SV801: $i,SV748: $i] :
( ( ( ~ ( in @ ( kpair @ SV748 @ SV801 )
@ ( dpsetconstr @ SV151 @ SV447
@ ^ [SY3791: $i,SY3792: $i] : ( SV655 @ SY3791 @ SY3792 ) ) ) )
= $true )
| ( ( SV655 @ SV748 @ SV801 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2358]) ).
thf(2624,plain,
! [SV152: $i > $o,SV448: $i > $o] :
( ( ( ( ( sK12_SY3425 @ SV448 @ SV152 )
!= ( sK28_SY3994 @ SV152 @ SV448 ) )
| ~ ( ~ ( ~ ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
| ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) ) )
| ~ ( ~ ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
| ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2359]) ).
thf(2625,plain,
! [SV153: $i,SV449: $i] :
( ( ( subset @ SV449 @ SV153 )
= $false )
| ( ( SV153 = SV449 )
= $true )
| ( ( subset @ SV153 @ SV449 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2360]) ).
thf(2626,plain,
! [SV657: $i,SV451: $o,SV155: $i,SV873: $i] :
( ( ( ~ ( in @ SV873 @ SV155 )
| ~ ~ SV451
| ( ( dsetconstr @ SV155
@ ^ [SY4063: $i] :
( ~ ( ~ SV451
| ( SY4063 != SV657 ) )
| ~ ( ~ ~ SV451
| ( SY4063 != SV873 ) ) ) )
= ( setadjoin @ SV873 @ emptyset ) ) )
= $true )
| ( ( in @ SV657 @ SV155 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(2627,plain,
! [SV658: $i,SV155: $i,SV874: $i] :
( ( ( ~ ( in @ SV874 @ SV155 )
| ~ ~ $true
| ( ( dsetconstr @ SV155
@ ^ [SY4064: $i] :
( ~ ( ~ $true
| ( SY4064 != SV658 ) )
| ~ ( ~ ~ $true
| ( SY4064 != SV874 ) ) ) )
= ( setadjoin @ SV874 @ emptyset ) ) )
= $true )
| ( ( in @ SV658 @ SV155 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(2628,plain,
! [SV659: $i,SV155: $i,SV875: $i] :
( ( ( ~ ( in @ SV875 @ SV155 )
| ~ ~ $false
| ( ( dsetconstr @ SV155
@ ^ [SY4065: $i] :
( ~ ( ~ $false
| ( SY4065 != SV659 ) )
| ~ ( ~ ~ $false
| ( SY4065 != SV875 ) ) ) )
= ( setadjoin @ SV875 @ emptyset ) ) )
= $true )
| ( ( in @ SV659 @ SV155 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(2629,plain,
! [SV156: $i,SV452: $i,SV660: $i] :
( ( ( ~ ( in @ SV660 @ SV452 ) )
= $true )
| ( ( in @ SV660 @ SV156 )
= $true )
| ( ( in @ SV452 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2365]) ).
thf(2630,plain,
! [SV453: $i,SV157: $i,SV802: $i] :
( ( ( ~ ( in @ SV802 @ SV157 ) )
= $true )
| ( ( ! [SY3995: $i] :
( ~ ( in @ SY3995 @ SV157 )
| ~ ( in @ ( kpair @ SV802 @ SY3995 ) @ SV453 )
| ( in @ ( kpair @ SY3995 @ SV802 ) @ ( breln1invset @ SV157 @ SV453 ) ) ) )
= $true )
| ( ( breln1 @ SV157 @ SV453 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2631,plain,
! [SV158: $i,SV661: $i,SV454: $i] :
( ( ( ~ ( subset @ SV454 @ SV661 ) )
= $true )
| ( ( subset @ SV158 @ SV661 )
= $true )
| ( ( subset @ SV158 @ SV454 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2367]) ).
thf(2632,plain,
! [SV159: $i,SV662: $i,SV455: $i > $o] :
( ( ( ~ ( SV455 @ SV662 ) )
= $true )
| ( ( ( dsetconstr @ SV159
@ ^ [SY3442: $i] : ( SV455 @ SY3442 ) )
!= emptyset )
= $true )
| ( ( in @ SV662 @ SV159 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2368]) ).
thf(2633,plain,
! [SV456: $i,SV160: $i,SV663: $i] :
( ( ( ~ ( in @ SV663 @ SV160 ) )
= $true )
| ( ( in @ SV663 @ SV456 )
= $true )
| ( ( subset @ SV160 @ SV456 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2369]) ).
thf(2634,plain,
! [SV458: $i,SV162: $i,SV803: $i] :
( ( ( ~ ( in @ SV803 @ ( powerset @ SV162 ) ) )
= $true )
| ( ( in @ ( setminus @ SV162 @ ( binunion @ SV458 @ SV803 ) ) @ ( powerset @ ( setminus @ SV162 @ SV458 ) ) )
= $true )
| ( ( in @ SV458 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2370]) ).
thf(2635,plain,
! [SV459: $i,SV163: $i,SV804: $i] :
( ( ( ~ ( in @ SV804 @ ( powerset @ SV163 ) ) )
= $true )
| ( ( ! [SY3996: $i] :
( ~ ( in @ SY3996 @ ( powerset @ SV163 ) )
| ~ ( subset @ SV804 @ SY3996 )
| ( subset @ ( binintersect @ SV459 @ SV804 ) @ SY3996 ) ) )
= $true )
| ( ( in @ SV459 @ ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2371]) ).
thf(2636,plain,
! [SV460: $i,SV164: $i,SV664: $i] :
( ( ( in @ SV664 @ SV164 )
= $true )
| ( ( ~ ( in @ SV664 @ ( setminus @ SV164 @ SV460 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2372]) ).
thf(2637,plain,
! [SV462: $i,SV166: $i,SV665: $i] :
( ( ( in @ SV665 @ ( setminus @ SV166 @ SV462 ) )
= $false )
| ( ( in @ SV665 @ SV462 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2638,plain,
! [SV463: $i,SV167: $i,SV876: $i,SV805: $i] :
( ( ( ( SV805 != SV876 )
| ~ ( in @ SV805 @ SV167 )
| ( in @ SV876 @ SV463 ) )
= $true )
| ( ( SV167 = SV463 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(2639,plain,
! [SV666: $i,SV877: $i,SV464: $i,SV168: $i] :
( ( ( ~ ( breln @ SV168 @ SV464 @ SV877 )
| ~ ! [SY4066: $i] :
( ~ ( in @ SY4066 @ SV168 )
| ! [SY4067: $i] :
( ~ ( in @ SY4067 @ SV464 )
| ~ ( in @ ( kpair @ SY4066 @ SY4067 ) @ SV666 )
| ( in @ ( kpair @ SY4066 @ SY4067 ) @ SV877 ) ) )
| ( subset @ SV666 @ SV877 ) )
= $true )
| ( ( breln @ SV168 @ SV464 @ SV666 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(2640,plain,
! [SV465: $i,SV806: $i,SV169: $i] :
( ( ( ~ ( breln1 @ SV169 @ SV806 ) )
= $true )
| ( ( ! [SY3998: $i] :
( ~ ( breln1 @ SV169 @ SY3998 )
| ( ( breln1compset @ SV169 @ ( binunion @ SV465 @ SV806 ) @ SY3998 )
= ( binunion @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SY3998 ) @ ( breln1invset @ SV169 @ SV806 ) ) ) @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SY3998 ) @ ( breln1invset @ SV169 @ SV465 ) ) ) ) ) ) )
= $true )
| ( ( breln1 @ SV169 @ SV465 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2376]) ).
thf(2641,plain,
! [SV466: $i,SV171: $i,SV807: $i] :
( ( ( ~ ( in @ SV807 @ ( powerset @ SV171 ) ) )
= $true )
| ( ( ! [SY3999: $i] :
( ~ ( in @ SY3999 @ ( binintersect @ SV466 @ SV807 ) )
| ( in @ SY3999 @ SV171 ) ) )
= $true )
| ( ( in @ SV466 @ ( powerset @ SV171 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2377]) ).
thf(2642,plain,
! [SV468: $i,SV173: $i,SV808: $i] :
( ( ( ~ ( in @ SV808 @ ( powerset @ SV173 ) ) )
= $true )
| ( ( ~ ( subset @ SV468 @ ( setminus @ SV173 @ SV808 ) )
| ( subset @ SV808 @ ( setminus @ SV173 @ SV468 ) ) )
= $true )
| ( ( in @ SV468 @ ( powerset @ SV173 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2378]) ).
thf(2643,plain,
! [SV749: $i,SV667: $i,SV469: $i,SV174: $i] :
( ( ( ( kpair @ SV174 @ SV469 )
= ( kpair @ SV667 @ SV749 ) )
= $false )
| ( ( SV174 = SV667 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2379]) ).
thf(2644,plain,
! [SV175: $i,SV470: $i > $i] :
( ( ~ ! [SY3923: $i] :
~ ( ~ ( ~ ( in @ SY3923 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
| ~ ! [SY3464: $i] :
~ ~ ( ~ ( in @ SY3464 @ SV175 )
| ( SY3923
!= ( SV470 @ SY3464 ) ) ) )
| ~ ( ~ ~ ! [SY3465: $i] :
~ ~ ( ~ ( in @ SY3465 @ SV175 )
| ( SY3923
!= ( SV470 @ SY3465 ) ) )
| ( in @ SY3923 @ ( sK3_SY3462 @ SV470 @ SV175 ) ) ) )
| ~ ! [SY3926: $i] :
( ~ ! [SY3467: $i] :
~ ( ~ ( ~ ( in @ SY3467 @ SY3926 )
| ~ ! [SY3468: $i] :
~ ~ ( ~ ( in @ SY3468 @ SV175 )
| ( SY3467
!= ( SV470 @ SY3468 ) ) ) )
| ~ ( ~ ~ ! [SY3469: $i] :
~ ~ ( ~ ( in @ SY3469 @ SV175 )
| ( SY3467
!= ( SV470 @ SY3469 ) ) )
| ( in @ SY3467 @ SY3926 ) ) )
| ( ( sK3_SY3462 @ SV470 @ SV175 )
= SY3926 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2380]) ).
thf(2645,plain,
! [SV471: $i,SV176: $i,SV809: $i] :
( ( ( ~ ( in @ SV809 @ ( powerset @ SV176 ) ) )
= $true )
| ( ( in @ ( setminus @ SV471 @ SV809 ) @ ( powerset @ SV176 ) )
= $true )
| ( ( in @ SV471 @ ( powerset @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2381]) ).
thf(2646,plain,
! [SV668: $i,SV472: $i,SV177: $i] :
( ( ( ~ ( injective @ SV177 @ SV472 @ SV668 ) )
= $true )
| ( ( in @ SV668 @ ( injFuncSet @ SV177 @ SV472 ) )
= $true )
| ( ( in @ SV668 @ ( funcSet @ SV177 @ SV472 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2382]) ).
thf(2647,plain,
! [SV473: $i,SV810: $i,SV178: $i] :
( ( ( ~ ( breln1 @ SV178 @ SV810 ) )
= $true )
| ( ( ( breln1invset @ SV178 @ ( breln1compset @ SV178 @ SV473 @ SV810 ) )
= ( breln1compset @ SV178 @ ( breln1invset @ SV178 @ SV810 ) @ ( breln1invset @ SV178 @ SV473 ) ) )
= $true )
| ( ( breln1 @ SV178 @ SV473 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2383]) ).
thf(2648,plain,
! [SV180: $i,SV475: $i,SV670: $i > $i > $o] :
( ( ( ~ ( in @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV180 )
| ~ ! [SY4068: $i] :
~ ~ ( ~ ( in @ SY4068 @ SV475 )
| ~ ( SV670 @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SY4068 ) ) )
= $false )
| ( ( ! [SY3807: $i] :
( ~ ( in @ SY3807 @ ( breln1Set @ SV475 ) )
| ~ ( reflwellordering @ SV475 @ SY3807 )
| ! [SY3808: $i] :
( ~ ( in @ SY3808 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY3809: $i] :
~ ( ~ ( SV670 @ SY3808 @ SY3809 )
| ~ ! [SY3810: $i] :
( ~ ( in @ SY3810 @ SV475 )
| ~ ( SV670 @ SY3808 @ SY3810 )
| ( in @ ( kpair @ SY3809 @ SY3810 ) @ SY3807 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2385]) ).
thf(2649,plain,
! [SV181: $i,SV671: $i,SV476: $i,SV878: $i] :
( ( ( ~ ( in @ SV878 @ SV476 )
| ( in @ ( setadjoin @ ( setadjoin @ SV671 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV671 @ ( setadjoin @ SV878 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV181 @ SV476 ) ) ) ) )
= $true )
| ( ( in @ SV671 @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(2650,plain,
! [SV182: $i,SV672: $i > $i,SV477: $i] :
( ( ( ~ ( in @ ( sK30_SY3812 @ SV477 @ SV672 @ SV182 ) @ SV182 )
| ( in @ ( SV672 @ ( sK30_SY3812 @ SV477 @ SV672 @ SV182 ) ) @ SV477 ) )
= $false )
| ( ( ! [SY3813: $i] :
( ~ ( in @ SY3813 @ SV182 )
| ( ( ap @ SV182 @ SV477
@ ( lam @ SV182 @ SV477
@ ^ [SY3814: $i] : ( SV672 @ SY3814 ) )
@ SY3813 )
= ( SV672 @ SY3813 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2387]) ).
thf(2651,plain,
! [SV183: $i,SV478: $i,SV673: $i] :
( ( ( ~ ~ ( in @ SV673 @ SV478 ) )
= $true )
| ( ( ~ ( subset @ SV183 @ SV478 ) )
= $true )
| ( ( in @ SV673 @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2388]) ).
thf(2652,plain,
! [SV184: $i,SV479: $i,SV674: $i] :
( ( ( ~ ~ ( in @ SV674 @ SV479 ) )
= $true )
| ( ( SV184 != SV479 )
= $true )
| ( ( in @ SV674 @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2389]) ).
thf(2653,plain,
! [SV480: $i,SV185: $i,SV811: $i] :
( ( ( ~ ( in @ SV811 @ ( powerset @ SV185 ) ) )
= $true )
| ( ( in @ ( binintersect @ SV480 @ SV811 ) @ ( powerset @ SV185 ) )
= $true )
| ( ( in @ SV480 @ ( powerset @ SV185 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2390]) ).
thf(2654,plain,
! [SV481: $i,SV186: $i,SV812: $i] :
( ( ( ~ ( in @ SV812 @ ( powerset @ SV186 ) ) )
= $true )
| ( ( ! [SY4000: $i] :
( ~ ( in @ SY4000 @ SV186 )
| ~ ( in @ SV481 @ ( powerset @ SV812 ) )
| ~ ( in @ SY4000 @ SV481 )
| ( in @ SY4000 @ SV812 ) ) )
= $true )
| ( ( in @ SV481 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2391]) ).
thf(2655,plain,
! [SV483: $i > $o,SV188: $i,SV675: $i] :
( ( ( ~ ( ~ ( in @ SV675
@ ( dsetconstr @ SV188
@ ^ [SY3494: $i] : ( SV483 @ SY3494 ) ) )
| ( SV483 @ SV675 ) )
| ~ ( ~ ( SV483 @ SV675 )
| ( in @ SV675
@ ( dsetconstr @ SV188
@ ^ [SY3495: $i] : ( SV483 @ SY3495 ) ) ) ) )
= $false )
| ( ( in @ SV675 @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2392]) ).
thf(2656,plain,
! [SV484: $i > $o,SV189: $i,SV879: $i] :
( ( ( ~ ( in @ SV879 @ SV189 )
| ( SV484 @ SV879 ) )
= $true )
| ( ( ~ ! [SY3497: $i] :
~ ~ ( ~ ( in @ SY3497 @ SV189 )
| ~ ~ ( SV484 @ SY3497 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(2657,plain,
! [SV813: $o,SV190: $i,SV485: $i] :
( ( ( ~ ! [SY4001: $i] :
( ~ ( in @ SV485 @ SY4001 )
| ~ ( in @ SY4001 @ SV190 )
| SV813 ) )
= $true )
| ( SV813 = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2394]) ).
thf(2658,plain,
! [SV190: $i,SV485: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV485 @ SX0 )
| ~ ( in @ SX0 @ SV190 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2395]) ).
thf(2659,plain,
! [SV190: $i,SV485: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV485 @ SX0 )
| ~ ( in @ SX0 @ SV190 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2396]) ).
thf(2660,plain,
! [SV676: $i,SV486: $i,SV191: $i,SV880: $i] :
( ( ( ~ ( in @ SV880 @ SV191 )
| ! [SY4069: $i] :
( ~ ( in @ SY4069 @ SV486 )
| ~ ( in @ ( kpair @ SV880 @ SY4069 ) @ SV676 )
| ( ( ap @ SV191 @ SV486 @ SV676 @ SV880 )
= SY4069 ) ) )
= $true )
| ( ( in @ SV676 @ ( funcSet @ SV191 @ SV486 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(2661,plain,
! [SV192: $i,SV487: $i,SV677: $i] :
( ( ( ~ ( subset @ SV677 @ SV487 ) )
= $true )
| ( ( subset @ SV677 @ ( binintersect @ SV192 @ SV487 ) )
= $true )
| ( ( subset @ SV677 @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2398]) ).
thf(2662,plain,
! [SV193: $i,SV488: $i > $i,SV881: $i] :
( ( ~ ( ~ ( ~ ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
| ~ ! [SY4070: $i] :
~ ~ ( ~ ( in @ SY4070 @ SV193 )
| ( SV881
!= ( SV488 @ SY4070 ) ) ) )
| ~ ( ~ ~ ! [SY4071: $i] :
~ ~ ( ~ ( in @ SY4071 @ SV193 )
| ( SV881
!= ( SV488 @ SY4071 ) ) )
| ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2399]) ).
thf(2663,plain,
! [SV489: $i,SV194: $i,SV814: $i] :
( ( ( ~ ( in @ SV814 @ SV194 ) )
= $true )
| ( ( ~ ~ ( in @ SV814 @ ( setminus @ SV194 @ SV489 ) )
| ( in @ SV814 @ SV489 ) )
= $true )
| ( ( in @ SV489 @ ( powerset @ SV194 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2400]) ).
thf(2664,plain,
! [SV815: $i] :
( ( ( ~ ( in @ SV815 @ sK1_SX0 ) )
= $true )
| ( ( subset @ SV815 @ sK1_SX0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2402]) ).
thf(2665,plain,
( ( ! [SY3933: $i] :
( ~ ( in @ SY3933 @ sK5_SY3512 )
| ( subset @ SY3933 @ sK5_SY3512 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2403]) ).
thf(2666,plain,
( ( ~ ( in @ sK31_SY3934 @ ( binintersect @ sK1_SX0 @ sK5_SY3512 ) )
| ( subset @ sK31_SY3934 @ ( binintersect @ sK1_SX0 @ sK5_SY3512 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[2404]) ).
thf(2667,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ~ ( ~ ( SV196 @ SV816 )
| ~ ! [SY4002: $i] :
( ~ ( SV196 @ SY4002 )
| ( SV816 = SY4002 ) ) ) )
= $false )
| ( ( ~ ! [SY2855: $i] :
~ ~ ( ~ ( SV196 @ SY2855 )
| ~ ! [SY2856: $i] :
( ~ ( SV196 @ SY2856 )
| ( SY2855 = SY2856 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2405]) ).
thf(2668,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ( ( sK13_SY3515 @ SV491 @ SV197 )
!= ( sK32_SY4003 @ SV197 @ SV491 ) )
| ~ ( ~ ( ~ ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
| ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) ) )
| ~ ( ~ ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
| ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2406]) ).
thf(2669,plain,
! [SV679: $i,SV492: $i,SV199: $i] :
( ( ( ! [SY3820: $i] :
~ ~ ( ~ ( in @ SY3820 @ SV199 )
| ~ ~ ! [SY3821: $i] :
~ ~ ( ~ ( in @ SY3821 @ SV492 )
| ( SV679
!= ( kpair @ SY3820 @ SY3821 ) ) ) ) )
= $false )
| ( ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2408]) ).
thf(2670,plain,
! [SV493: $i,SV200: $i,SV817: $i] :
( ( ( ~ ( in @ SV817 @ ( powerset @ SV200 ) ) )
= $true )
| ( ( ! [SY4004: $i] :
( ~ ( in @ SY4004 @ SV200 )
| ~ ~ ( in @ SY4004 @ ( binunion @ SV493 @ SV817 ) )
| ~ ( in @ SY4004 @ SV817 ) ) )
= $true )
| ( ( in @ SV493 @ ( powerset @ SV200 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2409]) ).
thf(2671,plain,
! [SV680: $i,SV495: $o,SV202: $i,SV882: $i] :
( ( ( ~ ( in @ SV882 @ SV202 )
| ( in @ ( if @ SV202 @ SV495 @ SV680 @ SV882 ) @ SV202 ) )
= $true )
| ( ( in @ SV680 @ SV202 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(2672,plain,
! [SV681: $i,SV202: $i,SV883: $i] :
( ( ( ~ ( in @ SV883 @ SV202 )
| ( in @ ( if @ SV202 @ $true @ SV681 @ SV883 ) @ SV202 ) )
= $true )
| ( ( in @ SV681 @ SV202 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2411]) ).
thf(2673,plain,
! [SV682: $i,SV202: $i,SV884: $i] :
( ( ( ~ ( in @ SV884 @ SV202 )
| ( in @ ( if @ SV202 @ $false @ SV682 @ SV884 ) @ SV202 ) )
= $true )
| ( ( in @ SV682 @ SV202 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2412]) ).
thf(2674,plain,
! [SV885: $o,SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( ~ ( in @ SV683 @ SV203 )
| ~ ~ ( in @ SV683 @ SV496 )
| SV885 )
| ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SV885 )
| SV885 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2413]) ).
thf(2675,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( ~ ( in @ SV683 @ SV203 )
| ~ ~ ( in @ SV683 @ SV496 )
| $true )
| ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $true )
| $true )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2413]) ).
thf(2676,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( ~ ( in @ SV683 @ SV203 )
| ~ ~ ( in @ SV683 @ SV496 )
| $false )
| ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $false )
| $false )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2413]) ).
thf(2677,plain,
! [SV204: $i,SV684: $i > $i,SV497: $i] :
( ( ( ~ ( in @ ( sK33_SY3826 @ SV497 @ SV684 @ SV204 ) @ SV204 )
| ( in @ ( SV684 @ ( sK33_SY3826 @ SV497 @ SV684 @ SV204 ) ) @ SV497 ) )
= $false )
| ( ( func @ SV204 @ SV497
@ ( lam @ SV204 @ SV497
@ ^ [SY3827: $i] : ( SV684 @ SY3827 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2414]) ).
thf(2678,plain,
! [SV686: $i,SV499: $o,SV206: $i,SV886: $i] :
( ( ( ~ ( in @ SV886 @ SV206 )
| ( in @ ( if @ SV206 @ SV499 @ SV686 @ SV886 ) @ ( setadjoin @ SV686 @ ( setadjoin @ SV886 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV686 @ SV206 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(2679,plain,
! [SV687: $i,SV206: $i,SV887: $i] :
( ( ( ~ ( in @ SV887 @ SV206 )
| ( in @ ( if @ SV206 @ $true @ SV687 @ SV887 ) @ ( setadjoin @ SV687 @ ( setadjoin @ SV887 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV687 @ SV206 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(2680,plain,
! [SV688: $i,SV206: $i,SV888: $i] :
( ( ( ~ ( in @ SV888 @ SV206 )
| ( in @ ( if @ SV206 @ $false @ SV688 @ SV888 ) @ ( setadjoin @ SV688 @ ( setadjoin @ SV888 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV688 @ SV206 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2418]) ).
thf(2681,plain,
! [SV500: $i > $o,SV207: $i] :
( ( ( ! [SY3540: $i] :
~ ~ ( ~ ( in @ SY3540 @ SV207 )
| ~ ( SV500 @ SY3540 ) ) )
= $false )
| ( ( ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SV207 )
| ~ ( SV500 @ SY3541 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2682,plain,
! [SV501: $i,SV208: $i,SV818: $i] :
( ( ( ~ ( in @ SV818 @ ( powerset @ SV208 ) ) )
= $true )
| ( ( ! [SY4005: $o,SY4006: $i] :
( ~ ( in @ SY4006 @ SV208 )
| ~ ( in @ SY4006 @ ( binunion @ SV501 @ SV818 ) )
| ~ ( ~ ( in @ SY4006 @ SV501 )
| SY4005 )
| ~ ( ~ ( in @ SY4006 @ SV818 )
| SY4005 )
| SY4005 ) )
= $true )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2420]) ).
thf(2683,plain,
! [SV889: $i > $o,SV689: $i,SV502: $i,SV209: $i] :
( ( ( ~ ! [SY4072: $i] :
( ~ ( in @ SY4072 @ SV209 )
| ! [SY4073: $i] :
( ~ ( in @ SY4073 @ SV502 )
| ~ ( in @ ( kpair @ SY4072 @ SY4073 ) @ SV689 )
| ( SV889 @ ( kpair @ SY4072 @ SY4073 ) ) ) )
| ! [SY4074: $i] :
( ~ ( in @ SY4074 @ SV689 )
| ( SV889 @ SY4074 ) ) )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(2684,plain,
! [SV690: $i,SV503: $o,SV210: $i,SV890: $i] :
( ( ( ~ ( in @ SV890 @ SV210 )
| ~ SV503
| ( in @ SV690
@ ( dsetconstr @ SV210
@ ^ [SY4075: $i] :
( ~ ( ~ SV503
| ( SY4075 != SV690 ) )
| ~ ( ~ ~ SV503
| ( SY4075 != SV890 ) ) ) ) ) )
= $true )
| ( ( in @ SV690 @ SV210 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(2685,plain,
! [SV691: $i,SV210: $i,SV891: $i] :
( ( ( ~ ( in @ SV891 @ SV210 )
| ~ $true
| ( in @ SV691
@ ( dsetconstr @ SV210
@ ^ [SY4076: $i] :
( ~ ( ~ $true
| ( SY4076 != SV691 ) )
| ~ ( ~ ~ $true
| ( SY4076 != SV891 ) ) ) ) ) )
= $true )
| ( ( in @ SV691 @ SV210 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2423]) ).
thf(2686,plain,
! [SV692: $i,SV210: $i,SV892: $i] :
( ( ( ~ ( in @ SV892 @ SV210 )
| ~ $false
| ( in @ SV692
@ ( dsetconstr @ SV210
@ ^ [SY4077: $i] :
( ~ ( ~ $false
| ( SY4077 != SV692 ) )
| ~ ( ~ ~ $false
| ( SY4077 != SV892 ) ) ) ) ) )
= $true )
| ( ( in @ SV692 @ SV210 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2424]) ).
thf(2687,plain,
! [SV212: $i,SV504: $i,SV693: $i] :
( ( ( ~ ~ ( in @ SV693 @ SV504 ) )
= $true )
| ( ( ~ ( in @ SV693 @ SV212 ) )
= $true )
| ( ( subset @ SV212 @ SV504 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2425]) ).
thf(2688,plain,
! [SV750: $i,SV694: $i,SV505: $i,SV213: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV213 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV213 @ ( setadjoin @ SV505 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV694 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV694 @ ( setadjoin @ SV750 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV213 = SV694 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2426]) ).
thf(2689,plain,
! [SV508: $i,SV819: $i,SV216: $i] :
( ( ( ~ ( breln1 @ SV216 @ SV819 ) )
= $true )
| ( ( ! [SY4007: $i] :
( ~ ( in @ SY4007 @ SV216 )
| ! [SY4008: $i] :
( ~ ( in @ SY4008 @ SV216 )
| ~ ( in @ ( kpair @ SY4007 @ SY4008 ) @ ( binunion @ SV508 @ SV819 ) )
| ! [SY4009: $o] :
( ~ ( ~ ( in @ ( kpair @ SY4007 @ SY4008 ) @ SV508 )
| SY4009 )
| ~ ( ~ ( in @ ( kpair @ SY4007 @ SY4008 ) @ SV819 )
| SY4009 )
| SY4009 ) ) ) )
= $true )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2428]) ).
thf(2690,plain,
! [SV509: $i,SV217: $i,SV820: $i] :
( ( ( ~ ( in @ SV820 @ ( powerset @ SV217 ) ) )
= $true )
| ( ( ! [SY4010: $i] :
( ~ ( in @ SY4010 @ SV217 )
| ~ ( in @ SY4010 @ ( setminus @ SV217 @ ( binunion @ SV509 @ SV820 ) ) )
| ( in @ SY4010 @ ( binintersect @ ( setminus @ SV217 @ SV509 ) @ ( setminus @ SV217 @ SV820 ) ) ) ) )
= $true )
| ( ( in @ SV509 @ ( powerset @ SV217 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2429]) ).
thf(2691,plain,
! [SV510: $i > $i,SV696: $i,SV218: $i] :
( ( ( ! [SY3843: $i] :
~ ~ ( ~ ( in @ SY3843 @ SV218 )
| ( SV696
!= ( SV510 @ SY3843 ) ) ) )
= $false )
| ( ( in @ SV696
@ ( image1 @ SV218
@ ^ [SY3564: $i] : ( SV510 @ SY3564 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2430]) ).
thf(2692,plain,
! [SV511: $i,SV220: $i,SV697: $i] :
( ( ( SV697 = SV220 )
= $true )
| ( ( SV697 = SV511 )
= $true )
| ( ( in @ SV697 @ ( setadjoin @ SV220 @ ( setadjoin @ SV511 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2431]) ).
thf(2693,plain,
! [SV699: $i,SV514: $o,SV223: $i,SV893: $i] :
( ( ( ~ ( in @ SV893 @ SV223 )
| ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY4078: $i] :
( ~ ( ~ SV514
| ( SY4078 != SV699 ) )
| ~ ( ~ ~ SV514
| ( SY4078 != SV893 ) ) ) ) ) )
= $true )
| ( ( in @ SV699 @ SV223 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(2694,plain,
! [SV700: $i,SV223: $i,SV894: $i] :
( ( ( ~ ( in @ SV894 @ SV223 )
| ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY4079: $i] :
( ~ ( ~ $true
| ( SY4079 != SV700 ) )
| ~ ( ~ ~ $true
| ( SY4079 != SV894 ) ) ) ) ) )
= $true )
| ( ( in @ SV700 @ SV223 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2434]) ).
thf(2695,plain,
! [SV701: $i,SV223: $i,SV895: $i] :
( ( ( ~ ( in @ SV895 @ SV223 )
| ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY4080: $i] :
( ~ ( ~ $false
| ( SY4080 != SV701 ) )
| ~ ( ~ ~ $false
| ( SY4080 != SV895 ) ) ) ) ) )
= $true )
| ( ( in @ SV701 @ SV223 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2435]) ).
thf(2696,plain,
! [SV515: $i,SV224: $i,SV821: $i] :
( ( ( ~ ( in @ SV821 @ ( powerset @ SV224 ) ) )
= $true )
| ( ( ~ ( subset @ SV515 @ SV821 )
| ( subset @ ( setminus @ SV224 @ SV821 ) @ ( setminus @ SV224 @ SV515 ) ) )
= $true )
| ( ( in @ SV515 @ ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2436]) ).
thf(2697,plain,
! [SV751: $i,SV702: $i,SV516: $i,SV225: $i] :
( ( ( ( kpair @ SV225 @ SV516 )
= ( kpair @ SV702 @ SV751 ) )
= $false )
| ( ( SV516 = SV751 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2698,plain,
! [SV226: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY3851: $i] :
( ~ ( in @ SY3851 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY2945: $i] :
( ~ ( in @ SY2945 @ SY3851 )
| ( in @ SY2945 @ SV226 ) ) )
| ~ ! [SY3853: $i,SY3854: $i] :
( ~ ~ ( ~ ( in @ SY3853 @ SV226 )
| ~ ( in @ SY3854 @ SV226 ) )
| ~ ! [SY3855: $i] :
( ~ ( in @ SY3855 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SY3853 @ SY3855 )
| ( in @ SY3854 @ SY3855 ) )
| ~ ( ~ ( in @ SY3854 @ SY3855 )
| ( in @ SY3853 @ SY3855 ) ) ) )
| ( SY3853 = SY3854 ) ) )
| ~ ! [SY3856: $i,SY3857: $i] :
( ~ ~ ( ~ ( in @ SY3856 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY3857 @ ( sK2_SY2943 @ SV226 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3856 )
| ( in @ SX4 @ SY3857 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3857 )
| ( in @ SX4 @ SY3856 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2438]) ).
thf(2699,plain,
! [SV226: $i] :
( ( ~ ! [SY3860: $i] :
( ~ ~ ( ~ ! [SY2954: $i] :
( ~ ( in @ SY2954 @ SY3860 )
| ( in @ SY2954 @ SV226 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY3860 ) )
| ~ ! [SY3863: $i] :
~ ~ ! [SY3864: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3863 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY3864 @ SY3860 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY3863 )
| ~ ( in @ SX5 @ SY3860 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY3863 ) )
| ( in @ SY3864 @ SY3866 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2438]) ).
thf(2700,plain,
! [SV703: $i > $i > $o,SV517: $i,SV227: $i,SV752: $i] :
( ( ( in @ SV752 @ SV227 )
= $false )
| ( ( ! [SY3935: $i] :
( ~ ( in @ SY3935 @ SV517 )
| ~ ( in @ ( kpair @ SV752 @ SY3935 )
@ ( dpsetconstr @ SV227 @ SV517
@ ^ [SY3870: $i,SY3871: $i] : ( SV703 @ SY3870 @ SY3871 ) ) )
| ( SV703 @ SV752 @ SY3935 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(2701,plain,
! [SV518: $i,SV228: $i,SV704: $i] :
( ( ( ~ ( in @ SV704 @ SV228 ) )
= $true )
| ( ( in @ SV518 @ ( setunion @ SV228 ) )
= $true )
| ( ( in @ SV518 @ SV704 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2440]) ).
thf(2702,plain,
! [SV519: $i,SV229: $i,SV822: $i] :
( ( ( ~ ( in @ SV822 @ ( powerset @ SV229 ) ) )
= $true )
| ( ( ! [SY4011: $i] :
( ~ ( in @ SY4011 @ SV229 )
| ~ ~ ( in @ SY4011 @ ( binunion @ SV519 @ SV822 ) )
| ~ ( in @ SY4011 @ SV519 ) ) )
= $true )
| ( ( in @ SV519 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2441]) ).
thf(2703,plain,
! [SV520: $i,SV230: $i > $i > $o] :
( ( ( ~ ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 ) )
= $false )
| ( ( ~ ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2442]) ).
thf(2704,plain,
! [SV520: $i,SV230: $i > $i > $o] :
( ( ( ~ ! [SY4012: $i] :
~ ~ ( ~ ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SY4012 )
| ~ ! [SY4013: $i] :
( ~ ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SY4013 )
| ( SY4012 = SY4013 ) ) ) )
= $false )
| ( ( ~ ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2442]) ).
thf(2705,plain,
! [SV705: $i,SV896: $i,SV521: $i,SV231: $i] :
( ( ( ~ ( func @ SV231 @ SV521 @ SV896 )
| ~ ! [SY4081: $i] :
( ~ ( in @ SY4081 @ SV231 )
| ( ( ap @ SV231 @ SV521 @ SV705 @ SY4081 )
= ( ap @ SV231 @ SV521 @ SV896 @ SY4081 ) ) )
| ( SV705 = SV896 ) )
= $true )
| ( ( func @ SV231 @ SV521 @ SV705 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(2706,plain,
! [SV706: $i,SV522: $o,SV232: $i,SV897: $i] :
( ( ( ~ ( in @ SV897 @ SV232 )
| ~ SV522
| ( ( if @ SV232 @ SV522 @ SV706 @ SV897 )
= SV706 ) )
= $true )
| ( ( in @ SV706 @ SV232 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2444]) ).
thf(2707,plain,
! [SV707: $i,SV232: $i,SV898: $i] :
( ( ( ~ ( in @ SV898 @ SV232 )
| ~ $true
| ( ( if @ SV232 @ $true @ SV707 @ SV898 )
= SV707 ) )
= $true )
| ( ( in @ SV707 @ SV232 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2445]) ).
thf(2708,plain,
! [SV708: $i,SV232: $i,SV899: $i] :
( ( ( ~ ( in @ SV899 @ SV232 )
| ~ $false
| ( ( if @ SV232 @ $false @ SV708 @ SV899 )
= SV708 ) )
= $true )
| ( ( in @ SV708 @ SV232 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2446]) ).
thf(2709,plain,
! [SV823: $i > $o,SV523: $i,SV233: $i] :
( ( ( ~ ! [SY4014: $i] :
( ~ ( in @ SY4014 @ SV233 )
| ! [SY4015: $i] :
( ~ ( in @ SY4015 @ SV233 )
| ~ ( in @ ( kpair @ SY4014 @ SY4015 ) @ SV523 )
| ( SV823 @ ( kpair @ SY4014 @ SY4015 ) ) ) ) )
= $true )
| ( ( ! [SY4016: $i] :
( ~ ( in @ SY4016 @ SV523 )
| ( SV823 @ SY4016 ) ) )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(2710,plain,
! [SV524: $i,SV234: $i] :
( ( ( ~ ( in @ ( sK15_SY3598 @ SV234 @ SV524 ) @ SV524 ) )
= $false )
| ( ( in @ SV524 @ ( powerset @ SV234 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2448]) ).
thf(2711,plain,
! [SV524: $i,SV234: $i] :
( ( ( in @ ( sK15_SY3598 @ SV234 @ SV524 ) @ SV234 )
= $false )
| ( ( in @ SV524 @ ( powerset @ SV234 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2448]) ).
thf(2712,plain,
! [SV235: $i,SV525: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK34_SY3599 @ SV525 @ SV235 ) @ SV235 )
| ~ ( in @ SV525 @ ( sK34_SY3599 @ SV525 @ SV235 ) ) ) )
= $false )
| ( ( in @ SV525 @ ( setunion @ SV235 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2449]) ).
thf(2713,plain,
! [SV528: $i,SV239: $i,SV710: $i] :
( ( ( in @ SV710 @ SV239 )
= $true )
| ( ( in @ SV710 @ SV528 )
= $true )
| ( ( in @ SV710 @ ( binunion @ SV239 @ SV528 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2451]) ).
thf(2714,plain,
! [SV711: $i,SV529: $i,SV240: $i,SV900: $i] :
( ( ( ~ ( in @ SV900 @ SV240 )
| ( in @ ( kpair @ SV900 @ ( ap @ SV240 @ SV529 @ SV711 @ SV900 ) ) @ SV711 ) )
= $true )
| ( ( func @ SV240 @ SV529 @ SV711 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(2715,plain,
! [SV530: $i,SV241: $i,SV824: $i] :
( ( ( ~ ( in @ SV824 @ ( powerset @ SV241 ) ) )
= $true )
| ( ( in @ ( setminus @ SV241 @ SV530 ) @ ( powerset @ ( setminus @ SV241 @ ( binintersect @ SV530 @ SV824 ) ) ) )
= $true )
| ( ( in @ SV530 @ ( powerset @ SV241 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2453]) ).
thf(2716,plain,
! [SV242: $i] :
( ( ( ~ ( in @ ( sK35_SY3006 @ SV242 ) @ SV242 ) )
= $false )
| ( ( SV242 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2454]) ).
thf(2717,plain,
! [SV531: $i,SV243: $i,SV825: $i] :
( ( ( ~ ( in @ SV825 @ ( powerset @ SV243 ) ) )
= $true )
| ( ( ! [SY4017: $i] :
( ~ ( in @ SY4017 @ ( powerset @ SV243 ) )
| ( in @ ( binintersect @ SV531 @ SV825 ) @ ( powerset @ ( binintersect @ ( binunion @ SV531 @ SY4017 ) @ ( binunion @ SV825 @ SY4017 ) ) ) ) ) )
= $true )
| ( ( in @ SV531 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2455]) ).
thf(2718,plain,
! [SV532: $i,SV244: $i,SV826: $i] :
( ( ( ~ ( in @ SV826 @ SV244 ) )
= $true )
| ( ( ~ ( in @ SV826 @ ( setminus @ SV244 @ ( setminus @ SV244 @ SV532 ) ) )
| ( in @ SV826 @ SV532 ) )
= $true )
| ( ( in @ SV532 @ ( powerset @ SV244 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2456]) ).
thf(2719,plain,
! [SV533: $i > $o,SV245: $i,SV901: $i] :
( ( ( ~ ~ ( ~ ( in @ SV901 @ SV245 )
| ~ ( SV533 @ SV901 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV245
@ ^ [SY3609: $i] : ( SV533 @ SY3609 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2457]) ).
thf(2720,plain,
! [SV712: $i,SV534: $i,SV246: $i,SV902: $i] :
( ( ( ~ ( in @ SV902 @ SV246 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV534
@ ^ [SY4082: $i] : ( in @ ( kpair @ SV902 @ SY4082 ) @ SV712 ) ) )
@ SV534 ) )
= $true )
| ( ( func @ SV246 @ SV534 @ SV712 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(2721,plain,
! [SV535: $i,SV247: $i,SV827: $i] :
( ( ( ~ ( in @ SV827 @ SV247 ) )
= $true )
| ( ( ! [SY4018: $i] :
( ~ ( in @ SY4018 @ SV247 )
| ~ ( in @ ( kpair @ SY4018 @ SV827 ) @ ( breln1invset @ SV247 @ SV535 ) )
| ( in @ ( kpair @ SV827 @ SY4018 ) @ SV535 ) ) )
= $true )
| ( ( breln1 @ SV247 @ SV535 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2459]) ).
thf(2722,plain,
! [SV249: $i] :
( ( ( in @ ( sK7_SY3023 @ SV249 ) @ SV249 )
= $true )
| ( ( ! [SY3024: $i] :
( ~ ( in @ SY3024 @ SV249 )
| ( subset @ SY3024 @ SV249 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2460]) ).
thf(2723,plain,
! [SV249: $i,SV903: $i] :
( ( ( ~ ( in @ SV903 @ SV249 )
| ( subset @ SV903 @ SV249 ) )
= $true )
| ( ( subset @ ( sK7_SY3023 @ SV249 ) @ SV249 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(2724,plain,
! [SV537: $i,SV250: $i,SV713: $i] :
( ( ( SV713 = SV250 )
= $true )
| ( ( SV713 = SV537 )
= $true )
| ( ( in @ SV713 @ ( setadjoin @ SV250 @ ( setadjoin @ SV537 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2462]) ).
thf(2725,plain,
! [SV538: $i,SV251: $i,SV828: $i] :
( ( ( ~ ( in @ SV828 @ ( powerset @ SV251 ) ) )
= $true )
| ( ( ! [SY4019: $i] :
( ~ ( in @ SY4019 @ SV251 )
| ~ ~ ( in @ SY4019 @ SV538 )
| ~ ~ ( in @ SY4019 @ SV828 )
| ~ ( in @ SY4019 @ ( binunion @ SV538 @ SV828 ) ) ) )
= $true )
| ( ( in @ SV538 @ ( powerset @ SV251 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2463]) ).
thf(2726,plain,
! [SV714: $i,SV539: $o,SV252: $i,SV904: $i] :
( ( ( ~ ( in @ SV904 @ SV252 )
| ~ SV539
| ( ( dsetconstr @ SV252
@ ^ [SY4083: $i] :
( ~ ( ~ SV539
| ( SY4083 != SV714 ) )
| ~ ( ~ ~ SV539
| ( SY4083 != SV904 ) ) ) )
= ( setadjoin @ SV714 @ emptyset ) ) )
= $true )
| ( ( in @ SV714 @ SV252 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2464]) ).
thf(2727,plain,
! [SV715: $i,SV252: $i,SV905: $i] :
( ( ( ~ ( in @ SV905 @ SV252 )
| ~ $true
| ( ( dsetconstr @ SV252
@ ^ [SY4084: $i] :
( ~ ( ~ $true
| ( SY4084 != SV715 ) )
| ~ ( ~ ~ $true
| ( SY4084 != SV905 ) ) ) )
= ( setadjoin @ SV715 @ emptyset ) ) )
= $true )
| ( ( in @ SV715 @ SV252 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2465]) ).
thf(2728,plain,
! [SV716: $i,SV252: $i,SV906: $i] :
( ( ( ~ ( in @ SV906 @ SV252 )
| ~ $false
| ( ( dsetconstr @ SV252
@ ^ [SY4085: $i] :
( ~ ( ~ $false
| ( SY4085 != SV716 ) )
| ~ ( ~ ~ $false
| ( SY4085 != SV906 ) ) ) )
= ( setadjoin @ SV716 @ emptyset ) ) )
= $true )
| ( ( in @ SV716 @ SV252 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(2729,plain,
! [SV717: $i,SV541: $i,SV254: $i,SV907: $i] :
( ( ( ~ ( in @ SV907 @ SV254 )
| ( ( ap @ SV254 @ SV541 @ SV717 @ SV907 )
= ( ap @ SV254 @ SV541 @ SV717 @ SV907 ) ) )
= $true )
| ( ( func @ SV254 @ SV541 @ SV717 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2467]) ).
thf(2730,plain,
! [SV753: $i,SV718: $i,SV543: $i,SV256: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV256 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV256 @ ( setadjoin @ SV543 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV718 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV718 @ ( setadjoin @ SV753 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( ( SV718 != SV753 )
| ( SV543 = SV753 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2468]) ).
thf(2731,plain,
! [SV719: $i,SV548: $i,SV259: $i,SV908: $i] :
( ( ( ~ ( in @ SV908 @ SV259 )
| ! [SY4086: $i] :
( ~ ( in @ SY4086 @ SV548 )
| ~ ( in @ ( kpair @ SV908 @ SY4086 ) @ SV719 )
| ( ( ap @ SV259 @ SV548 @ SV719 @ SV908 )
= SY4086 ) ) )
= $true )
| ( ( func @ SV259 @ SV548 @ SV719 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(2732,plain,
! [SV549: $i,SV829: $i,SV260: $i] :
( ( ( ~ ( breln1 @ SV260 @ SV829 ) )
= $true )
| ( ( ~ ! [SY4020: $i] :
( ~ ( in @ SY4020 @ SV260 )
| ! [SY4021: $i] :
( ~ ( in @ SY4021 @ SV260 )
| ~ ( in @ ( kpair @ SY4020 @ SY4021 ) @ SV549 )
| ( in @ ( kpair @ SY4020 @ SY4021 ) @ SV829 ) ) )
| ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) )
| ( SV549 = SV829 ) )
= $true )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2470]) ).
thf(2733,plain,
! [SV263: $i,SV552: $i,SV721: $i] :
( ( ( ~ ( in @ SV721 @ SV552 ) )
= $true )
| ( ( in @ SV721 @ ( binintersect @ SV263 @ SV552 ) )
= $true )
| ( ( in @ SV721 @ SV263 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2472]) ).
thf(2734,plain,
! [SV553: $i,SV830: $i,SV264: $i] :
( ( ( ~ ( breln1 @ SV264 @ SV830 ) )
= $true )
| ( ( ! [SY4024: $i] :
( ~ ( in @ SY4024 @ SV264 )
| ! [SY4025: $i] :
( ~ ( in @ SY4025 @ SV264 )
| ~ ( ( in @ ( kpair @ SY4024 @ SY4025 ) @ SV553 )
| ( in @ ( kpair @ SY4024 @ SY4025 ) @ SV830 ) )
| ( in @ ( kpair @ SY4024 @ SY4025 ) @ ( binunion @ SV553 @ SV830 ) ) ) ) )
= $true )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2735,plain,
! [SV265: $i,SV722: $i,SV554: $i,SV909: $i] :
( ( ( ~ ( in @ SV909 @ SV554 )
| ( subset @ ( setadjoin @ SV722 @ ( setadjoin @ SV909 @ emptyset ) ) @ ( binunion @ SV265 @ SV554 ) ) )
= $true )
| ( ( in @ SV722 @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2474]) ).
thf(2736,plain,
! [SV555: $i,SV266: $i,SV831: $i] :
( ( ( ~ ( in @ SV831 @ ( powerset @ SV266 ) ) )
= $true )
| ( ( in @ ( setminus @ SV266 @ SV555 ) @ ( powerset @ ( setminus @ SV266 @ ( binintersect @ SV555 @ SV831 ) ) ) )
= $true )
| ( ( in @ SV555 @ ( powerset @ SV266 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2475]) ).
thf(2737,plain,
! [SV558: $i,SV270: $i,SV832: $i] :
( ( ( ~ ( in @ SV832 @ ( powerset @ SV270 ) ) )
= $true )
| ( ( ( setminus @ SV270 @ ( binunion @ SV558 @ SV832 ) )
= ( binintersect @ ( setminus @ SV270 @ SV558 ) @ ( setminus @ SV270 @ SV832 ) ) )
= $true )
| ( ( in @ SV558 @ ( powerset @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(2738,plain,
! [SV833: $i > $o,SV559: $i,SV271: $i] :
( ( ( ~ ! [SY4026: $i] :
( ~ ( in @ SY4026 @ SV271 )
| ! [SY4027: $i] :
( ~ ( in @ SY4027 @ SV271 )
| ~ ( in @ ( kpair @ SY4026 @ SY4027 ) @ SV559 )
| ( SV833 @ ( kpair @ SY4026 @ SY4027 ) ) ) ) )
= $true )
| ( ( ! [SY4028: $i] :
( ~ ( in @ SY4028 @ SV559 )
| ( SV833 @ SY4028 ) ) )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2479]) ).
thf(2739,plain,
! [SV272: $i,SV560: $i,SV725: $i] :
( ( ( ~ ~ ( in @ SV725 @ SV560 ) )
= $true )
| ( ( in @ SV725 @ ( symdiff @ SV272 @ SV560 ) )
= $true )
| ( ( in @ SV725 @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2480]) ).
thf(2740,plain,
! [SV273: $i,SV726: $i,SV561: $i,SV910: $i] :
( ( ( ~ ( in @ SV910 @ SV561 )
| ( ( kfst @ ( kpair @ SV726 @ SV910 ) )
= SV726 ) )
= $true )
| ( ( in @ SV726 @ SV273 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2481]) ).
thf(2741,plain,
! [SV562: $i,SV274: $i,SV834: $i] :
( ( ( ~ ( in @ SV834 @ ( powerset @ SV274 ) ) )
= $true )
| ( ( ~ ( subset @ ( setminus @ SV274 @ SV834 ) @ ( setminus @ SV274 @ SV562 ) )
| ( subset @ SV562 @ SV834 ) )
= $true )
| ( ( in @ SV562 @ ( powerset @ SV274 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2482]) ).
thf(2742,plain,
! [SV275: $i,SV563: $i > $o] :
( ( ( ~ ( in @ ( sK16_SY3653 @ SV563 @ SV275 ) @ SV275 ) )
= $false )
| ( ( ~ ~ ! [SY3654: $i] :
~ ~ ( ~ ( in @ SY3654 @ SV275 )
| ~ ( SV563 @ SY3654 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2483]) ).
thf(2743,plain,
! [SV275: $i,SV563: $i > $o] :
( ( ( ~ ( SV563 @ ( sK16_SY3653 @ SV563 @ SV275 ) ) )
= $false )
| ( ( ~ ~ ! [SY3654: $i] :
~ ~ ( ~ ( in @ SY3654 @ SV275 )
| ~ ( SV563 @ SY3654 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2483]) ).
thf(2744,plain,
! [SV565: $i,SV277: $i,SV835: $i] :
( ( ( ~ ( in @ SV835 @ ( powerset @ SV277 ) ) )
= $true )
| ( ( ! [SY4029: $i] :
( ~ ( in @ SY4029 @ SV277 )
| ~ ( in @ SY4029 @ ( setminus @ SV277 @ ( binunion @ SV565 @ SV835 ) ) )
| ( in @ SY4029 @ ( setminus @ SV277 @ SV565 ) ) ) )
= $true )
| ( ( in @ SV565 @ ( powerset @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2484]) ).
thf(2745,plain,
! [SV278: $i,SV566: $i] :
( ( ( ~ ( in @ ( sK17_SY3657 @ SV566 @ SV278 ) @ SV278 ) )
= $false )
| ( ( ~ ! [SY3658: $i] :
( ~ ( in @ SY3658 @ SV566 )
| ( in @ SY3658 @ SV278 ) )
| ( SV278 = SV566 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2485]) ).
thf(2746,plain,
! [SV278: $i,SV566: $i] :
( ( ( in @ ( sK17_SY3657 @ SV566 @ SV278 ) @ SV566 )
= $false )
| ( ( ~ ! [SY3658: $i] :
( ~ ( in @ SY3658 @ SV566 )
| ( in @ SY3658 @ SV278 ) )
| ( SV278 = SV566 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2485]) ).
thf(2747,plain,
! [SV568: $i,SV836: $i,SV280: $i] :
( ( ( ~ ( breln1 @ SV280 @ SV836 ) )
= $true )
| ( ( ! [SY4030: $i] :
( ~ ( in @ SY4030 @ SV280 )
| ! [SY4031: $i] :
( ~ ( in @ SY4031 @ SV280 )
| ~ ( in @ ( kpair @ SY4030 @ SY4031 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
| ! [SY4032: $o] :
( ~ ! [SY4033: $i] :
( ~ ( in @ SY4033 @ SV280 )
| ~ ( in @ ( kpair @ SY4030 @ SY4033 ) @ SV568 )
| ~ ( in @ ( kpair @ SY4033 @ SY4031 ) @ SV836 )
| SY4032 )
| SY4032 ) ) ) )
= $true )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2487]) ).
thf(2748,plain,
! [SV570: $i,SV282: $i,SV728: $i] :
( ( ( in @ SV728 @ SV282 )
= $true )
| ( ( ~ ( in @ SV728 @ SV570 )
| ( in @ SV728 @ ( symdiff @ SV282 @ SV570 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2488]) ).
thf(2749,plain,
! [SV571: $i,SV283: $i,SV754: $i,SV729: $i] :
( ( ( in @ ( kpair @ SV729 @ SV754 ) @ ( cartprod @ SV283 @ SV571 ) )
= $false )
| ( ( in @ SV754 @ SV571 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2489]) ).
thf(2750,plain,
! [SV572: $i,SV284: $i] :
( ( ( ! [SY3668: $i] :
~ ~ ( ~ ( in @ SY3668 @ SV284 )
| ~ ( in @ SY3668 @ SV572 ) ) )
= $false )
| ( ( ( binintersect @ SV284 @ SV572 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2490]) ).
thf(2751,plain,
! [SV837: $i,SV288: $i > $o] :
( ( ( ~ ( ~ ( SV288 @ SV837 )
| ~ ! [SY4034: $i] :
( ~ ( SV288 @ SY4034 )
| ( SV837 = SY4034 ) ) ) )
= $false )
| ( ( ! [SY3119: $i,SY3120: $i] :
( ~ ( SV288 @ SY3119 )
| ~ ( SV288 @ SY3120 )
| ( SY3119 = SY3120 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2492]) ).
thf(2752,plain,
! [SV575: $i > $o,SV289: $i] :
( ( ( ! [SY3670: $i] :
~ ~ ( ~ ( in @ SY3670 @ SV289 )
| ~ ( SV575 @ SY3670 ) ) )
= $false )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV289 )
| ~ ( SV575 @ SY3671 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(2753,plain,
! [SV291: $i,SV731: $i,SV577: $i > $o] :
( ( ( ~ ( SV577 @ SV731 ) )
= $true )
| ( ( in @ SV731
@ ( dsetconstr @ SV291
@ ^ [SY3673: $i] : ( SV577 @ SY3673 ) ) )
= $true )
| ( ( in @ SV731 @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2494]) ).
thf(2754,plain,
! [SV578: $i,SV838: $i,SV292: $i] :
( ( ( ~ ( breln1 @ SV292 @ SV838 ) )
= $true )
| ( ( breln1 @ SV292 @ ( binunion @ SV578 @ SV838 ) )
= $true )
| ( ( breln1 @ SV292 @ SV578 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2495]) ).
thf(2755,plain,
! [SV732: $i > $i > $o,SV579: $i,SV293: $i,SV755: $i] :
( ( ( in @ SV755 @ SV293 )
= $false )
| ( ( ! [SY3938: $i] :
( ~ ( in @ SY3938 @ SV579 )
| ~ ( SV732 @ SV755 @ SY3938 )
| ( in @ ( kpair @ SV755 @ SY3938 )
@ ( dpsetconstr @ SV293 @ SV579
@ ^ [SY3897: $i,SY3898: $i] : ( SV732 @ SY3897 @ SY3898 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2496]) ).
thf(2756,plain,
! [SV294: $i,SV756: $i] :
( ( ( in @ SV756 @ SV294 )
= $false )
| ( ( ( setunion @ SV294 )
= SV756 )
= $true )
| ( ( singleton @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2497]) ).
thf(2757,plain,
! [SV581: $i,SV296: $i] :
( ( ( SV296 = SV581 )
= $false )
| ( ( subset @ SV296 @ SV581 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2758,plain,
! [SV582: $i,SV839: $i,SV297: $i] :
( ( ( ~ ( breln1 @ SV297 @ SV839 ) )
= $true )
| ( ( ( binunion @ SV582 @ SV839 )
= ( binunion @ SV839 @ SV582 ) )
= $true )
| ( ( breln1 @ SV297 @ SV582 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2499]) ).
thf(2759,plain,
! [SV757: $o,SV583: $i,SV298: $i,SV733: $i] :
( ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV733 @ SV298 )
| SV757 )
| ~ ( ~ ( in @ SV733 @ SV583 )
| SV757 )
| SV757 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2500]) ).
thf(2760,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV733 @ SV298 )
| $true )
| ~ ( ~ ( in @ SV733 @ SV583 )
| $true )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2761,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV733 @ SV298 )
| $false )
| ~ ( ~ ( in @ SV733 @ SV583 )
| $false )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2502]) ).
thf(2762,plain,
! [SV584: $i,SV299: $i,SV840: $i] :
( ( ( ~ ( in @ SV840 @ ( powerset @ SV299 ) ) )
= $true )
| ( ( ~ ! [SY4035: $i] :
( ~ ( in @ SY4035 @ SV299 )
| ~ ( in @ SY4035 @ SV584 )
| ( in @ SY4035 @ SV840 ) )
| ~ ! [SY4036: $i] :
( ~ ( in @ SY4036 @ SV299 )
| ~ ( in @ SY4036 @ SV840 )
| ( in @ SY4036 @ SV584 ) )
| ( SV584 = SV840 ) )
= $true )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2503]) ).
thf(2763,plain,
! [SV585: $i,SV841: $i,SV300: $i] :
( ( ( ~ ( breln1 @ SV300 @ SV841 ) )
= $true )
| ( ( ! [SY4037: $i] :
( ~ ( in @ SY4037 @ SV300 )
| ! [SY4038: $i] :
( ~ ( in @ SY4038 @ SV300 )
| ~ ( in @ ( kpair @ SY4037 @ SY4038 ) @ SV585 )
| ( in @ ( kpair @ SY4037 @ SY4038 ) @ ( binunion @ SV585 @ SV841 ) ) ) ) )
= $true )
| ( ( breln1 @ SV300 @ SV585 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2504]) ).
thf(2764,plain,
! [SV734: $i,SV911: $i,SV586: $i,SV301: $i] :
( ( ( ~ ( func @ SV301 @ SV586 @ SV911 )
| ~ ! [SY4087: $i] :
( ~ ( in @ SY4087 @ SV301 )
| ( ( ap @ SV301 @ SV586 @ SV734 @ SY4087 )
= ( ap @ SV301 @ SV586 @ SV911 @ SY4087 ) ) )
| ! [SY4088: $i] :
( ~ ( in @ SY4088 @ SV301 )
| ! [SY4089: $i] :
( ~ ( in @ SY4089 @ SV586 )
| ~ ( in @ ( kpair @ SY4088 @ SY4089 ) @ SV911 )
| ( in @ ( kpair @ SY4088 @ SY4089 ) @ SV734 ) ) ) )
= $true )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2505]) ).
thf(2765,plain,
! [SV587: $i,SV302: $i,SV842: $i] :
( ( ( ~ ( in @ SV842 @ ( powerset @ SV302 ) ) )
= $true )
| ( ( ! [SY4039: $i] :
( ~ ( in @ SY4039 @ SV302 )
| ~ ( in @ SY4039 @ ( binunion @ ( setminus @ SV302 @ SV587 ) @ ( setminus @ SV302 @ SV842 ) ) )
| ( in @ SY4039 @ ( setminus @ SV302 @ ( binintersect @ SV587 @ SV842 ) ) ) ) )
= $true )
| ( ( in @ SV587 @ ( powerset @ SV302 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2506]) ).
thf(2766,plain,
! [SV589: $i,SV305: $i,SV843: $i] :
( ( ( ~ ( in @ SV843 @ ( powerset @ SV305 ) ) )
= $true )
| ( ( ! [SY4040: $i] :
( ~ ( in @ SY4040 @ ( powerset @ SV305 ) )
| ( in @ ( binintersect @ SV589 @ SV843 ) @ ( powerset @ ( binintersect @ ( binunion @ SV589 @ SY4040 ) @ ( binunion @ SV843 @ SY4040 ) ) ) ) ) )
= $true )
| ( ( in @ SV589 @ ( powerset @ SV305 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2507]) ).
thf(2767,plain,
! [SV590: $i,SV307: $i,SV844: $i] :
( ( ( ~ ( in @ SV844 @ ( powerset @ SV307 ) ) )
= $true )
| ( ( ! [SY4041: $i] :
( ~ ( in @ SY4041 @ SV307 )
| ~ ( in @ SY4041 @ ( binintersect @ ( setminus @ SV307 @ SV590 ) @ ( setminus @ SV307 @ SV844 ) ) )
| ( in @ SY4041 @ ( setminus @ SV307 @ ( binunion @ SV590 @ SV844 ) ) ) ) )
= $true )
| ( ( in @ SV590 @ ( powerset @ SV307 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2509]) ).
thf(2768,plain,
! [SV591: $i,SV308: $i,SV845: $i] :
( ( ( ~ ( in @ SV845 @ ( powerset @ SV308 ) ) )
= $true )
| ( ( ~ ! [SY4042: $i] :
( ~ ( in @ SY4042 @ SV308 )
| ~ ( in @ SY4042 @ SV591 )
| ( in @ SY4042 @ SV845 ) )
| ( in @ SV591 @ ( powerset @ SV845 ) ) )
= $true )
| ( ( in @ SV591 @ ( powerset @ SV308 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2510]) ).
thf(2769,plain,
! [SV592: $i,SV309: $i,SV846: $i] :
( ( ( ~ ( in @ SV846 @ ( powerset @ SV309 ) ) )
= $true )
| ( ( ! [SY4043: $i] :
( ~ ( in @ SY4043 @ SV309 )
| ~ ( in @ SY4043 @ ( setminus @ SV309 @ SV592 ) )
| ~ ( in @ SY4043 @ ( setminus @ SV309 @ SV846 ) )
| ( in @ SY4043 @ ( setminus @ SV309 @ ( binunion @ SV592 @ SV846 ) ) ) ) )
= $true )
| ( ( in @ SV592 @ ( powerset @ SV309 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2511]) ).
thf(2770,plain,
! [SV311: $i,SV594: $i] :
( ( ( in @ SV594 @ ( setadjoin @ SV311 @ emptyset ) )
= $false )
| ( ( SV311 = SV594 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2512]) ).
thf(2771,plain,
! [SV313: $i,SV736: $i,SV596: $i,SV912: $i] :
( ( ( ~ ( in @ SV912 @ SV596 )
| ( in @ ( setadjoin @ SV736 @ ( setadjoin @ SV912 @ emptyset ) ) @ ( powerset @ ( binunion @ SV313 @ SV596 ) ) ) )
= $true )
| ( ( in @ SV736 @ SV313 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2514]) ).
thf(2772,plain,
! [SV314: $i,SV737: $i,SV597: $i,SV913: $i] :
( ( ( ~ ( in @ SV913 @ SV597 )
| ( ( ksnd @ ( kpair @ SV737 @ SV913 ) )
= SV913 ) )
= $true )
| ( ( in @ SV737 @ SV314 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2515]) ).
thf(2773,plain,
! [SV598: $i,SV315: $i,SV847: $i] :
( ( ( ~ ( in @ SV847 @ ( powerset @ SV315 ) ) )
= $true )
| ( ( ! [SY4044: $i] :
( ~ ( in @ SY4044 @ SV315 )
| ~ ( in @ SY4044 @ ( setminus @ SV315 @ ( binunion @ SV598 @ SV847 ) ) )
| ~ ( in @ SY4044 @ SV598 ) ) )
= $true )
| ( ( in @ SV598 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2516]) ).
thf(2774,plain,
! [SV848: $i,SV316: $i > $o] :
( ( ( ~ ( ~ ( SV316 @ SV848 )
| ~ ! [SY4045: $i] :
( ~ ( SV316 @ SY4045 )
| ( SV848 = SY4045 ) ) ) )
= $false )
| ( ( ~ ! [SY3190: $i] :
~ ! [SY3191: $i] :
~ ( ~ ( ~ ( SV316 @ SY3191 )
| ( SY3191 = SY3190 ) )
| ~ ( ( SY3191 != SY3190 )
| ( SV316 @ SY3191 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2517]) ).
thf(2775,plain,
! [SV599: $i,SV317: $i,SV849: $i] :
( ( ( ~ ( in @ SV849 @ ( powerset @ SV317 ) ) )
= $true )
| ( ( ! [SY4046: $i] :
( ~ ( in @ SY4046 @ ( powerset @ SV317 ) )
| ! [SY4047: $i] :
( ~ ( in @ SY4047 @ ( powerset @ SV317 ) )
| ~ ( subset @ SV599 @ SY4046 )
| ~ ( subset @ SV849 @ SY4047 )
| ( subset @ ( binintersect @ SV599 @ SV849 ) @ ( binintersect @ SY4046 @ SY4047 ) ) ) ) )
= $true )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2518]) ).
thf(2776,plain,
! [SV600: $i,SV318: $i,SV850: $i] :
( ( ( ~ ( in @ SV850 @ ( powerset @ SV318 ) ) )
= $true )
| ( ( ! [SY4048: $i] :
( ~ ( in @ SY4048 @ SV318 )
| ~ ~ ( in @ SY4048 @ SV850 )
| ~ ( in @ SY4048 @ ( binintersect @ SV600 @ SV850 ) ) ) )
= $true )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2519]) ).
thf(2777,plain,
! [SV914: $i > $o,SV738: $i,SV601: $i,SV319: $i] :
( ( ( ~ ! [SY4090: $i] :
( ~ ( in @ SY4090 @ SV319 )
| ! [SY4091: $i] :
( ~ ( in @ SY4091 @ SV601 )
| ~ ( in @ ( kpair @ SY4090 @ SY4091 ) @ SV738 )
| ( SV914 @ ( kpair @ SY4090 @ SY4091 ) ) ) )
| ! [SY4092: $i] :
( ~ ( in @ SY4092 @ SV738 )
| ( SV914 @ SY4092 ) ) )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2520]) ).
thf(2778,plain,
! [SV320: $i,SV602: $i] :
( ( ( ~ ( in @ ( sK18_SY3721 @ SV602 @ SV320 ) @ SV320 ) )
= $false )
| ( ( subset @ SV320 @ SV602 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2521]) ).
thf(2779,plain,
! [SV320: $i,SV602: $i] :
( ( ( in @ ( sK18_SY3721 @ SV602 @ SV320 ) @ SV602 )
= $false )
| ( ( subset @ SV320 @ SV602 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2521]) ).
thf(2780,plain,
! [SV739: $i,SV603: $o,SV321: $i,SV915: $i] :
( ( ( ~ ( in @ SV915 @ SV321 )
| ~ ~ SV603
| ( ( if @ SV321 @ SV603 @ SV739 @ SV915 )
= SV915 ) )
= $true )
| ( ( in @ SV739 @ SV321 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(2781,plain,
! [SV740: $i,SV321: $i,SV916: $i] :
( ( ( ~ ( in @ SV916 @ SV321 )
| ~ ~ $true
| ( ( if @ SV321 @ $true @ SV740 @ SV916 )
= SV916 ) )
= $true )
| ( ( in @ SV740 @ SV321 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2523]) ).
thf(2782,plain,
! [SV741: $i,SV321: $i,SV917: $i] :
( ( ( ~ ( in @ SV917 @ SV321 )
| ~ ~ $false
| ( ( if @ SV321 @ $false @ SV741 @ SV917 )
= SV917 ) )
= $true )
| ( ( in @ SV741 @ SV321 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2524]) ).
thf(2783,plain,
! [SV322: $i,SV851: $i] :
( ( ( in @ SV851 @ SV322 )
= $false )
| ( ( ~ ! [SY3211: $i] :
~ ~ ( ~ ( in @ SY3211 @ SV322 )
| ~ ~ ~ ! [SY3212: $i] :
~ ~ ( ~ ( in @ SY3212 @ SY3211 )
| ~ ( in @ SY3212 @ SV322 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2525]) ).
thf(2784,plain,
! [SV604: $i,SV323: $i,SV758: $i,SV742: $i] :
( ( ( in @ ( kpair @ SV742 @ SV758 ) @ ( cartprod @ SV323 @ SV604 ) )
= $false )
| ( ( in @ SV742 @ SV323 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2526]) ).
thf(2785,plain,
! [SV324: $i,SV605: $i] :
( ( ( ~ ( in @ ( sK19_SY3726 @ SV605 @ SV324 ) @ SV324 ) )
= $false )
| ( ( subset @ SV324 @ SV605 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2527]) ).
thf(2786,plain,
! [SV324: $i,SV605: $i] :
( ( ( in @ ( sK19_SY3726 @ SV605 @ SV324 ) @ SV605 )
= $false )
| ( ( subset @ SV324 @ SV605 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2527]) ).
thf(2787,plain,
! [SV606: $i,SV325: $i,SV852: $i] :
( ( ( ~ ( in @ SV852 @ ( powerset @ SV325 ) ) )
= $true )
| ( ( ! [SY4049: $i] :
( ~ ( in @ SY4049 @ ( powerset @ SV325 ) )
| ~ ( subset @ SV606 @ SV852 )
| ~ ( subset @ SV606 @ SY4049 )
| ( subset @ SV606 @ ( binintersect @ SV852 @ SY4049 ) ) ) )
= $true )
| ( ( in @ SV606 @ ( powerset @ SV325 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2528]) ).
thf(2788,plain,
! [SV37: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY2402 @ SV37 ) @ SV37 )
| ~ $true ) )
= $true )
| ( ( SV37 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2529]) ).
thf(2789,plain,
! [SV743: $i,SV38: $i] :
( ( ( ( omegaS @ SV38 )
!= ( omegaS @ SV743 ) )
= $true )
| ( ( SV38 = SV743 )
= $true )
| ( ( in @ SV743 @ omega )
= $false )
| ( ( in @ SV38 @ omega )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2530]) ).
thf(2790,plain,
! [SV39: $i,SV610: $i > $i,SV350: $i] :
( ( ( ~ ( in @ ( sK21_SY3733 @ SV350 @ SV610 @ SV39 ) @ SV39 ) )
= $false )
| ( ( func @ SV39 @ SV350
@ ( dpsetconstr @ SV39 @ SV350
@ ^ [SY3734: $i,SY3735: $i] :
( ( SV610 @ SY3734 )
= SY3735 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2531]) ).
thf(2791,plain,
! [SV39: $i,SV350: $i,SV610: $i > $i] :
( ( ( in @ ( SV610 @ ( sK21_SY3733 @ SV350 @ SV610 @ SV39 ) ) @ SV350 )
= $false )
| ( ( func @ SV39 @ SV350
@ ( dpsetconstr @ SV39 @ SV350
@ ^ [SY3734: $i,SY3735: $i] :
( ( SV610 @ SY3734 )
= SY3735 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2531]) ).
thf(2792,plain,
! [SV759: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ SV759 )
| ~ ! [SY3941: $i] :
( ~ ( SV40 @ SY3941 )
| ( SV759 = SY3941 ) ) )
= $true )
| ( ( ~ ! [SY2411: $i] :
~ ( SV40 @ SY2411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2532]) ).
thf(2793,plain,
! [SV41: $i,SV611: $i,SV351: $i,SV853: $i] :
( ( ( ~ ( in @ SV853 @ SV351 ) )
= $true )
| ( ( ( kpair @ SV611 @ SV853 )
= ( kpair @ SV611 @ SV853 ) )
= $true )
| ( ( in @ SV611 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2533]) ).
thf(2794,plain,
! [SV760: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV760 )
| ~ ! [SY3942: $i] :
( ~ ( SV42 @ SY3942 )
| ( SV760 = SY3942 ) ) )
= $true )
| ( ( SV42
@ ( descr
@ ^ [SY2417: $i] : ( SV42 @ SY2417 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2534]) ).
thf(2795,plain,
! [SV44: $i,SV353: $i > $o] :
( ( ( in @ ( sK9_SY3238 @ SV353 @ SV44 ) @ SV44 )
= $true )
| ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) )
| ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2535]) ).
thf(2796,plain,
! [SV44: $i,SV353: $i > $o] :
( ( ( ~ ( in @ ( sK36_SY3943 @ SV353 @ SV44 ) @ SV44 )
| ~ ( SV353 @ ( sK9_SY3238 @ SV353 @ SV44 ) )
| ~ ( SV353 @ ( sK36_SY3943 @ SV353 @ SV44 ) )
| ( ( sK9_SY3238 @ SV353 @ SV44 )
= ( sK36_SY3943 @ SV353 @ SV44 ) ) )
= $false )
| ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) )
| ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2536]) ).
thf(2797,plain,
! [SV612: $i,SV354: $i,SV45: $i,SV854: $i] :
( ( ( ~ ( in @ SV854 @ ( funcSet @ SV45 @ SV354 ) ) )
= $true )
| ( ( ~ ! [SY4050: $i] :
( ~ ( in @ SY4050 @ SV45 )
| ( ( ap @ SV45 @ SV354 @ SV612 @ SY4050 )
= ( ap @ SV45 @ SV354 @ SV854 @ SY4050 ) ) )
| ( SV612 = SV854 ) )
= $true )
| ( ( in @ SV612 @ ( funcSet @ SV45 @ SV354 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2537]) ).
thf(2798,plain,
! [SV614: $i,SV356: $i,SV47: $i,SV855: $i] :
( ( ( ~ ( in @ SV855 @ SV47 ) )
= $true )
| ( ( in @ ( kpair @ SV855 @ ( ap @ SV47 @ SV356 @ SV614 @ SV855 ) ) @ SV614 )
= $true )
| ( ( in @ SV614 @ ( funcSet @ SV47 @ SV356 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2538]) ).
thf(2799,plain,
! [SV616: $i,SV358: $i,SV49: $i,SV856: $i] :
( ( ( ~ ( in @ SV856 @ SV49 ) )
= $true )
| ( ( in @ ( ap @ SV49 @ SV358 @ SV616 @ SV856 ) @ SV358 )
= $true )
| ( ( in @ SV616 @ ( funcSet @ SV49 @ SV358 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2540]) ).
thf(2800,plain,
! [SV359: $i,SV50: $i,SV857: $i,SV761: $i] :
( ( ( SV761 != SV857 )
= $true )
| ( ( ( setadjoin @ SV50 @ SV761 )
= ( setadjoin @ SV359 @ SV857 ) )
= $true )
| ( ( SV50 = SV359 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2541]) ).
thf(2801,plain,
! [SV361: $i,SV52: $i,SV762: $i] :
( ( ( in @ SV762 @ ( powerset @ SV52 ) )
= $false )
| ( ( ! [SY3945: $i] :
( ~ ( in @ SY3945 @ ( powerset @ SV52 ) )
| ! [SY3946: $i] :
( ~ ( in @ SY3946 @ SV52 )
| ~ ( in @ SY3946 @ ( binintersect @ SV361 @ SV762 ) )
| ( in @ SY3946 @ ( binunion @ SV762 @ SY3945 ) ) ) ) )
= $true )
| ( ( in @ SV361 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2542]) ).
thf(2802,plain,
! [SV54: $i,SV618: $i > $i,SV363: $i] :
( ( ( ~ ( in @ ( sK22_SY3742 @ SV363 @ SV618 @ SV54 ) @ SV54 ) )
= $false )
| ( ( in
@ ( lam @ SV54 @ SV363
@ ^ [SY3743: $i] : ( SV618 @ SY3743 ) )
@ ( funcSet @ SV54 @ SV363 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2543]) ).
thf(2803,plain,
! [SV54: $i,SV363: $i,SV618: $i > $i] :
( ( ( in @ ( SV618 @ ( sK22_SY3742 @ SV363 @ SV618 @ SV54 ) ) @ SV363 )
= $false )
| ( ( in
@ ( lam @ SV54 @ SV363
@ ^ [SY3743: $i] : ( SV618 @ SY3743 ) )
@ ( funcSet @ SV54 @ SV363 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2543]) ).
thf(2804,plain,
! [SV364: $i,SV55: $i,SV763: $i] :
( ( ( in @ SV763 @ ( powerset @ SV55 ) )
= $false )
| ( ( ~ ( subset @ SV364 @ ( setminus @ SV55 @ SV763 ) )
| ( subset @ SV763 @ ( setminus @ SV55 @ SV364 ) ) )
= $true )
| ( ( in @ SV364 @ ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2544]) ).
thf(2805,plain,
! [SV365: $i,SV56: $i,SV764: $i] :
( ( ( in @ SV764 @ ( powerset @ SV56 ) )
= $false )
| ( ( ! [SY3947: $i] :
( ~ ( in @ SY3947 @ ( powerset @ SV56 ) )
| ! [SY3948: $i] :
( ~ ( in @ SY3948 @ ( powerset @ SV56 ) )
| ( ( setminus @ SV56 @ ( binintersect @ ( binunion @ SV365 @ SV764 ) @ ( binunion @ SY3947 @ SY3948 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV56 @ SV365 ) @ ( setminus @ SV56 @ SV764 ) ) @ ( binintersect @ ( setminus @ SV56 @ SY3947 ) @ ( setminus @ SV56 @ SY3948 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV365 @ ( powerset @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2545]) ).
thf(2806,plain,
! [SV57: $i,SV366: $i] :
( ( ( in @ SV366 @ ( setunion @ SV57 ) )
= $false )
| ( ( ~ ! [SY3265: $i] :
~ ~ ( ~ ( in @ SV366 @ SY3265 )
| ~ ( in @ SY3265 @ SV57 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2546]) ).
thf(2807,plain,
! [SV57: $i,SV366: $i] :
( ( ( ~ ! [SY3266: $i] :
~ ~ ( ~ ( in @ SV366 @ SY3266 )
| ~ ( in @ SY3266 @ SV57 ) ) )
= $false )
| ( ( in @ SV366 @ ( setunion @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2547]) ).
thf(2808,plain,
! [SV765: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV765 )
| ~ ! [SY3949: $i] :
( ~ ( SV58 @ SY3949 )
| ( SV765 = SY3949 ) ) )
= $true )
| ( ( ! [SY2464: $i,SY2465: $i] :
( ~ ( SV58 @ SY2464 )
| ~ ( SV58 @ SY2465 )
| ( SY2464 = SY2465 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2548]) ).
thf(2809,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
| ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 ) )
| ~ ( ( ( sK37_SY3950 @ SV766 @ SV59 )
!= SV766 )
| ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) ) ) ) )
= $false )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2549]) ).
thf(2810,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ~ ( SV60 @ SV767 )
| ~ ! [SY3951: $i] :
( ~ ( SV60 @ SY3951 )
| ( SV767 = SY3951 ) ) )
= $true )
| ( ( ~ ! [SY2472: $i] :
~ ~ ( ~ ( SV60 @ SY2472 )
| ~ ! [SY2473: $i] :
( ~ ( SV60 @ SY2473 )
| ( SY2472 = SY2473 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2550]) ).
thf(2811,plain,
! [SV367: $i > $o,SV61: $i,SV858: $i] :
( ( ( ~ ( in @ SV858 @ SV61 ) )
= $true )
| ( ( SV367 @ SV858 )
= $true )
| ( ( ~ ! [SY3268: $i] :
~ ~ ( ~ ( in @ SY3268 @ SV61 )
| ~ ~ ( SV367 @ SY3268 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2551]) ).
thf(2812,plain,
! [SV619: $i,SV369: $i,SV63: $i,SV859: $i] :
( ( ( ~ ( in @ SV859 @ SV63 ) )
= $true )
| ( ( in @ ( ap @ SV63 @ SV369 @ SV619 @ SV859 ) @ SV369 )
= $true )
| ( ( func @ SV63 @ SV369 @ SV619 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2552]) ).
thf(2813,plain,
! [SV64: $i,SV620: $i > $i,SV370: $i] :
( ( ( ~ ( in @ ( sK23_SY3745 @ SV370 @ SV620 @ SV64 ) @ SV64 ) )
= $false )
| ( ( ( lam @ SV64 @ SV370
@ ^ [SY3746: $i] : ( SV620 @ SY3746 ) )
= ( lam @ SV64 @ SV370
@ ^ [SY3747: $i] : ( SV620 @ SY3747 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2553]) ).
thf(2814,plain,
! [SV64: $i,SV370: $i,SV620: $i > $i] :
( ( ( in @ ( SV620 @ ( sK23_SY3745 @ SV370 @ SV620 @ SV64 ) ) @ SV370 )
= $false )
| ( ( ( lam @ SV64 @ SV370
@ ^ [SY3746: $i] : ( SV620 @ SY3746 ) )
= ( lam @ SV64 @ SV370
@ ^ [SY3747: $i] : ( SV620 @ SY3747 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2553]) ).
thf(2815,plain,
! [SV65: $i,SV371: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 )
| ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 )
| ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 ) ) )
= $true )
| ( ( SV65 = SV371 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2554]) ).
thf(2816,plain,
! [SV372: $i,SV68: $i,SV768: $i] :
( ( ( in @ SV768 @ ( powerset @ SV68 ) )
= $false )
| ( ( ~ ( subset @ SV372 @ ( setminus @ SV68 @ SV768 ) )
| ! [SY3952: $i] :
( ~ ( in @ SY3952 @ SV68 )
| ~ ( in @ SY3952 @ SV768 )
| ( in @ SY3952 @ ( setminus @ SV68 @ SV372 ) ) ) )
= $true )
| ( ( in @ SV372 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2555]) ).
thf(2817,plain,
! [SV373: $i,SV69: $i,SV769: $i] :
( ( ( in @ SV769 @ ( powerset @ SV69 ) )
= $false )
| ( ( ! [SY3953: $i] :
( ~ ( in @ SY3953 @ SV69 )
| ~ ( in @ SY3953 @ ( setminus @ SV69 @ ( binintersect @ SV373 @ SV769 ) ) )
| ( in @ SY3953 @ ( binunion @ ( setminus @ SV69 @ SV373 ) @ ( setminus @ SV69 @ SV769 ) ) ) ) )
= $true )
| ( ( in @ SV373 @ ( powerset @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2556]) ).
thf(2818,plain,
! [SV375: $i,SV71: $i,SV770: $i] :
( ( ( in @ SV770 @ ( powerset @ SV71 ) )
= $false )
| ( ( in @ ( binunion @ SV375 @ SV770 ) @ ( powerset @ SV71 ) )
= $true )
| ( ( in @ SV375 @ ( powerset @ SV71 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2557]) ).
thf(2819,plain,
! [SV376: $i,SV860: $o,SV72: $i,SV621: $i] :
( ( ( ~ ( ( SV621 != SV72 )
| SV860 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| SV860 )
| SV860 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2558]) ).
thf(2820,plain,
! [SV376: $i,SV72: $i,SV621: $i] :
( ( ( ~ ( ( SV621 != SV72 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| $true )
| $true )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2559]) ).
thf(2821,plain,
! [SV376: $i,SV72: $i,SV621: $i] :
( ( ( ~ ( ( SV621 != SV72 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| $false )
| $false )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2560]) ).
thf(2822,plain,
! [SV377: $i,SV771: $i,SV73: $i] :
( ( ( breln1 @ SV73 @ SV771 )
= $false )
| ( ( breln1 @ SV73 @ ( breln1compset @ SV73 @ SV377 @ SV771 ) )
= $true )
| ( ( breln1 @ SV73 @ SV377 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2561]) ).
thf(2823,plain,
! [SV379: $i,SV75: $i,SV772: $i] :
( ( ( in @ SV772 @ ( powerset @ SV75 ) )
= $false )
| ( ( ! [SY3954: $i] :
( ~ ( in @ SY3954 @ SV75 )
| ~ ( in @ SY3954 @ ( setminus @ SV75 @ ( binunion @ SV379 @ SV772 ) ) )
| ( in @ SY3954 @ ( setminus @ SV75 @ SV772 ) ) ) )
= $true )
| ( ( in @ SV379 @ ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2562]) ).
thf(2824,plain,
! [SV380: $i > $i,SV76: $i,SV622: $i] :
( ( ( ~ ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3287: $i] : ( SV380 @ SY3287 ) ) ) )
= $true )
| ( ( ~ ! [SY3750: $i] :
~ ~ ( ~ ( in @ SY3750 @ SV76 )
| ( SV622
!= ( SV380 @ SY3750 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2563]) ).
thf(2825,plain,
! [SV380: $i > $i,SV622: $i,SV76: $i] :
( ( ( ~ ~ ! [SY3751: $i] :
~ ~ ( ~ ( in @ SY3751 @ SV76 )
| ( SV622
!= ( SV380 @ SY3751 ) ) ) )
= $true )
| ( ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3290: $i] : ( SV380 @ SY3290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2564]) ).
thf(2826,plain,
! [SV381: $i > $i,SV623: $i,SV77: $i,SV918: $i] :
( ( ( ~ ~ ( ~ ( in @ SV918 @ SV77 )
| ( SV623
!= ( SV381 @ SV918 ) ) ) )
= $true )
| ( ( in @ SV623
@ ( image1 @ SV77
@ ^ [SY3293: $i] : ( SV381 @ SY3293 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(2827,plain,
! [SV382: $i,SV773: $i,SV78: $i] :
( ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( ! [SY3955: $i] :
( ~ ( in @ SY3955 @ SV78 )
| ! [SY3956: $i] :
( ~ ( in @ SY3956 @ SV78 )
| ~ ( in @ ( kpair @ SY3955 @ SY3956 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
| ~ ! [SY3957: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3957 @ SV78 )
| ~ ( in @ ( kpair @ SY3955 @ SY3957 ) @ SV382 ) )
| ~ ( in @ ( kpair @ SY3957 @ SY3956 ) @ SV773 ) ) ) ) )
= $true )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2566]) ).
thf(2828,plain,
! [SV384: $i,SV80: $i,SV625: $i] :
( ( ( ~ ( in @ SV625 @ ( setadjoin @ SV80 @ SV384 ) ) )
= $true )
| ( ( ( SV625 = SV80 )
| ( in @ SV625 @ SV384 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2567]) ).
thf(2829,plain,
! [SV384: $i,SV80: $i,SV625: $i] :
( ( ( ~ ( ( SV625 = SV80 )
| ( in @ SV625 @ SV384 ) ) )
= $true )
| ( ( in @ SV625 @ ( setadjoin @ SV80 @ SV384 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2568]) ).
thf(2830,plain,
! [SV386: $i,SV774: $i,SV82: $i] :
( ( ( breln1 @ SV82 @ SV774 )
= $false )
| ( ( ! [SY3958: $i] :
( ~ ( in @ SY3958 @ SV82 )
| ! [SY3959: $i] :
( ~ ( in @ SY3959 @ SV82 )
| ~ ( in @ ( kpair @ SY3958 @ SY3959 ) @ ( binunion @ SV386 @ SV774 ) )
| ( in @ ( kpair @ SY3958 @ SY3959 ) @ SV386 )
| ( in @ ( kpair @ SY3958 @ SY3959 ) @ SV774 ) ) ) )
= $true )
| ( ( breln1 @ SV82 @ SV386 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2569]) ).
thf(2831,plain,
! [SV388: $i,SV85: $i,SV775: $i] :
( ( ( in @ SV775 @ ( powerset @ SV85 ) )
= $false )
| ( ( ( setminus @ SV85 @ ( binintersect @ SV388 @ SV775 ) )
= ( binunion @ ( setminus @ SV85 @ SV388 ) @ ( setminus @ SV85 @ SV775 ) ) )
= $true )
| ( ( in @ SV388 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2570]) ).
thf(2832,plain,
! [SV389: $i,SV86: $i,SV776: $i] :
( ( ( in @ SV776 @ ( powerset @ SV86 ) )
= $false )
| ( ( ! [SY3960: $i] :
( ~ ( in @ SY3960 @ SV86 )
| ~ ( subset @ SV389 @ ( setminus @ SV86 @ SV776 ) )
| ~ ( in @ SY3960 @ SV776 )
| ~ ( in @ SY3960 @ SV389 ) ) )
= $true )
| ( ( in @ SV389 @ ( powerset @ SV86 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2571]) ).
thf(2833,plain,
! [SV390: $i,SV87: $i,SV777: $i] :
( ( ( in @ SV777 @ ( powerset @ SV87 ) )
= $false )
| ( ( ! [SY3961: $i] :
( ~ ( in @ SY3961 @ SV87 )
| ~ ( subset @ SV390 @ SV777 )
| ~ ~ ( in @ SY3961 @ SV777 )
| ~ ( in @ SY3961 @ SV390 ) ) )
= $true )
| ( ( in @ SV390 @ ( powerset @ SV87 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2834,plain,
! [SV391: $i,SV88: $i,SV778: $i] :
( ( ( in @ SV778 @ ( powerset @ SV88 ) )
= $false )
| ( ( subset @ ( setminus @ SV88 @ SV391 ) @ ( setminus @ SV88 @ ( binintersect @ SV391 @ SV778 ) ) )
= $true )
| ( ( in @ SV391 @ ( powerset @ SV88 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2573]) ).
thf(2835,plain,
! [SV393: $i,SV90: $i,SV779: $i] :
( ( ( in @ SV779 @ ( powerset @ SV90 ) )
= $false )
| ( ( ! [SY3962: $i] :
( ~ ( in @ SY3962 @ ( powerset @ SV90 ) )
| ! [SY3963: $i] :
( ~ ( in @ SY3963 @ SV90 )
| ~ ( in @ SY3963 @ ( binintersect @ SV393 @ SV779 ) )
| ( in @ SY3963 @ ( binintersect @ ( binunion @ SV393 @ SY3962 ) @ ( binunion @ SV779 @ SY3962 ) ) ) ) ) )
= $true )
| ( ( in @ SV393 @ ( powerset @ SV90 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2836,plain,
! [SV92: $i,SV394: $i,SV627: $i] :
( ( ( ~ ( in @ SV627 @ SV394 ) )
= $false )
| ( ( in @ SV627 @ ( setminus @ SV92 @ SV394 ) )
= $true )
| ( ( in @ SV627 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2837,plain,
! [SV628: $i,SV396: $i,SV95: $i,SV861: $i] :
( ( ( ~ ( in @ SV861 @ SV95 ) )
= $true )
| ( ( ( ap @ SV95 @ SV396 @ SV628 @ SV861 )
= ( ap @ SV95 @ SV396 @ SV628 @ SV861 ) )
= $true )
| ( ( in @ SV628 @ ( funcSet @ SV95 @ SV396 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2576]) ).
thf(2838,plain,
! [SV397: $i,SV96: $i,SV629: $i] :
( ( ( ~ ( in @ SV629 @ SV96 ) )
= $true )
| ( ( in @ SV629 @ SV397 )
= $true )
| ( ( in @ SV629 @ ( setminus @ SV96 @ SV397 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2577]) ).
thf(2839,plain,
! [SV400: $i,SV99: $i,SV780: $i] :
( ( ( in @ SV780 @ ( powerset @ SV99 ) )
= $false )
| ( ( ! [SY3964: $i] :
( ~ ( in @ SY3964 @ SV99 )
| ~ ( in @ SY3964 @ ( setminus @ SV99 @ ( binunion @ SV400 @ SV780 ) ) )
| ( in @ SY3964 @ ( setminus @ SV99 @ SV400 ) ) ) )
= $true )
| ( ( in @ SV400 @ ( powerset @ SV99 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2578]) ).
thf(2840,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ! [SY2563: $i,SY2564: $i] :
( ~ ( SV100 @ SY2563 )
| ~ ( SV100 @ SY2564 )
| ( SY2563 = SY2564 ) ) )
= $true )
| ( ( ~ ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2579]) ).
thf(2841,plain,
! [SV102: $i,SV402: $i,SV631: $i] :
( ( ( ~ ~ ( in @ SV631 @ SV402 ) )
= $true )
| ( ( ~ ( in @ SV631 @ SV102 ) )
= $true )
| ( ( in @ SV631 @ ( setminus @ SV102 @ SV402 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2580]) ).
thf(2842,plain,
! [SV404: $i > $o,SV104: $i,SV862: $i] :
( ( ( ~ ( ~ ( in @ SV862 @ SV104 )
| ~ ~ ( SV404 @ SV862 ) ) )
= $false )
| ( ( ~ ! [SY3324: $i] :
( ~ ( in @ SY3324 @ SV104 )
| ( SV404 @ SY3324 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2581]) ).
thf(2843,plain,
! [SV106: $i] :
( ( ( ! [SY2577: $i] :
( ~ ~ ( ~ ( in @ SY2577 @ omega )
| ~ ( in @ SY2577 @ SV106 ) )
| ( in @ ( setadjoin @ SY2577 @ SY2577 ) @ SV106 ) ) )
= $false )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( ! [SY2578: $i] :
( ~ ( in @ SY2578 @ omega )
| ( in @ SY2578 @ SV106 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2582]) ).
thf(2844,plain,
! [SV633: $i,SV406: $i,SV108: $i,SV863: $i] :
( ( ( ~ ( in @ SV863 @ SV108 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV406
@ ^ [SY4051: $i] : ( in @ ( kpair @ SV863 @ SY4051 ) @ SV633 ) ) )
= $true )
| ( ( func @ SV108 @ SV406 @ SV633 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2583]) ).
thf(2845,plain,
! [SV407: $i,SV109: $i,SV782: $i] :
( ( ( in @ SV782 @ ( powerset @ SV109 ) )
= $false )
| ( ( ~ ! [SY3965: $i] :
( ~ ( in @ SY3965 @ SV109 )
| ~ ( in @ SY3965 @ SV407 )
| ( in @ SY3965 @ SV782 ) )
| ( subset @ SV407 @ SV782 ) )
= $true )
| ( ( in @ SV407 @ ( powerset @ SV109 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2584]) ).
thf(2846,plain,
! [SV408: $i,SV110: $i,SV783: $i] :
( ( ( in @ SV783 @ ( powerset @ SV110 ) )
= $false )
| ( ( ! [SY3966: $i] :
( ~ ( in @ SY3966 @ SV110 )
| ~ ~ ( in @ SY3966 @ SV408 )
| ~ ( in @ SY3966 @ ( binintersect @ SV408 @ SV783 ) ) ) )
= $true )
| ( ( in @ SV408 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2847,plain,
! [SV112: $i,SV635: $i,SV410: $i,SV864: $i] :
( ( ( ~ ( in @ SV864 @ SV410 ) )
= $true )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV635 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV635 @ ( setadjoin @ SV864 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV112 @ SV410 ) ) )
= $true )
| ( ( in @ SV635 @ SV112 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2586]) ).
thf(2848,plain,
! [SV411: $i,SV113: $i,SV784: $i] :
( ( ( in @ SV784 @ ( powerset @ SV113 ) )
= $false )
| ( ( ! [SY3967: $i] :
( ~ ( in @ SY3967 @ SV113 )
| ~ ( in @ SY3967 @ ( setminus @ SV113 @ SV411 ) )
| ( in @ SY3967 @ ( setminus @ SV113 @ ( binintersect @ SV411 @ SV784 ) ) ) ) )
= $true )
| ( ( in @ SV411 @ ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2587]) ).
thf(2849,plain,
! [SV412: $i,SV114: $i,SV785: $i] :
( ( ( in @ SV785 @ SV114 )
= $false )
| ( ( ~ ( in @ SV785 @ SV412 )
| ~ ( in @ SV785 @ ( setminus @ SV114 @ SV412 ) ) )
= $true )
| ( ( in @ SV412 @ ( powerset @ SV114 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2588]) ).
thf(2850,plain,
! [SV636: $i > $i > $o,SV413: $i,SV115: $i,SV786: $i,SV746: $i] :
( ( ( in @ ( kpair @ SV746 @ SV786 )
@ ( dpsetconstr @ SV115 @ SV413
@ ^ [SY3762: $i,SY3763: $i] : ( SV636 @ SY3762 @ SY3763 ) ) )
= $false )
| ( ( in @ SV746 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2589]) ).
thf(2851,plain,
! [SV637: $i > $i > $o,SV414: $i,SV116: $i,SV787: $i,SV747: $i] :
( ( ( in @ ( kpair @ SV747 @ SV787 )
@ ( dpsetconstr @ SV116 @ SV414
@ ^ [SY3766: $i,SY3767: $i] : ( SV637 @ SY3766 @ SY3767 ) ) )
= $false )
| ( ( in @ SV787 @ SV414 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2590]) ).
thf(2852,plain,
! [SV118: $i,SV639: $i,SV416: $i > $o] :
( ( ( SV416 @ SV639 )
= $false )
| ( ( ~ ! [SY3768: $i] :
( ~ ( in @ SY3768 @ SV118 )
| ~ ( SV416 @ SY3768 )
| ( SY3768 = SV639 ) )
| ( ex1 @ SV118
@ ^ [SY3351: $i] : ( SV416 @ SY3351 ) ) )
= $true )
| ( ( in @ SV639 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2592]) ).
thf(2853,plain,
! [SV120: $i,SV418: $i,SV640: $i] :
( ( ( ~ ~ ( in @ SV640 @ SV418 ) )
= $true )
| ( ( ~ ( in @ SV640 @ ( symdiff @ SV120 @ SV418 ) ) )
= $true )
| ( ( in @ SV640 @ SV120 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2593]) ).
thf(2854,plain,
! [SV121: $i,SV641: $i > $i,SV419: $i] :
( ( ( ~ ( in @ ( sK24_SY3770 @ SV419 @ SV641 @ SV121 ) @ SV121 ) )
= $false )
| ( ( ! [SY3771: $i] :
( ~ ( in @ SY3771 @ SV121 )
| ( ( ap @ SV121 @ SV419
@ ( lam @ SV121 @ SV419
@ ^ [SY3772: $i] : ( SV641 @ SY3772 ) )
@ SY3771 )
= ( SV641 @ SY3771 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2594]) ).
thf(2855,plain,
! [SV121: $i,SV419: $i,SV641: $i > $i] :
( ( ( in @ ( SV641 @ ( sK24_SY3770 @ SV419 @ SV641 @ SV121 ) ) @ SV419 )
= $false )
| ( ( ! [SY3771: $i] :
( ~ ( in @ SY3771 @ SV121 )
| ( ( ap @ SV121 @ SV419
@ ( lam @ SV121 @ SV419
@ ^ [SY3772: $i] : ( SV641 @ SY3772 ) )
@ SY3771 )
= ( SV641 @ SY3771 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2594]) ).
thf(2856,plain,
! [SV865: $i > $o,SV788: $i > $o,SV420: $i,SV122: $i] :
( ( ( ~ ! [SY4052: $i] :
( ~ ( in @ SY4052 @ SV122 )
| ! [SY4053: $i] :
( ~ ( in @ SY4053 @ SV420 )
| ( SY4052 != SY4053 )
| ~ ( ~ ( ~ ( SV788 @ SY4052 )
| ( SV865 @ SY4053 ) )
| ~ ( ~ ( SV865 @ SY4053 )
| ( SV788 @ SY4052 ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2595]) ).
thf(2857,plain,
! [SV421: $i > $o,SV123: $i,SV789: $i] :
( ( ( in @ SV789 @ SV123 )
= $false )
| ( ( ! [SY3977: $i] :
( ~ ( in @ SY3977 @ SV123 )
| ~ ( SV421 @ SV789 )
| ~ ( SV421 @ SY3977 )
| ( SV789 = SY3977 ) ) )
= $true )
| ( ( ex1 @ SV123
@ ^ [SY3363: $i] : ( SV421 @ SY3363 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2596]) ).
thf(2858,plain,
! [SV423: $i,SV790: $i,SV125: $i] :
( ( ( breln1 @ SV125 @ SV790 )
= $false )
| ( ( ! [SY3978: $i] :
( ~ ( in @ SY3978 @ SV125 )
| ! [SY3979: $i] :
( ~ ( in @ SY3979 @ SV125 )
| ~ ( in @ ( kpair @ SY3978 @ SY3979 ) @ SV790 )
| ( in @ ( kpair @ SY3978 @ SY3979 ) @ ( binunion @ SV423 @ SV790 ) ) ) ) )
= $true )
| ( ( breln1 @ SV125 @ SV423 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2597]) ).
thf(2859,plain,
! [SV642: $i,SV424: $o,SV126: $i,SV866: $i] :
( ( ( ~ ( in @ SV866 @ SV126 ) )
= $true )
| ( ( ~ ~ SV424
| ( in @ SV866
@ ( dsetconstr @ SV126
@ ^ [SY4056: $i] :
( ~ ( ~ SV424
| ( SY4056 != SV642 ) )
| ~ ( ~ ~ SV424
| ( SY4056 != SV866 ) ) ) ) ) )
= $true )
| ( ( in @ SV642 @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2598]) ).
thf(2860,plain,
! [SV643: $i,SV126: $i,SV867: $i] :
( ( ( ~ ( in @ SV867 @ SV126 ) )
= $true )
| ( ( ~ ~ $true
| ( in @ SV867
@ ( dsetconstr @ SV126
@ ^ [SY4057: $i] :
( ~ ( ~ $true
| ( SY4057 != SV643 ) )
| ~ ( ~ ~ $true
| ( SY4057 != SV867 ) ) ) ) ) )
= $true )
| ( ( in @ SV643 @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2599]) ).
thf(2861,plain,
! [SV644: $i,SV126: $i,SV868: $i] :
( ( ( ~ ( in @ SV868 @ SV126 ) )
= $true )
| ( ( ~ ~ $false
| ( in @ SV868
@ ( dsetconstr @ SV126
@ ^ [SY4058: $i] :
( ~ ( ~ $false
| ( SY4058 != SV644 ) )
| ~ ( ~ ~ $false
| ( SY4058 != SV868 ) ) ) ) ) )
= $true )
| ( ( in @ SV644 @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2600]) ).
thf(2862,plain,
! [SV128: $i,SV426: $i,SV646: $i] :
( ( ( in @ SV646 @ SV426 )
= $false )
| ( ( ~ ( in @ SV646 @ ( symdiff @ SV128 @ SV426 ) ) )
= $true )
| ( ( in @ SV646 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2602]) ).
thf(2863,plain,
! [SV791: $i,SV129: $i] :
( ( ( SV129 = emptyset )
= $false )
| ( ( in @ SV791 @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2603]) ).
thf(2864,plain,
! [SV130: $i,SV427: $i] :
( ( ( in @ SV427 @ ( powerset @ SV130 ) )
= $false )
| ( ( ! [SY3374: $i] :
( ~ ( in @ SY3374 @ SV427 )
| ( in @ SY3374 @ SV130 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2604]) ).
thf(2865,plain,
! [SV130: $i,SV427: $i] :
( ( ( ! [SY3375: $i] :
( ~ ( in @ SY3375 @ SV427 )
| ( in @ SY3375 @ SV130 ) ) )
= $false )
| ( ( in @ SV427 @ ( powerset @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2605]) ).
thf(2866,plain,
! [SV428: $i,SV792: $i,SV131: $i] :
( ( ( breln1 @ SV131 @ SV792 )
= $false )
| ( ( ! [SY3980: $i] :
( ~ ( in @ SY3980 @ SV131 )
| ! [SY3981: $i] :
( ~ ( in @ SY3981 @ SV131 )
| ! [SY3982: $i] :
( ~ ( in @ SY3982 @ SV131 )
| ~ ( in @ ( kpair @ SY3980 @ SY3982 ) @ SV428 )
| ~ ( in @ ( kpair @ SY3982 @ SY3981 ) @ SV792 )
| ( in @ ( kpair @ SY3980 @ SY3981 ) @ ( breln1compset @ SV131 @ SV428 @ SV792 ) ) ) ) ) )
= $true )
| ( ( breln1 @ SV131 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2606]) ).
thf(2867,plain,
! [SV429: $i,SV132: $i,SV793: $i] :
( ( ( in @ SV793 @ ( powerset @ SV132 ) )
= $false )
| ( ( in @ ( setminus @ SV132 @ ( binunion @ SV429 @ SV793 ) ) @ ( powerset @ ( setminus @ SV132 @ SV429 ) ) )
= $true )
| ( ( in @ SV429 @ ( powerset @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2607]) ).
thf(2868,plain,
! [SV432: $i,SV794: $i,SV135: $i] :
( ( ( breln1 @ SV135 @ SV794 )
= $false )
| ( ( ~ ! [SY3983: $i] :
( ~ ( in @ SY3983 @ SV135 )
| ! [SY3984: $i] :
( ~ ( in @ SY3984 @ SV135 )
| ~ ( in @ ( kpair @ SY3983 @ SY3984 ) @ SV432 )
| ( in @ ( kpair @ SY3983 @ SY3984 ) @ SV794 ) ) )
| ( subset @ SV432 @ SV794 ) )
= $true )
| ( ( breln1 @ SV135 @ SV432 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2608]) ).
thf(2869,plain,
! [SV136: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY2669 @ SV136 ) @ SV136 )
| ( ( binintersect @ ( sK25_SY2669 @ SV136 ) @ SV136 )
!= emptyset ) ) )
= $true )
| ( ( SV136 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2609]) ).
thf(2870,plain,
! [SV434: $i,SV138: $i,SV869: $i,SV795: $i] :
( ( ( SV795 != SV869 )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV795 @ SV138 )
| ( in @ SV869 @ SV434 ) )
| ~ ( ~ ( in @ SV869 @ SV434 )
| ( in @ SV795 @ SV138 ) ) ) )
= $true )
| ( ( SV138 = SV434 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2610]) ).
thf(2871,plain,
! [SV435: $i,SV139: $i,SV796: $i] :
( ( ( in @ SV796 @ ( powerset @ SV139 ) )
= $false )
| ( ( ! [SY3986: $i] :
( ~ ( in @ SY3986 @ ( powerset @ SV139 ) )
| ~ ( subset @ SV435 @ SY3986 )
| ( subset @ ( binintersect @ SV435 @ SV796 ) @ SY3986 ) ) )
= $true )
| ( ( in @ SV435 @ ( powerset @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2611]) ).
thf(2872,plain,
! [SV650: $i,SV870: $i,SV436: $i,SV140: $i] :
( ( ( ~ ( breln @ SV140 @ SV436 @ SV870 ) )
= $true )
| ( ( ~ ! [SY4059: $i] :
( ~ ( in @ SY4059 @ SV140 )
| ! [SY4060: $i] :
( ~ ( in @ SY4060 @ SV436 )
| ~ ( in @ ( kpair @ SY4059 @ SY4060 ) @ SV650 )
| ( in @ ( kpair @ SY4059 @ SY4060 ) @ SV870 ) ) )
| ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) )
| ( SV650 = SV870 ) )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2612]) ).
thf(2873,plain,
! [SV141: $i,SV651: $i,SV437: $i,SV871: $i] :
( ( ( ~ ( in @ SV871 @ SV437 ) )
= $true )
| ( ( in @ ( kpair @ SV651 @ SV871 ) @ ( cartprod @ SV141 @ SV437 ) )
= $true )
| ( ( in @ SV651 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2613]) ).
thf(2874,plain,
! [SV142: $i,SV652: $i,SV438: $i,SV872: $i] :
( ( ( ~ ( in @ SV872 @ SV438 ) )
= $true )
| ( ( in @ ( kpair @ SV652 @ SV872 ) @ ( powerset @ ( powerset @ ( binunion @ SV142 @ SV438 ) ) ) )
= $true )
| ( ( in @ SV652 @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2614]) ).
thf(2875,plain,
! [SV144: $i,SV654: $i > $i,SV440: $i] :
( ( ( ~ ( in @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) @ SV144 ) )
= $false )
| ( ( ! [SY3787: $i] :
( ~ ( in @ SY3787 @ ( funcSet @ SV440 @ SV144 ) )
| ~ ! [SY3788: $i] :
( ~ ( in @ SY3788 @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SY3787 @ ( SV654 @ SY3788 ) )
= SY3788 ) )
| ( surjective @ SV440 @ SV144 @ SY3787 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2615]) ).
thf(2876,plain,
! [SV144: $i,SV440: $i,SV654: $i > $i] :
( ( ( in @ ( SV654 @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) ) @ SV440 )
= $false )
| ( ( ! [SY3787: $i] :
( ~ ( in @ SY3787 @ ( funcSet @ SV440 @ SV144 ) )
| ~ ! [SY3788: $i] :
( ~ ( in @ SY3788 @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SY3787 @ ( SV654 @ SY3788 ) )
= SY3788 ) )
| ( surjective @ SV440 @ SV144 @ SY3787 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2615]) ).
thf(2877,plain,
! [SV441: $i,SV145: $i,SV797: $i] :
( ( ( in @ SV797 @ SV145 )
= $false )
| ( ( ~ ( in @ SV797 @ SV441 )
| ( in @ SV797 @ ( setminus @ SV145 @ ( setminus @ SV145 @ SV441 ) ) ) )
= $true )
| ( ( in @ SV441 @ ( powerset @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2616]) ).
thf(2878,plain,
! [SV146: $i,SV442: $i > $o] :
( ( ( in @ ( sK11_SY3407 @ SV442 @ SV146 ) @ SV146 )
= $true )
| ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) )
| ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2617]) ).
thf(2879,plain,
! [SV146: $i,SV442: $i > $o] :
( ( ( ~ ( in @ ( sK38_SY3987 @ SV442 @ SV146 ) @ SV146 )
| ~ ( SV442 @ ( sK11_SY3407 @ SV442 @ SV146 ) )
| ~ ( SV442 @ ( sK38_SY3987 @ SV442 @ SV146 ) )
| ( ( sK11_SY3407 @ SV442 @ SV146 )
= ( sK38_SY3987 @ SV442 @ SV146 ) ) )
= $false )
| ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) )
| ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2618]) ).
thf(2880,plain,
! [SV443: $i,SV147: $i,SV798: $i] :
( ( ( in @ SV798 @ ( powerset @ SV147 ) )
= $false )
| ( ( ! [SY3988: $i] :
( ~ ( in @ SY3988 @ SV147 )
| ~ ( in @ SY3988 @ ( setminus @ SV147 @ SV443 ) )
| ~ ( in @ SY3988 @ ( binintersect @ SV443 @ SV798 ) ) ) )
= $true )
| ( ( in @ SV443 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2619]) ).
thf(2881,plain,
! [SV444: $i,SV148: $i,SV799: $i] :
( ( ( in @ SV799 @ ( powerset @ SV148 ) )
= $false )
| ( ( ! [SY3989: $i] :
( ~ ( in @ SY3989 @ ( powerset @ SV148 ) )
| ! [SY3990: $i] :
( ~ ( in @ SY3990 @ SV148 )
| ~ ( in @ SY3990 @ ( binintersect @ SV444 @ SV799 ) )
| ( in @ SY3990 @ ( binunion @ SV444 @ SY3989 ) ) ) ) )
= $true )
| ( ( in @ SV444 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2620]) ).
thf(2882,plain,
! [SV149: $i,SV445: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK27_SY3417 @ SV445 @ SV149 ) @ SV149 )
| ~ ( SV445 @ ( sK27_SY3417 @ SV445 @ SV149 ) ) ) )
= $true )
| ( ( ex1 @ SV149
@ ^ [SY3416: $i] : ( SV445 @ SY3416 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2621]) ).
thf(2883,plain,
! [SV446: $i,SV800: $i,SV150: $i] :
( ( ( breln1 @ SV150 @ SV800 )
= $false )
| ( ( ! [SY3991: $i] :
( ~ ( breln1 @ SV150 @ SY3991 )
| ( ( breln1compset @ SV150 @ ( binunion @ SV446 @ SV800 ) @ SY3991 )
= ( binunion @ ( breln1compset @ SV150 @ SV446 @ SY3991 ) @ ( breln1compset @ SV150 @ SV800 @ SY3991 ) ) ) ) )
= $true )
| ( ( breln1 @ SV150 @ SV446 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2622]) ).
thf(2884,plain,
! [SV655: $i > $i > $o,SV447: $i,SV151: $i,SV801: $i,SV748: $i] :
( ( ( in @ ( kpair @ SV748 @ SV801 )
@ ( dpsetconstr @ SV151 @ SV447
@ ^ [SY3791: $i,SY3792: $i] : ( SV655 @ SY3791 @ SY3792 ) ) )
= $false )
| ( ( SV655 @ SV748 @ SV801 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2623]) ).
thf(2885,plain,
! [SV152: $i > $o,SV448: $i > $o] :
( ( ( ( sK12_SY3425 @ SV448 @ SV152 )
!= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2624]) ).
thf(2886,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
| ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) ) )
| ~ ( ~ ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
| ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2624]) ).
thf(2887,plain,
! [SV657: $i,SV451: $o,SV155: $i,SV873: $i] :
( ( ( ~ ( in @ SV873 @ SV155 ) )
= $true )
| ( ( ~ ~ SV451
| ( ( dsetconstr @ SV155
@ ^ [SY4063: $i] :
( ~ ( ~ SV451
| ( SY4063 != SV657 ) )
| ~ ( ~ ~ SV451
| ( SY4063 != SV873 ) ) ) )
= ( setadjoin @ SV873 @ emptyset ) ) )
= $true )
| ( ( in @ SV657 @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2626]) ).
thf(2888,plain,
! [SV658: $i,SV155: $i,SV874: $i] :
( ( ( ~ ( in @ SV874 @ SV155 ) )
= $true )
| ( ( ~ ~ $true
| ( ( dsetconstr @ SV155
@ ^ [SY4064: $i] :
( ~ ( ~ $true
| ( SY4064 != SV658 ) )
| ~ ( ~ ~ $true
| ( SY4064 != SV874 ) ) ) )
= ( setadjoin @ SV874 @ emptyset ) ) )
= $true )
| ( ( in @ SV658 @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2627]) ).
thf(2889,plain,
! [SV659: $i,SV155: $i,SV875: $i] :
( ( ( ~ ( in @ SV875 @ SV155 ) )
= $true )
| ( ( ~ ~ $false
| ( ( dsetconstr @ SV155
@ ^ [SY4065: $i] :
( ~ ( ~ $false
| ( SY4065 != SV659 ) )
| ~ ( ~ ~ $false
| ( SY4065 != SV875 ) ) ) )
= ( setadjoin @ SV875 @ emptyset ) ) )
= $true )
| ( ( in @ SV659 @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2628]) ).
thf(2890,plain,
! [SV156: $i,SV452: $i,SV660: $i] :
( ( ( in @ SV660 @ SV452 )
= $false )
| ( ( in @ SV660 @ SV156 )
= $true )
| ( ( in @ SV452 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2629]) ).
thf(2891,plain,
! [SV453: $i,SV157: $i,SV802: $i] :
( ( ( in @ SV802 @ SV157 )
= $false )
| ( ( ! [SY3995: $i] :
( ~ ( in @ SY3995 @ SV157 )
| ~ ( in @ ( kpair @ SV802 @ SY3995 ) @ SV453 )
| ( in @ ( kpair @ SY3995 @ SV802 ) @ ( breln1invset @ SV157 @ SV453 ) ) ) )
= $true )
| ( ( breln1 @ SV157 @ SV453 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2630]) ).
thf(2892,plain,
! [SV158: $i,SV661: $i,SV454: $i] :
( ( ( subset @ SV454 @ SV661 )
= $false )
| ( ( subset @ SV158 @ SV661 )
= $true )
| ( ( subset @ SV158 @ SV454 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2631]) ).
thf(2893,plain,
! [SV159: $i,SV662: $i,SV455: $i > $o] :
( ( ( SV455 @ SV662 )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY3442: $i] : ( SV455 @ SY3442 ) )
!= emptyset )
= $true )
| ( ( in @ SV662 @ SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2632]) ).
thf(2894,plain,
! [SV456: $i,SV160: $i,SV663: $i] :
( ( ( in @ SV663 @ SV160 )
= $false )
| ( ( in @ SV663 @ SV456 )
= $true )
| ( ( subset @ SV160 @ SV456 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2633]) ).
thf(2895,plain,
! [SV458: $i,SV162: $i,SV803: $i] :
( ( ( in @ SV803 @ ( powerset @ SV162 ) )
= $false )
| ( ( in @ ( setminus @ SV162 @ ( binunion @ SV458 @ SV803 ) ) @ ( powerset @ ( setminus @ SV162 @ SV458 ) ) )
= $true )
| ( ( in @ SV458 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2634]) ).
thf(2896,plain,
! [SV459: $i,SV163: $i,SV804: $i] :
( ( ( in @ SV804 @ ( powerset @ SV163 ) )
= $false )
| ( ( ! [SY3996: $i] :
( ~ ( in @ SY3996 @ ( powerset @ SV163 ) )
| ~ ( subset @ SV804 @ SY3996 )
| ( subset @ ( binintersect @ SV459 @ SV804 ) @ SY3996 ) ) )
= $true )
| ( ( in @ SV459 @ ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2635]) ).
thf(2897,plain,
! [SV460: $i,SV164: $i,SV664: $i] :
( ( ( in @ SV664 @ ( setminus @ SV164 @ SV460 ) )
= $false )
| ( ( in @ SV664 @ SV164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2636]) ).
thf(2898,plain,
! [SV463: $i,SV167: $i,SV876: $i,SV805: $i] :
( ( ( SV805 != SV876 )
= $true )
| ( ( ~ ( in @ SV805 @ SV167 )
| ( in @ SV876 @ SV463 ) )
= $true )
| ( ( SV167 = SV463 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2638]) ).
thf(2899,plain,
! [SV666: $i,SV877: $i,SV464: $i,SV168: $i] :
( ( ( ~ ( breln @ SV168 @ SV464 @ SV877 ) )
= $true )
| ( ( ~ ! [SY4066: $i] :
( ~ ( in @ SY4066 @ SV168 )
| ! [SY4067: $i] :
( ~ ( in @ SY4067 @ SV464 )
| ~ ( in @ ( kpair @ SY4066 @ SY4067 ) @ SV666 )
| ( in @ ( kpair @ SY4066 @ SY4067 ) @ SV877 ) ) )
| ( subset @ SV666 @ SV877 ) )
= $true )
| ( ( breln @ SV168 @ SV464 @ SV666 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2639]) ).
thf(2900,plain,
! [SV465: $i,SV806: $i,SV169: $i] :
( ( ( breln1 @ SV169 @ SV806 )
= $false )
| ( ( ! [SY3998: $i] :
( ~ ( breln1 @ SV169 @ SY3998 )
| ( ( breln1compset @ SV169 @ ( binunion @ SV465 @ SV806 ) @ SY3998 )
= ( binunion @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SY3998 ) @ ( breln1invset @ SV169 @ SV806 ) ) ) @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SY3998 ) @ ( breln1invset @ SV169 @ SV465 ) ) ) ) ) ) )
= $true )
| ( ( breln1 @ SV169 @ SV465 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2640]) ).
thf(2901,plain,
! [SV466: $i,SV171: $i,SV807: $i] :
( ( ( in @ SV807 @ ( powerset @ SV171 ) )
= $false )
| ( ( ! [SY3999: $i] :
( ~ ( in @ SY3999 @ ( binintersect @ SV466 @ SV807 ) )
| ( in @ SY3999 @ SV171 ) ) )
= $true )
| ( ( in @ SV466 @ ( powerset @ SV171 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2641]) ).
thf(2902,plain,
! [SV468: $i,SV173: $i,SV808: $i] :
( ( ( in @ SV808 @ ( powerset @ SV173 ) )
= $false )
| ( ( ~ ( subset @ SV468 @ ( setminus @ SV173 @ SV808 ) )
| ( subset @ SV808 @ ( setminus @ SV173 @ SV468 ) ) )
= $true )
| ( ( in @ SV468 @ ( powerset @ SV173 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2642]) ).
thf(2903,plain,
! [SV175: $i,SV470: $i > $i] :
( ( ~ ! [SY3923: $i] :
~ ( ~ ( ~ ( in @ SY3923 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
| ~ ! [SY3464: $i] :
~ ~ ( ~ ( in @ SY3464 @ SV175 )
| ( SY3923
!= ( SV470 @ SY3464 ) ) ) )
| ~ ( ~ ~ ! [SY3465: $i] :
~ ~ ( ~ ( in @ SY3465 @ SV175 )
| ( SY3923
!= ( SV470 @ SY3465 ) ) )
| ( in @ SY3923 @ ( sK3_SY3462 @ SV470 @ SV175 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2644]) ).
thf(2904,plain,
! [SV470: $i > $i,SV175: $i] :
( ( ~ ! [SY3926: $i] :
( ~ ! [SY3467: $i] :
~ ( ~ ( ~ ( in @ SY3467 @ SY3926 )
| ~ ! [SY3468: $i] :
~ ~ ( ~ ( in @ SY3468 @ SV175 )
| ( SY3467
!= ( SV470 @ SY3468 ) ) ) )
| ~ ( ~ ~ ! [SY3469: $i] :
~ ~ ( ~ ( in @ SY3469 @ SV175 )
| ( SY3467
!= ( SV470 @ SY3469 ) ) )
| ( in @ SY3467 @ SY3926 ) ) )
| ( ( sK3_SY3462 @ SV470 @ SV175 )
= SY3926 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2644]) ).
thf(2905,plain,
! [SV471: $i,SV176: $i,SV809: $i] :
( ( ( in @ SV809 @ ( powerset @ SV176 ) )
= $false )
| ( ( in @ ( setminus @ SV471 @ SV809 ) @ ( powerset @ SV176 ) )
= $true )
| ( ( in @ SV471 @ ( powerset @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2645]) ).
thf(2906,plain,
! [SV668: $i,SV472: $i,SV177: $i] :
( ( ( injective @ SV177 @ SV472 @ SV668 )
= $false )
| ( ( in @ SV668 @ ( injFuncSet @ SV177 @ SV472 ) )
= $true )
| ( ( in @ SV668 @ ( funcSet @ SV177 @ SV472 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2646]) ).
thf(2907,plain,
! [SV473: $i,SV810: $i,SV178: $i] :
( ( ( breln1 @ SV178 @ SV810 )
= $false )
| ( ( ( breln1invset @ SV178 @ ( breln1compset @ SV178 @ SV473 @ SV810 ) )
= ( breln1compset @ SV178 @ ( breln1invset @ SV178 @ SV810 ) @ ( breln1invset @ SV178 @ SV473 ) ) )
= $true )
| ( ( breln1 @ SV178 @ SV473 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2647]) ).
thf(2908,plain,
! [SV180: $i,SV475: $i,SV670: $i > $i > $o] :
( ( ( ~ ( in @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV180 ) )
= $false )
| ( ( ! [SY3807: $i] :
( ~ ( in @ SY3807 @ ( breln1Set @ SV475 ) )
| ~ ( reflwellordering @ SV475 @ SY3807 )
| ! [SY3808: $i] :
( ~ ( in @ SY3808 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY3809: $i] :
~ ( ~ ( SV670 @ SY3808 @ SY3809 )
| ~ ! [SY3810: $i] :
( ~ ( in @ SY3810 @ SV475 )
| ~ ( SV670 @ SY3808 @ SY3810 )
| ( in @ ( kpair @ SY3809 @ SY3810 ) @ SY3807 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2648]) ).
thf(2909,plain,
! [SV180: $i,SV670: $i > $i > $o,SV475: $i] :
( ( ( ~ ! [SY4068: $i] :
~ ~ ( ~ ( in @ SY4068 @ SV475 )
| ~ ( SV670 @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SY4068 ) ) )
= $false )
| ( ( ! [SY3807: $i] :
( ~ ( in @ SY3807 @ ( breln1Set @ SV475 ) )
| ~ ( reflwellordering @ SV475 @ SY3807 )
| ! [SY3808: $i] :
( ~ ( in @ SY3808 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY3809: $i] :
~ ( ~ ( SV670 @ SY3808 @ SY3809 )
| ~ ! [SY3810: $i] :
( ~ ( in @ SY3810 @ SV475 )
| ~ ( SV670 @ SY3808 @ SY3810 )
| ( in @ ( kpair @ SY3809 @ SY3810 ) @ SY3807 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2648]) ).
thf(2910,plain,
! [SV181: $i,SV671: $i,SV476: $i,SV878: $i] :
( ( ( ~ ( in @ SV878 @ SV476 ) )
= $true )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV671 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV671 @ ( setadjoin @ SV878 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV181 @ SV476 ) ) ) )
= $true )
| ( ( in @ SV671 @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2649]) ).
thf(2911,plain,
! [SV182: $i,SV672: $i > $i,SV477: $i] :
( ( ( ~ ( in @ ( sK30_SY3812 @ SV477 @ SV672 @ SV182 ) @ SV182 ) )
= $false )
| ( ( ! [SY3813: $i] :
( ~ ( in @ SY3813 @ SV182 )
| ( ( ap @ SV182 @ SV477
@ ( lam @ SV182 @ SV477
@ ^ [SY3814: $i] : ( SV672 @ SY3814 ) )
@ SY3813 )
= ( SV672 @ SY3813 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2650]) ).
thf(2912,plain,
! [SV182: $i,SV477: $i,SV672: $i > $i] :
( ( ( in @ ( SV672 @ ( sK30_SY3812 @ SV477 @ SV672 @ SV182 ) ) @ SV477 )
= $false )
| ( ( ! [SY3813: $i] :
( ~ ( in @ SY3813 @ SV182 )
| ( ( ap @ SV182 @ SV477
@ ( lam @ SV182 @ SV477
@ ^ [SY3814: $i] : ( SV672 @ SY3814 ) )
@ SY3813 )
= ( SV672 @ SY3813 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2650]) ).
thf(2913,plain,
! [SV183: $i,SV478: $i,SV673: $i] :
( ( ( ~ ( in @ SV673 @ SV478 ) )
= $false )
| ( ( ~ ( subset @ SV183 @ SV478 ) )
= $true )
| ( ( in @ SV673 @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2651]) ).
thf(2914,plain,
! [SV184: $i,SV479: $i,SV674: $i] :
( ( ( ~ ( in @ SV674 @ SV479 ) )
= $false )
| ( ( SV184 != SV479 )
= $true )
| ( ( in @ SV674 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(2915,plain,
! [SV480: $i,SV185: $i,SV811: $i] :
( ( ( in @ SV811 @ ( powerset @ SV185 ) )
= $false )
| ( ( in @ ( binintersect @ SV480 @ SV811 ) @ ( powerset @ SV185 ) )
= $true )
| ( ( in @ SV480 @ ( powerset @ SV185 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2653]) ).
thf(2916,plain,
! [SV481: $i,SV186: $i,SV812: $i] :
( ( ( in @ SV812 @ ( powerset @ SV186 ) )
= $false )
| ( ( ! [SY4000: $i] :
( ~ ( in @ SY4000 @ SV186 )
| ~ ( in @ SV481 @ ( powerset @ SV812 ) )
| ~ ( in @ SY4000 @ SV481 )
| ( in @ SY4000 @ SV812 ) ) )
= $true )
| ( ( in @ SV481 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2654]) ).
thf(2917,plain,
! [SV483: $i > $o,SV188: $i,SV675: $i] :
( ( ( ~ ( ~ ( in @ SV675
@ ( dsetconstr @ SV188
@ ^ [SY3494: $i] : ( SV483 @ SY3494 ) ) )
| ( SV483 @ SV675 ) ) )
= $false )
| ( ( in @ SV675 @ SV188 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2655]) ).
thf(2918,plain,
! [SV188: $i,SV675: $i,SV483: $i > $o] :
( ( ( ~ ( ~ ( SV483 @ SV675 )
| ( in @ SV675
@ ( dsetconstr @ SV188
@ ^ [SY3495: $i] : ( SV483 @ SY3495 ) ) ) ) )
= $false )
| ( ( in @ SV675 @ SV188 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2655]) ).
thf(2919,plain,
! [SV484: $i > $o,SV189: $i,SV879: $i] :
( ( ( ~ ( in @ SV879 @ SV189 ) )
= $true )
| ( ( SV484 @ SV879 )
= $true )
| ( ( ~ ! [SY3497: $i] :
~ ~ ( ~ ( in @ SY3497 @ SV189 )
| ~ ~ ( SV484 @ SY3497 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2656]) ).
thf(2920,plain,
! [SV813: $o,SV190: $i,SV485: $i] :
( ( ( ! [SY4001: $i] :
( ~ ( in @ SV485 @ SY4001 )
| ~ ( in @ SY4001 @ SV190 )
| SV813 ) )
= $false )
| ( SV813 = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2657]) ).
thf(2921,plain,
! [SV190: $i,SV485: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV485 @ SX0 )
| ~ ( in @ SX0 @ SV190 )
| $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2658]) ).
thf(2922,plain,
! [SV190: $i,SV485: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV485 @ SX0 )
| ~ ( in @ SX0 @ SV190 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2659]) ).
thf(2923,plain,
! [SV676: $i,SV486: $i,SV191: $i,SV880: $i] :
( ( ( ~ ( in @ SV880 @ SV191 ) )
= $true )
| ( ( ! [SY4069: $i] :
( ~ ( in @ SY4069 @ SV486 )
| ~ ( in @ ( kpair @ SV880 @ SY4069 ) @ SV676 )
| ( ( ap @ SV191 @ SV486 @ SV676 @ SV880 )
= SY4069 ) ) )
= $true )
| ( ( in @ SV676 @ ( funcSet @ SV191 @ SV486 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2660]) ).
thf(2924,plain,
! [SV192: $i,SV487: $i,SV677: $i] :
( ( ( subset @ SV677 @ SV487 )
= $false )
| ( ( subset @ SV677 @ ( binintersect @ SV192 @ SV487 ) )
= $true )
| ( ( subset @ SV677 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2661]) ).
thf(2925,plain,
! [SV193: $i,SV488: $i > $i,SV881: $i] :
( ( ~ ( ~ ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
| ~ ! [SY4070: $i] :
~ ~ ( ~ ( in @ SY4070 @ SV193 )
| ( SV881
!= ( SV488 @ SY4070 ) ) ) )
| ~ ( ~ ~ ! [SY4071: $i] :
~ ~ ( ~ ( in @ SY4071 @ SV193 )
| ( SV881
!= ( SV488 @ SY4071 ) ) )
| ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2662]) ).
thf(2926,plain,
! [SV489: $i,SV194: $i,SV814: $i] :
( ( ( in @ SV814 @ SV194 )
= $false )
| ( ( ~ ~ ( in @ SV814 @ ( setminus @ SV194 @ SV489 ) )
| ( in @ SV814 @ SV489 ) )
= $true )
| ( ( in @ SV489 @ ( powerset @ SV194 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2663]) ).
thf(2927,plain,
! [SV815: $i] :
( ( ( in @ SV815 @ sK1_SX0 )
= $false )
| ( ( subset @ SV815 @ sK1_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(2928,plain,
! [SV919: $i] :
( ( ~ ( in @ SV919 @ sK5_SY3512 )
| ( subset @ SV919 @ sK5_SY3512 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2665]) ).
thf(2929,plain,
( ( ~ ( in @ sK31_SY3934 @ ( binintersect @ sK1_SX0 @ sK5_SY3512 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2666]) ).
thf(2930,plain,
( ( subset @ sK31_SY3934 @ ( binintersect @ sK1_SX0 @ sK5_SY3512 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2666]) ).
thf(2931,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ SV816 )
| ~ ! [SY4002: $i] :
( ~ ( SV196 @ SY4002 )
| ( SV816 = SY4002 ) ) )
= $true )
| ( ( ~ ! [SY2855: $i] :
~ ~ ( ~ ( SV196 @ SY2855 )
| ~ ! [SY2856: $i] :
( ~ ( SV196 @ SY2856 )
| ( SY2855 = SY2856 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2667]) ).
thf(2932,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ( sK13_SY3515 @ SV491 @ SV197 )
!= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2668]) ).
thf(2933,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
| ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) ) )
| ~ ( ~ ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
| ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2668]) ).
thf(2934,plain,
! [SV199: $i,SV492: $i,SV679: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK39_SY3820 @ SV679 @ SV492 @ SV199 ) @ SV199 )
| ~ ~ ! [SY4093: $i] :
~ ~ ( ~ ( in @ SY4093 @ SV492 )
| ( SV679
!= ( kpair @ ( sK39_SY3820 @ SV679 @ SV492 @ SV199 ) @ SY4093 ) ) ) ) )
= $false )
| ( ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2669]) ).
thf(2935,plain,
! [SV493: $i,SV200: $i,SV817: $i] :
( ( ( in @ SV817 @ ( powerset @ SV200 ) )
= $false )
| ( ( ! [SY4004: $i] :
( ~ ( in @ SY4004 @ SV200 )
| ~ ~ ( in @ SY4004 @ ( binunion @ SV493 @ SV817 ) )
| ~ ( in @ SY4004 @ SV817 ) ) )
= $true )
| ( ( in @ SV493 @ ( powerset @ SV200 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2670]) ).
thf(2936,plain,
! [SV680: $i,SV495: $o,SV202: $i,SV882: $i] :
( ( ( ~ ( in @ SV882 @ SV202 ) )
= $true )
| ( ( in @ ( if @ SV202 @ SV495 @ SV680 @ SV882 ) @ SV202 )
= $true )
| ( ( in @ SV680 @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2671]) ).
thf(2937,plain,
! [SV681: $i,SV202: $i,SV883: $i] :
( ( ( ~ ( in @ SV883 @ SV202 ) )
= $true )
| ( ( in @ ( if @ SV202 @ $true @ SV681 @ SV883 ) @ SV202 )
= $true )
| ( ( in @ SV681 @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2672]) ).
thf(2938,plain,
! [SV682: $i,SV202: $i,SV884: $i] :
( ( ( ~ ( in @ SV884 @ SV202 ) )
= $true )
| ( ( in @ ( if @ SV202 @ $false @ SV682 @ SV884 ) @ SV202 )
= $true )
| ( ( in @ SV682 @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2673]) ).
thf(2939,plain,
! [SV885: $o,SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( ~ ( in @ SV683 @ SV203 )
| ~ ~ ( in @ SV683 @ SV496 )
| SV885 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SV885 )
| SV885 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2674]) ).
thf(2940,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( ~ ( in @ SV683 @ SV203 )
| ~ ~ ( in @ SV683 @ SV496 )
| $true ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $true )
| $true )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2675]) ).
thf(2941,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( ~ ( in @ SV683 @ SV203 )
| ~ ~ ( in @ SV683 @ SV496 )
| $false ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $false )
| $false )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2676]) ).
thf(2942,plain,
! [SV204: $i,SV684: $i > $i,SV497: $i] :
( ( ( ~ ( in @ ( sK33_SY3826 @ SV497 @ SV684 @ SV204 ) @ SV204 ) )
= $false )
| ( ( func @ SV204 @ SV497
@ ( lam @ SV204 @ SV497
@ ^ [SY3827: $i] : ( SV684 @ SY3827 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2677]) ).
thf(2943,plain,
! [SV204: $i,SV497: $i,SV684: $i > $i] :
( ( ( in @ ( SV684 @ ( sK33_SY3826 @ SV497 @ SV684 @ SV204 ) ) @ SV497 )
= $false )
| ( ( func @ SV204 @ SV497
@ ( lam @ SV204 @ SV497
@ ^ [SY3827: $i] : ( SV684 @ SY3827 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2677]) ).
thf(2944,plain,
! [SV686: $i,SV499: $o,SV206: $i,SV886: $i] :
( ( ( ~ ( in @ SV886 @ SV206 ) )
= $true )
| ( ( in @ ( if @ SV206 @ SV499 @ SV686 @ SV886 ) @ ( setadjoin @ SV686 @ ( setadjoin @ SV886 @ emptyset ) ) )
= $true )
| ( ( in @ SV686 @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2678]) ).
thf(2945,plain,
! [SV687: $i,SV206: $i,SV887: $i] :
( ( ( ~ ( in @ SV887 @ SV206 ) )
= $true )
| ( ( in @ ( if @ SV206 @ $true @ SV687 @ SV887 ) @ ( setadjoin @ SV687 @ ( setadjoin @ SV887 @ emptyset ) ) )
= $true )
| ( ( in @ SV687 @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2679]) ).
thf(2946,plain,
! [SV688: $i,SV206: $i,SV888: $i] :
( ( ( ~ ( in @ SV888 @ SV206 ) )
= $true )
| ( ( in @ ( if @ SV206 @ $false @ SV688 @ SV888 ) @ ( setadjoin @ SV688 @ ( setadjoin @ SV888 @ emptyset ) ) )
= $true )
| ( ( in @ SV688 @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2680]) ).
thf(2947,plain,
! [SV207: $i,SV500: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK40_SY3540 @ SV500 @ SV207 ) @ SV207 )
| ~ ( SV500 @ ( sK40_SY3540 @ SV500 @ SV207 ) ) ) )
= $false )
| ( ( ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SV207 )
| ~ ( SV500 @ SY3541 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2681]) ).
thf(2948,plain,
! [SV501: $i,SV208: $i,SV818: $i] :
( ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( ! [SY4005: $o,SY4006: $i] :
( ~ ( in @ SY4006 @ SV208 )
| ~ ( in @ SY4006 @ ( binunion @ SV501 @ SV818 ) )
| ~ ( ~ ( in @ SY4006 @ SV501 )
| SY4005 )
| ~ ( ~ ( in @ SY4006 @ SV818 )
| SY4005 )
| SY4005 ) )
= $true )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2682]) ).
thf(2949,plain,
! [SV889: $i > $o,SV689: $i,SV502: $i,SV209: $i] :
( ( ( ~ ! [SY4072: $i] :
( ~ ( in @ SY4072 @ SV209 )
| ! [SY4073: $i] :
( ~ ( in @ SY4073 @ SV502 )
| ~ ( in @ ( kpair @ SY4072 @ SY4073 ) @ SV689 )
| ( SV889 @ ( kpair @ SY4072 @ SY4073 ) ) ) ) )
= $true )
| ( ( ! [SY4074: $i] :
( ~ ( in @ SY4074 @ SV689 )
| ( SV889 @ SY4074 ) ) )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2683]) ).
thf(2950,plain,
! [SV690: $i,SV503: $o,SV210: $i,SV890: $i] :
( ( ( ~ ( in @ SV890 @ SV210 ) )
= $true )
| ( ( ~ SV503
| ( in @ SV690
@ ( dsetconstr @ SV210
@ ^ [SY4075: $i] :
( ~ ( ~ SV503
| ( SY4075 != SV690 ) )
| ~ ( ~ ~ SV503
| ( SY4075 != SV890 ) ) ) ) ) )
= $true )
| ( ( in @ SV690 @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2684]) ).
thf(2951,plain,
! [SV691: $i,SV210: $i,SV891: $i] :
( ( ( ~ ( in @ SV891 @ SV210 ) )
= $true )
| ( ( ~ $true
| ( in @ SV691
@ ( dsetconstr @ SV210
@ ^ [SY4076: $i] :
( ~ ( ~ $true
| ( SY4076 != SV691 ) )
| ~ ( ~ ~ $true
| ( SY4076 != SV891 ) ) ) ) ) )
= $true )
| ( ( in @ SV691 @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2685]) ).
thf(2952,plain,
! [SV692: $i,SV210: $i,SV892: $i] :
( ( ( ~ ( in @ SV892 @ SV210 ) )
= $true )
| ( ( ~ $false
| ( in @ SV692
@ ( dsetconstr @ SV210
@ ^ [SY4077: $i] :
( ~ ( ~ $false
| ( SY4077 != SV692 ) )
| ~ ( ~ ~ $false
| ( SY4077 != SV892 ) ) ) ) ) )
= $true )
| ( ( in @ SV692 @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2686]) ).
thf(2953,plain,
! [SV212: $i,SV504: $i,SV693: $i] :
( ( ( ~ ( in @ SV693 @ SV504 ) )
= $false )
| ( ( ~ ( in @ SV693 @ SV212 ) )
= $true )
| ( ( subset @ SV212 @ SV504 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2687]) ).
thf(2954,plain,
! [SV508: $i,SV819: $i,SV216: $i] :
( ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( ! [SY4007: $i] :
( ~ ( in @ SY4007 @ SV216 )
| ! [SY4008: $i] :
( ~ ( in @ SY4008 @ SV216 )
| ~ ( in @ ( kpair @ SY4007 @ SY4008 ) @ ( binunion @ SV508 @ SV819 ) )
| ! [SY4009: $o] :
( ~ ( ~ ( in @ ( kpair @ SY4007 @ SY4008 ) @ SV508 )
| SY4009 )
| ~ ( ~ ( in @ ( kpair @ SY4007 @ SY4008 ) @ SV819 )
| SY4009 )
| SY4009 ) ) ) )
= $true )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2689]) ).
thf(2955,plain,
! [SV509: $i,SV217: $i,SV820: $i] :
( ( ( in @ SV820 @ ( powerset @ SV217 ) )
= $false )
| ( ( ! [SY4010: $i] :
( ~ ( in @ SY4010 @ SV217 )
| ~ ( in @ SY4010 @ ( setminus @ SV217 @ ( binunion @ SV509 @ SV820 ) ) )
| ( in @ SY4010 @ ( binintersect @ ( setminus @ SV217 @ SV509 ) @ ( setminus @ SV217 @ SV820 ) ) ) ) )
= $true )
| ( ( in @ SV509 @ ( powerset @ SV217 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2690]) ).
thf(2956,plain,
! [SV218: $i,SV696: $i,SV510: $i > $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK41_SY3843 @ SV510 @ SV696 @ SV218 ) @ SV218 )
| ( SV696
!= ( SV510 @ ( sK41_SY3843 @ SV510 @ SV696 @ SV218 ) ) ) ) )
= $false )
| ( ( in @ SV696
@ ( image1 @ SV218
@ ^ [SY3564: $i] : ( SV510 @ SY3564 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2691]) ).
thf(2957,plain,
! [SV699: $i,SV514: $o,SV223: $i,SV893: $i] :
( ( ( ~ ( in @ SV893 @ SV223 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY4078: $i] :
( ~ ( ~ SV514
| ( SY4078 != SV699 ) )
| ~ ( ~ ~ SV514
| ( SY4078 != SV893 ) ) ) ) )
= $true )
| ( ( in @ SV699 @ SV223 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2693]) ).
thf(2958,plain,
! [SV700: $i,SV223: $i,SV894: $i] :
( ( ( ~ ( in @ SV894 @ SV223 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY4079: $i] :
( ~ ( ~ $true
| ( SY4079 != SV700 ) )
| ~ ( ~ ~ $true
| ( SY4079 != SV894 ) ) ) ) )
= $true )
| ( ( in @ SV700 @ SV223 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2694]) ).
thf(2959,plain,
! [SV701: $i,SV223: $i,SV895: $i] :
( ( ( ~ ( in @ SV895 @ SV223 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY4080: $i] :
( ~ ( ~ $false
| ( SY4080 != SV701 ) )
| ~ ( ~ ~ $false
| ( SY4080 != SV895 ) ) ) ) )
= $true )
| ( ( in @ SV701 @ SV223 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2695]) ).
thf(2960,plain,
! [SV515: $i,SV224: $i,SV821: $i] :
( ( ( in @ SV821 @ ( powerset @ SV224 ) )
= $false )
| ( ( ~ ( subset @ SV515 @ SV821 )
| ( subset @ ( setminus @ SV224 @ SV821 ) @ ( setminus @ SV224 @ SV515 ) ) )
= $true )
| ( ( in @ SV515 @ ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2696]) ).
thf(2961,plain,
! [SV226: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY3851: $i] :
( ~ ( in @ SY3851 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY2945: $i] :
( ~ ( in @ SY2945 @ SY3851 )
| ( in @ SY2945 @ SV226 ) ) )
| ~ ! [SY3853: $i,SY3854: $i] :
( ~ ~ ( ~ ( in @ SY3853 @ SV226 )
| ~ ( in @ SY3854 @ SV226 ) )
| ~ ! [SY3855: $i] :
( ~ ( in @ SY3855 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SY3853 @ SY3855 )
| ( in @ SY3854 @ SY3855 ) )
| ~ ( ~ ( in @ SY3854 @ SY3855 )
| ( in @ SY3853 @ SY3855 ) ) ) )
| ( SY3853 = SY3854 ) ) )
| ~ ! [SY3856: $i,SY3857: $i] :
( ~ ~ ( ~ ( in @ SY3856 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY3857 @ ( sK2_SY2943 @ SV226 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3856 )
| ( in @ SX4 @ SY3857 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3857 )
| ( in @ SX4 @ SY3856 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2698]) ).
thf(2962,plain,
! [SV226: $i] :
( ( ! [SY3860: $i] :
( ~ ~ ( ~ ! [SY2954: $i] :
( ~ ( in @ SY2954 @ SY3860 )
| ( in @ SY2954 @ SV226 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY3860 ) )
| ~ ! [SY3863: $i] :
~ ~ ! [SY3864: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3863 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY3864 @ SY3860 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY3863 )
| ~ ( in @ SX5 @ SY3860 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY3863 ) )
| ( in @ SY3864 @ SY3866 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2699]) ).
thf(2963,plain,
! [SV703: $i > $i > $o,SV227: $i,SV752: $i,SV517: $i,SV920: $i] :
( ( ( ~ ( in @ SV920 @ SV517 )
| ~ ( in @ ( kpair @ SV752 @ SV920 )
@ ( dpsetconstr @ SV227 @ SV517
@ ^ [SY3870: $i,SY3871: $i] : ( SV703 @ SY3870 @ SY3871 ) ) )
| ( SV703 @ SV752 @ SV920 ) )
= $true )
| ( ( in @ SV752 @ SV227 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2700]) ).
thf(2964,plain,
! [SV518: $i,SV228: $i,SV704: $i] :
( ( ( in @ SV704 @ SV228 )
= $false )
| ( ( in @ SV518 @ ( setunion @ SV228 ) )
= $true )
| ( ( in @ SV518 @ SV704 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2701]) ).
thf(2965,plain,
! [SV519: $i,SV229: $i,SV822: $i] :
( ( ( in @ SV822 @ ( powerset @ SV229 ) )
= $false )
| ( ( ! [SY4011: $i] :
( ~ ( in @ SY4011 @ SV229 )
| ~ ~ ( in @ SY4011 @ ( binunion @ SV519 @ SV822 ) )
| ~ ( in @ SY4011 @ SV519 ) ) )
= $true )
| ( ( in @ SV519 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2702]) ).
thf(2966,plain,
! [SV520: $i,SV230: $i > $i > $o] :
( ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true )
| ( ( ~ ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2703]) ).
thf(2967,plain,
! [SV520: $i,SV230: $i > $i > $o] :
( ( ( ! [SY4012: $i] :
~ ~ ( ~ ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SY4012 )
| ~ ! [SY4013: $i] :
( ~ ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SY4013 )
| ( SY4012 = SY4013 ) ) ) )
= $true )
| ( ( ~ ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2704]) ).
thf(2968,plain,
! [SV705: $i,SV896: $i,SV521: $i,SV231: $i] :
( ( ( ~ ( func @ SV231 @ SV521 @ SV896 ) )
= $true )
| ( ( ~ ! [SY4081: $i] :
( ~ ( in @ SY4081 @ SV231 )
| ( ( ap @ SV231 @ SV521 @ SV705 @ SY4081 )
= ( ap @ SV231 @ SV521 @ SV896 @ SY4081 ) ) )
| ( SV705 = SV896 ) )
= $true )
| ( ( func @ SV231 @ SV521 @ SV705 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2705]) ).
thf(2969,plain,
! [SV706: $i,SV522: $o,SV232: $i,SV897: $i] :
( ( ( ~ ( in @ SV897 @ SV232 ) )
= $true )
| ( ( ~ SV522
| ( ( if @ SV232 @ SV522 @ SV706 @ SV897 )
= SV706 ) )
= $true )
| ( ( in @ SV706 @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2706]) ).
thf(2970,plain,
! [SV707: $i,SV232: $i,SV898: $i] :
( ( ( ~ ( in @ SV898 @ SV232 ) )
= $true )
| ( ( ~ $true
| ( ( if @ SV232 @ $true @ SV707 @ SV898 )
= SV707 ) )
= $true )
| ( ( in @ SV707 @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2707]) ).
thf(2971,plain,
! [SV708: $i,SV232: $i,SV899: $i] :
( ( ( ~ ( in @ SV899 @ SV232 ) )
= $true )
| ( ( ~ $false
| ( ( if @ SV232 @ $false @ SV708 @ SV899 )
= SV708 ) )
= $true )
| ( ( in @ SV708 @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2708]) ).
thf(2972,plain,
! [SV823: $i > $o,SV523: $i,SV233: $i] :
( ( ( ! [SY4014: $i] :
( ~ ( in @ SY4014 @ SV233 )
| ! [SY4015: $i] :
( ~ ( in @ SY4015 @ SV233 )
| ~ ( in @ ( kpair @ SY4014 @ SY4015 ) @ SV523 )
| ( SV823 @ ( kpair @ SY4014 @ SY4015 ) ) ) ) )
= $false )
| ( ( ! [SY4016: $i] :
( ~ ( in @ SY4016 @ SV523 )
| ( SV823 @ SY4016 ) ) )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2709]) ).
thf(2973,plain,
! [SV524: $i,SV234: $i] :
( ( ( in @ ( sK15_SY3598 @ SV234 @ SV524 ) @ SV524 )
= $true )
| ( ( in @ SV524 @ ( powerset @ SV234 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2710]) ).
thf(2974,plain,
! [SV235: $i,SV525: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_SY3599 @ SV525 @ SV235 ) @ SV235 )
| ~ ( in @ SV525 @ ( sK34_SY3599 @ SV525 @ SV235 ) ) ) )
= $true )
| ( ( in @ SV525 @ ( setunion @ SV235 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2712]) ).
thf(2975,plain,
! [SV711: $i,SV529: $i,SV240: $i,SV900: $i] :
( ( ( ~ ( in @ SV900 @ SV240 ) )
= $true )
| ( ( in @ ( kpair @ SV900 @ ( ap @ SV240 @ SV529 @ SV711 @ SV900 ) ) @ SV711 )
= $true )
| ( ( func @ SV240 @ SV529 @ SV711 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2714]) ).
thf(2976,plain,
! [SV530: $i,SV241: $i,SV824: $i] :
( ( ( in @ SV824 @ ( powerset @ SV241 ) )
= $false )
| ( ( in @ ( setminus @ SV241 @ SV530 ) @ ( powerset @ ( setminus @ SV241 @ ( binintersect @ SV530 @ SV824 ) ) ) )
= $true )
| ( ( in @ SV530 @ ( powerset @ SV241 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2715]) ).
thf(2977,plain,
! [SV242: $i] :
( ( ( in @ ( sK35_SY3006 @ SV242 ) @ SV242 )
= $true )
| ( ( SV242 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2716]) ).
thf(2978,plain,
! [SV531: $i,SV243: $i,SV825: $i] :
( ( ( in @ SV825 @ ( powerset @ SV243 ) )
= $false )
| ( ( ! [SY4017: $i] :
( ~ ( in @ SY4017 @ ( powerset @ SV243 ) )
| ( in @ ( binintersect @ SV531 @ SV825 ) @ ( powerset @ ( binintersect @ ( binunion @ SV531 @ SY4017 ) @ ( binunion @ SV825 @ SY4017 ) ) ) ) ) )
= $true )
| ( ( in @ SV531 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(2979,plain,
! [SV532: $i,SV244: $i,SV826: $i] :
( ( ( in @ SV826 @ SV244 )
= $false )
| ( ( ~ ( in @ SV826 @ ( setminus @ SV244 @ ( setminus @ SV244 @ SV532 ) ) )
| ( in @ SV826 @ SV532 ) )
= $true )
| ( ( in @ SV532 @ ( powerset @ SV244 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2718]) ).
thf(2980,plain,
! [SV533: $i > $o,SV245: $i,SV901: $i] :
( ( ( ~ ( ~ ( in @ SV901 @ SV245 )
| ~ ( SV533 @ SV901 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV245
@ ^ [SY3609: $i] : ( SV533 @ SY3609 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2719]) ).
thf(2981,plain,
! [SV712: $i,SV534: $i,SV246: $i,SV902: $i] :
( ( ( ~ ( in @ SV902 @ SV246 ) )
= $true )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV534
@ ^ [SY4082: $i] : ( in @ ( kpair @ SV902 @ SY4082 ) @ SV712 ) ) )
@ SV534 )
= $true )
| ( ( func @ SV246 @ SV534 @ SV712 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2720]) ).
thf(2982,plain,
! [SV535: $i,SV247: $i,SV827: $i] :
( ( ( in @ SV827 @ SV247 )
= $false )
| ( ( ! [SY4018: $i] :
( ~ ( in @ SY4018 @ SV247 )
| ~ ( in @ ( kpair @ SY4018 @ SV827 ) @ ( breln1invset @ SV247 @ SV535 ) )
| ( in @ ( kpair @ SV827 @ SY4018 ) @ SV535 ) ) )
= $true )
| ( ( breln1 @ SV247 @ SV535 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2721]) ).
thf(2983,plain,
! [SV249: $i,SV921: $i] :
( ( ( ~ ( in @ SV921 @ SV249 )
| ( subset @ SV921 @ SV249 ) )
= $true )
| ( ( in @ ( sK7_SY3023 @ SV249 ) @ SV249 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(2984,plain,
! [SV249: $i,SV903: $i] :
( ( ( ~ ( in @ SV903 @ SV249 ) )
= $true )
| ( ( subset @ SV903 @ SV249 )
= $true )
| ( ( subset @ ( sK7_SY3023 @ SV249 ) @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2723]) ).
thf(2985,plain,
! [SV538: $i,SV251: $i,SV828: $i] :
( ( ( in @ SV828 @ ( powerset @ SV251 ) )
= $false )
| ( ( ! [SY4019: $i] :
( ~ ( in @ SY4019 @ SV251 )
| ~ ~ ( in @ SY4019 @ SV538 )
| ~ ~ ( in @ SY4019 @ SV828 )
| ~ ( in @ SY4019 @ ( binunion @ SV538 @ SV828 ) ) ) )
= $true )
| ( ( in @ SV538 @ ( powerset @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2725]) ).
thf(2986,plain,
! [SV714: $i,SV539: $o,SV252: $i,SV904: $i] :
( ( ( ~ ( in @ SV904 @ SV252 ) )
= $true )
| ( ( ~ SV539
| ( ( dsetconstr @ SV252
@ ^ [SY4083: $i] :
( ~ ( ~ SV539
| ( SY4083 != SV714 ) )
| ~ ( ~ ~ SV539
| ( SY4083 != SV904 ) ) ) )
= ( setadjoin @ SV714 @ emptyset ) ) )
= $true )
| ( ( in @ SV714 @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2726]) ).
thf(2987,plain,
! [SV715: $i,SV252: $i,SV905: $i] :
( ( ( ~ ( in @ SV905 @ SV252 ) )
= $true )
| ( ( ~ $true
| ( ( dsetconstr @ SV252
@ ^ [SY4084: $i] :
( ~ ( ~ $true
| ( SY4084 != SV715 ) )
| ~ ( ~ ~ $true
| ( SY4084 != SV905 ) ) ) )
= ( setadjoin @ SV715 @ emptyset ) ) )
= $true )
| ( ( in @ SV715 @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2727]) ).
thf(2988,plain,
! [SV716: $i,SV252: $i,SV906: $i] :
( ( ( ~ ( in @ SV906 @ SV252 ) )
= $true )
| ( ( ~ $false
| ( ( dsetconstr @ SV252
@ ^ [SY4085: $i] :
( ~ ( ~ $false
| ( SY4085 != SV716 ) )
| ~ ( ~ ~ $false
| ( SY4085 != SV906 ) ) ) )
= ( setadjoin @ SV716 @ emptyset ) ) )
= $true )
| ( ( in @ SV716 @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2728]) ).
thf(2989,plain,
! [SV717: $i,SV541: $i,SV254: $i,SV907: $i] :
( ( ( ~ ( in @ SV907 @ SV254 ) )
= $true )
| ( ( ( ap @ SV254 @ SV541 @ SV717 @ SV907 )
= ( ap @ SV254 @ SV541 @ SV717 @ SV907 ) )
= $true )
| ( ( func @ SV254 @ SV541 @ SV717 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2729]) ).
thf(2990,plain,
! [SV256: $i,SV543: $i,SV753: $i,SV718: $i] :
( ( ( SV718 != SV753 )
= $true )
| ( ( SV543 = SV753 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV256 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV256 @ ( setadjoin @ SV543 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV718 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV718 @ ( setadjoin @ SV753 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2730]) ).
thf(2991,plain,
! [SV719: $i,SV548: $i,SV259: $i,SV908: $i] :
( ( ( ~ ( in @ SV908 @ SV259 ) )
= $true )
| ( ( ! [SY4086: $i] :
( ~ ( in @ SY4086 @ SV548 )
| ~ ( in @ ( kpair @ SV908 @ SY4086 ) @ SV719 )
| ( ( ap @ SV259 @ SV548 @ SV719 @ SV908 )
= SY4086 ) ) )
= $true )
| ( ( func @ SV259 @ SV548 @ SV719 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2731]) ).
thf(2992,plain,
! [SV549: $i,SV829: $i,SV260: $i] :
( ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( ~ ! [SY4020: $i] :
( ~ ( in @ SY4020 @ SV260 )
| ! [SY4021: $i] :
( ~ ( in @ SY4021 @ SV260 )
| ~ ( in @ ( kpair @ SY4020 @ SY4021 ) @ SV549 )
| ( in @ ( kpair @ SY4020 @ SY4021 ) @ SV829 ) ) )
| ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) )
| ( SV549 = SV829 ) )
= $true )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2732]) ).
thf(2993,plain,
! [SV263: $i,SV552: $i,SV721: $i] :
( ( ( in @ SV721 @ SV552 )
= $false )
| ( ( in @ SV721 @ ( binintersect @ SV263 @ SV552 ) )
= $true )
| ( ( in @ SV721 @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2733]) ).
thf(2994,plain,
! [SV553: $i,SV830: $i,SV264: $i] :
( ( ( breln1 @ SV264 @ SV830 )
= $false )
| ( ( ! [SY4024: $i] :
( ~ ( in @ SY4024 @ SV264 )
| ! [SY4025: $i] :
( ~ ( in @ SY4025 @ SV264 )
| ~ ( ( in @ ( kpair @ SY4024 @ SY4025 ) @ SV553 )
| ( in @ ( kpair @ SY4024 @ SY4025 ) @ SV830 ) )
| ( in @ ( kpair @ SY4024 @ SY4025 ) @ ( binunion @ SV553 @ SV830 ) ) ) ) )
= $true )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2734]) ).
thf(2995,plain,
! [SV265: $i,SV722: $i,SV554: $i,SV909: $i] :
( ( ( ~ ( in @ SV909 @ SV554 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV722 @ ( setadjoin @ SV909 @ emptyset ) ) @ ( binunion @ SV265 @ SV554 ) )
= $true )
| ( ( in @ SV722 @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2735]) ).
thf(2996,plain,
! [SV555: $i,SV266: $i,SV831: $i] :
( ( ( in @ SV831 @ ( powerset @ SV266 ) )
= $false )
| ( ( in @ ( setminus @ SV266 @ SV555 ) @ ( powerset @ ( setminus @ SV266 @ ( binintersect @ SV555 @ SV831 ) ) ) )
= $true )
| ( ( in @ SV555 @ ( powerset @ SV266 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2736]) ).
thf(2997,plain,
! [SV558: $i,SV270: $i,SV832: $i] :
( ( ( in @ SV832 @ ( powerset @ SV270 ) )
= $false )
| ( ( ( setminus @ SV270 @ ( binunion @ SV558 @ SV832 ) )
= ( binintersect @ ( setminus @ SV270 @ SV558 ) @ ( setminus @ SV270 @ SV832 ) ) )
= $true )
| ( ( in @ SV558 @ ( powerset @ SV270 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2737]) ).
thf(2998,plain,
! [SV833: $i > $o,SV559: $i,SV271: $i] :
( ( ( ! [SY4026: $i] :
( ~ ( in @ SY4026 @ SV271 )
| ! [SY4027: $i] :
( ~ ( in @ SY4027 @ SV271 )
| ~ ( in @ ( kpair @ SY4026 @ SY4027 ) @ SV559 )
| ( SV833 @ ( kpair @ SY4026 @ SY4027 ) ) ) ) )
= $false )
| ( ( ! [SY4028: $i] :
( ~ ( in @ SY4028 @ SV559 )
| ( SV833 @ SY4028 ) ) )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2738]) ).
thf(2999,plain,
! [SV272: $i,SV560: $i,SV725: $i] :
( ( ( ~ ( in @ SV725 @ SV560 ) )
= $false )
| ( ( in @ SV725 @ ( symdiff @ SV272 @ SV560 ) )
= $true )
| ( ( in @ SV725 @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2739]) ).
thf(3000,plain,
! [SV273: $i,SV726: $i,SV561: $i,SV910: $i] :
( ( ( ~ ( in @ SV910 @ SV561 ) )
= $true )
| ( ( ( kfst @ ( kpair @ SV726 @ SV910 ) )
= SV726 )
= $true )
| ( ( in @ SV726 @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2740]) ).
thf(3001,plain,
! [SV562: $i,SV274: $i,SV834: $i] :
( ( ( in @ SV834 @ ( powerset @ SV274 ) )
= $false )
| ( ( ~ ( subset @ ( setminus @ SV274 @ SV834 ) @ ( setminus @ SV274 @ SV562 ) )
| ( subset @ SV562 @ SV834 ) )
= $true )
| ( ( in @ SV562 @ ( powerset @ SV274 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2741]) ).
thf(3002,plain,
! [SV275: $i,SV563: $i > $o] :
( ( ( in @ ( sK16_SY3653 @ SV563 @ SV275 ) @ SV275 )
= $true )
| ( ( ~ ~ ! [SY3654: $i] :
~ ~ ( ~ ( in @ SY3654 @ SV275 )
| ~ ( SV563 @ SY3654 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2742]) ).
thf(3003,plain,
! [SV275: $i,SV563: $i > $o] :
( ( ( SV563 @ ( sK16_SY3653 @ SV563 @ SV275 ) )
= $true )
| ( ( ~ ~ ! [SY3654: $i] :
~ ~ ( ~ ( in @ SY3654 @ SV275 )
| ~ ( SV563 @ SY3654 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2743]) ).
thf(3004,plain,
! [SV565: $i,SV277: $i,SV835: $i] :
( ( ( in @ SV835 @ ( powerset @ SV277 ) )
= $false )
| ( ( ! [SY4029: $i] :
( ~ ( in @ SY4029 @ SV277 )
| ~ ( in @ SY4029 @ ( setminus @ SV277 @ ( binunion @ SV565 @ SV835 ) ) )
| ( in @ SY4029 @ ( setminus @ SV277 @ SV565 ) ) ) )
= $true )
| ( ( in @ SV565 @ ( powerset @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2744]) ).
thf(3005,plain,
! [SV278: $i,SV566: $i] :
( ( ( in @ ( sK17_SY3657 @ SV566 @ SV278 ) @ SV278 )
= $true )
| ( ( ~ ! [SY3658: $i] :
( ~ ( in @ SY3658 @ SV566 )
| ( in @ SY3658 @ SV278 ) )
| ( SV278 = SV566 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2745]) ).
thf(3006,plain,
! [SV278: $i,SV566: $i] :
( ( ( ~ ! [SY3658: $i] :
( ~ ( in @ SY3658 @ SV566 )
| ( in @ SY3658 @ SV278 ) ) )
= $true )
| ( ( SV278 = SV566 )
= $true )
| ( ( in @ ( sK17_SY3657 @ SV566 @ SV278 ) @ SV566 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2746]) ).
thf(3007,plain,
! [SV568: $i,SV836: $i,SV280: $i] :
( ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( ! [SY4030: $i] :
( ~ ( in @ SY4030 @ SV280 )
| ! [SY4031: $i] :
( ~ ( in @ SY4031 @ SV280 )
| ~ ( in @ ( kpair @ SY4030 @ SY4031 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
| ! [SY4032: $o] :
( ~ ! [SY4033: $i] :
( ~ ( in @ SY4033 @ SV280 )
| ~ ( in @ ( kpair @ SY4030 @ SY4033 ) @ SV568 )
| ~ ( in @ ( kpair @ SY4033 @ SY4031 ) @ SV836 )
| SY4032 )
| SY4032 ) ) ) )
= $true )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2747]) ).
thf(3008,plain,
! [SV282: $i,SV570: $i,SV728: $i] :
( ( ( ~ ( in @ SV728 @ SV570 ) )
= $true )
| ( ( in @ SV728 @ ( symdiff @ SV282 @ SV570 ) )
= $true )
| ( ( in @ SV728 @ SV282 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2748]) ).
thf(3009,plain,
! [SV284: $i,SV572: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK42_SY3668 @ SV572 @ SV284 ) @ SV284 )
| ~ ( in @ ( sK42_SY3668 @ SV572 @ SV284 ) @ SV572 ) ) )
= $false )
| ( ( ( binintersect @ SV284 @ SV572 )
= emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2750]) ).
thf(3010,plain,
! [SV837: $i,SV288: $i > $o] :
( ( ( ~ ( SV288 @ SV837 )
| ~ ! [SY4034: $i] :
( ~ ( SV288 @ SY4034 )
| ( SV837 = SY4034 ) ) )
= $true )
| ( ( ! [SY3119: $i,SY3120: $i] :
( ~ ( SV288 @ SY3119 )
| ~ ( SV288 @ SY3120 )
| ( SY3119 = SY3120 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2751]) ).
thf(3011,plain,
! [SV289: $i,SV575: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK43_SY3670 @ SV575 @ SV289 ) @ SV289 )
| ~ ( SV575 @ ( sK43_SY3670 @ SV575 @ SV289 ) ) ) )
= $false )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV289 )
| ~ ( SV575 @ SY3671 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2752]) ).
thf(3012,plain,
! [SV291: $i,SV731: $i,SV577: $i > $o] :
( ( ( SV577 @ SV731 )
= $false )
| ( ( in @ SV731
@ ( dsetconstr @ SV291
@ ^ [SY3673: $i] : ( SV577 @ SY3673 ) ) )
= $true )
| ( ( in @ SV731 @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(3013,plain,
! [SV578: $i,SV838: $i,SV292: $i] :
( ( ( breln1 @ SV292 @ SV838 )
= $false )
| ( ( breln1 @ SV292 @ ( binunion @ SV578 @ SV838 ) )
= $true )
| ( ( breln1 @ SV292 @ SV578 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2754]) ).
thf(3014,plain,
! [SV293: $i,SV755: $i,SV732: $i > $i > $o,SV579: $i,SV922: $i] :
( ( ( ~ ( in @ SV922 @ SV579 )
| ~ ( SV732 @ SV755 @ SV922 )
| ( in @ ( kpair @ SV755 @ SV922 )
@ ( dpsetconstr @ SV293 @ SV579
@ ^ [SY3897: $i,SY3898: $i] : ( SV732 @ SY3897 @ SY3898 ) ) ) )
= $true )
| ( ( in @ SV755 @ SV293 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2755]) ).
thf(3015,plain,
! [SV582: $i,SV839: $i,SV297: $i] :
( ( ( breln1 @ SV297 @ SV839 )
= $false )
| ( ( ( binunion @ SV582 @ SV839 )
= ( binunion @ SV839 @ SV582 ) )
= $true )
| ( ( breln1 @ SV297 @ SV582 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(3016,plain,
! [SV583: $i,SV757: $o,SV298: $i,SV733: $i] :
( ( ( ~ ( ~ ( in @ SV733 @ SV298 )
| SV757 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| SV757 )
| SV757 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2759]) ).
thf(3017,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( ( ~ ( ~ ( in @ SV733 @ SV298 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| $true )
| $true )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2760]) ).
thf(3018,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( ( ~ ( ~ ( in @ SV733 @ SV298 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| $false )
| $false )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2761]) ).
thf(3019,plain,
! [SV584: $i,SV299: $i,SV840: $i] :
( ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( ~ ! [SY4035: $i] :
( ~ ( in @ SY4035 @ SV299 )
| ~ ( in @ SY4035 @ SV584 )
| ( in @ SY4035 @ SV840 ) )
| ~ ! [SY4036: $i] :
( ~ ( in @ SY4036 @ SV299 )
| ~ ( in @ SY4036 @ SV840 )
| ( in @ SY4036 @ SV584 ) )
| ( SV584 = SV840 ) )
= $true )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2762]) ).
thf(3020,plain,
! [SV585: $i,SV841: $i,SV300: $i] :
( ( ( breln1 @ SV300 @ SV841 )
= $false )
| ( ( ! [SY4037: $i] :
( ~ ( in @ SY4037 @ SV300 )
| ! [SY4038: $i] :
( ~ ( in @ SY4038 @ SV300 )
| ~ ( in @ ( kpair @ SY4037 @ SY4038 ) @ SV585 )
| ( in @ ( kpair @ SY4037 @ SY4038 ) @ ( binunion @ SV585 @ SV841 ) ) ) ) )
= $true )
| ( ( breln1 @ SV300 @ SV585 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2763]) ).
thf(3021,plain,
! [SV734: $i,SV911: $i,SV586: $i,SV301: $i] :
( ( ( ~ ( func @ SV301 @ SV586 @ SV911 ) )
= $true )
| ( ( ~ ! [SY4087: $i] :
( ~ ( in @ SY4087 @ SV301 )
| ( ( ap @ SV301 @ SV586 @ SV734 @ SY4087 )
= ( ap @ SV301 @ SV586 @ SV911 @ SY4087 ) ) )
| ! [SY4088: $i] :
( ~ ( in @ SY4088 @ SV301 )
| ! [SY4089: $i] :
( ~ ( in @ SY4089 @ SV586 )
| ~ ( in @ ( kpair @ SY4088 @ SY4089 ) @ SV911 )
| ( in @ ( kpair @ SY4088 @ SY4089 ) @ SV734 ) ) ) )
= $true )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2764]) ).
thf(3022,plain,
! [SV587: $i,SV302: $i,SV842: $i] :
( ( ( in @ SV842 @ ( powerset @ SV302 ) )
= $false )
| ( ( ! [SY4039: $i] :
( ~ ( in @ SY4039 @ SV302 )
| ~ ( in @ SY4039 @ ( binunion @ ( setminus @ SV302 @ SV587 ) @ ( setminus @ SV302 @ SV842 ) ) )
| ( in @ SY4039 @ ( setminus @ SV302 @ ( binintersect @ SV587 @ SV842 ) ) ) ) )
= $true )
| ( ( in @ SV587 @ ( powerset @ SV302 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2765]) ).
thf(3023,plain,
! [SV589: $i,SV305: $i,SV843: $i] :
( ( ( in @ SV843 @ ( powerset @ SV305 ) )
= $false )
| ( ( ! [SY4040: $i] :
( ~ ( in @ SY4040 @ ( powerset @ SV305 ) )
| ( in @ ( binintersect @ SV589 @ SV843 ) @ ( powerset @ ( binintersect @ ( binunion @ SV589 @ SY4040 ) @ ( binunion @ SV843 @ SY4040 ) ) ) ) ) )
= $true )
| ( ( in @ SV589 @ ( powerset @ SV305 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2766]) ).
thf(3024,plain,
! [SV590: $i,SV307: $i,SV844: $i] :
( ( ( in @ SV844 @ ( powerset @ SV307 ) )
= $false )
| ( ( ! [SY4041: $i] :
( ~ ( in @ SY4041 @ SV307 )
| ~ ( in @ SY4041 @ ( binintersect @ ( setminus @ SV307 @ SV590 ) @ ( setminus @ SV307 @ SV844 ) ) )
| ( in @ SY4041 @ ( setminus @ SV307 @ ( binunion @ SV590 @ SV844 ) ) ) ) )
= $true )
| ( ( in @ SV590 @ ( powerset @ SV307 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2767]) ).
thf(3025,plain,
! [SV591: $i,SV308: $i,SV845: $i] :
( ( ( in @ SV845 @ ( powerset @ SV308 ) )
= $false )
| ( ( ~ ! [SY4042: $i] :
( ~ ( in @ SY4042 @ SV308 )
| ~ ( in @ SY4042 @ SV591 )
| ( in @ SY4042 @ SV845 ) )
| ( in @ SV591 @ ( powerset @ SV845 ) ) )
= $true )
| ( ( in @ SV591 @ ( powerset @ SV308 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2768]) ).
thf(3026,plain,
! [SV592: $i,SV309: $i,SV846: $i] :
( ( ( in @ SV846 @ ( powerset @ SV309 ) )
= $false )
| ( ( ! [SY4043: $i] :
( ~ ( in @ SY4043 @ SV309 )
| ~ ( in @ SY4043 @ ( setminus @ SV309 @ SV592 ) )
| ~ ( in @ SY4043 @ ( setminus @ SV309 @ SV846 ) )
| ( in @ SY4043 @ ( setminus @ SV309 @ ( binunion @ SV592 @ SV846 ) ) ) ) )
= $true )
| ( ( in @ SV592 @ ( powerset @ SV309 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2769]) ).
thf(3027,plain,
! [SV313: $i,SV736: $i,SV596: $i,SV912: $i] :
( ( ( ~ ( in @ SV912 @ SV596 ) )
= $true )
| ( ( in @ ( setadjoin @ SV736 @ ( setadjoin @ SV912 @ emptyset ) ) @ ( powerset @ ( binunion @ SV313 @ SV596 ) ) )
= $true )
| ( ( in @ SV736 @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2771]) ).
thf(3028,plain,
! [SV314: $i,SV737: $i,SV597: $i,SV913: $i] :
( ( ( ~ ( in @ SV913 @ SV597 ) )
= $true )
| ( ( ( ksnd @ ( kpair @ SV737 @ SV913 ) )
= SV913 )
= $true )
| ( ( in @ SV737 @ SV314 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2772]) ).
thf(3029,plain,
! [SV598: $i,SV315: $i,SV847: $i] :
( ( ( in @ SV847 @ ( powerset @ SV315 ) )
= $false )
| ( ( ! [SY4044: $i] :
( ~ ( in @ SY4044 @ SV315 )
| ~ ( in @ SY4044 @ ( setminus @ SV315 @ ( binunion @ SV598 @ SV847 ) ) )
| ~ ( in @ SY4044 @ SV598 ) ) )
= $true )
| ( ( in @ SV598 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2773]) ).
thf(3030,plain,
! [SV848: $i,SV316: $i > $o] :
( ( ( ~ ( SV316 @ SV848 )
| ~ ! [SY4045: $i] :
( ~ ( SV316 @ SY4045 )
| ( SV848 = SY4045 ) ) )
= $true )
| ( ( ~ ! [SY3190: $i] :
~ ! [SY3191: $i] :
~ ( ~ ( ~ ( SV316 @ SY3191 )
| ( SY3191 = SY3190 ) )
| ~ ( ( SY3191 != SY3190 )
| ( SV316 @ SY3191 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2774]) ).
thf(3031,plain,
! [SV599: $i,SV317: $i,SV849: $i] :
( ( ( in @ SV849 @ ( powerset @ SV317 ) )
= $false )
| ( ( ! [SY4046: $i] :
( ~ ( in @ SY4046 @ ( powerset @ SV317 ) )
| ! [SY4047: $i] :
( ~ ( in @ SY4047 @ ( powerset @ SV317 ) )
| ~ ( subset @ SV599 @ SY4046 )
| ~ ( subset @ SV849 @ SY4047 )
| ( subset @ ( binintersect @ SV599 @ SV849 ) @ ( binintersect @ SY4046 @ SY4047 ) ) ) ) )
= $true )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2775]) ).
thf(3032,plain,
! [SV600: $i,SV318: $i,SV850: $i] :
( ( ( in @ SV850 @ ( powerset @ SV318 ) )
= $false )
| ( ( ! [SY4048: $i] :
( ~ ( in @ SY4048 @ SV318 )
| ~ ~ ( in @ SY4048 @ SV850 )
| ~ ( in @ SY4048 @ ( binintersect @ SV600 @ SV850 ) ) ) )
= $true )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2776]) ).
thf(3033,plain,
! [SV914: $i > $o,SV738: $i,SV601: $i,SV319: $i] :
( ( ( ~ ! [SY4090: $i] :
( ~ ( in @ SY4090 @ SV319 )
| ! [SY4091: $i] :
( ~ ( in @ SY4091 @ SV601 )
| ~ ( in @ ( kpair @ SY4090 @ SY4091 ) @ SV738 )
| ( SV914 @ ( kpair @ SY4090 @ SY4091 ) ) ) ) )
= $true )
| ( ( ! [SY4092: $i] :
( ~ ( in @ SY4092 @ SV738 )
| ( SV914 @ SY4092 ) ) )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2777]) ).
thf(3034,plain,
! [SV320: $i,SV602: $i] :
( ( ( in @ ( sK18_SY3721 @ SV602 @ SV320 ) @ SV320 )
= $true )
| ( ( subset @ SV320 @ SV602 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2778]) ).
thf(3035,plain,
! [SV739: $i,SV603: $o,SV321: $i,SV915: $i] :
( ( ( ~ ( in @ SV915 @ SV321 ) )
= $true )
| ( ( ~ ~ SV603
| ( ( if @ SV321 @ SV603 @ SV739 @ SV915 )
= SV915 ) )
= $true )
| ( ( in @ SV739 @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2780]) ).
thf(3036,plain,
! [SV740: $i,SV321: $i,SV916: $i] :
( ( ( ~ ( in @ SV916 @ SV321 ) )
= $true )
| ( ( ~ ~ $true
| ( ( if @ SV321 @ $true @ SV740 @ SV916 )
= SV916 ) )
= $true )
| ( ( in @ SV740 @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2781]) ).
thf(3037,plain,
! [SV741: $i,SV321: $i,SV917: $i] :
( ( ( ~ ( in @ SV917 @ SV321 ) )
= $true )
| ( ( ~ ~ $false
| ( ( if @ SV321 @ $false @ SV741 @ SV917 )
= SV917 ) )
= $true )
| ( ( in @ SV741 @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2782]) ).
thf(3038,plain,
! [SV851: $i,SV322: $i] :
( ( ( ! [SY3211: $i] :
~ ~ ( ~ ( in @ SY3211 @ SV322 )
| ~ ~ ~ ! [SY3212: $i] :
~ ~ ( ~ ( in @ SY3212 @ SY3211 )
| ~ ( in @ SY3212 @ SV322 ) ) ) )
= $false )
| ( ( in @ SV851 @ SV322 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2783]) ).
thf(3039,plain,
! [SV324: $i,SV605: $i] :
( ( ( in @ ( sK19_SY3726 @ SV605 @ SV324 ) @ SV324 )
= $true )
| ( ( subset @ SV324 @ SV605 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2785]) ).
thf(3040,plain,
! [SV606: $i,SV325: $i,SV852: $i] :
( ( ( in @ SV852 @ ( powerset @ SV325 ) )
= $false )
| ( ( ! [SY4049: $i] :
( ~ ( in @ SY4049 @ ( powerset @ SV325 ) )
| ~ ( subset @ SV606 @ SV852 )
| ~ ( subset @ SV606 @ SY4049 )
| ( subset @ SV606 @ ( binintersect @ SV852 @ SY4049 ) ) ) )
= $true )
| ( ( in @ SV606 @ ( powerset @ SV325 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2787]) ).
thf(3041,plain,
! [SV37: $i] :
( ( ( ~ ( in @ ( sK20_SY2402 @ SV37 ) @ SV37 )
| ~ $true )
= $false )
| ( ( SV37 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2788]) ).
thf(3042,plain,
! [SV743: $i,SV38: $i] :
( ( ( ( omegaS @ SV38 )
= ( omegaS @ SV743 ) )
= $false )
| ( ( SV38 = SV743 )
= $true )
| ( ( in @ SV743 @ omega )
= $false )
| ( ( in @ SV38 @ omega )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(3043,plain,
! [SV39: $i,SV610: $i > $i,SV350: $i] :
( ( ( in @ ( sK21_SY3733 @ SV350 @ SV610 @ SV39 ) @ SV39 )
= $true )
| ( ( func @ SV39 @ SV350
@ ( dpsetconstr @ SV39 @ SV350
@ ^ [SY3734: $i,SY3735: $i] :
( ( SV610 @ SY3734 )
= SY3735 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2790]) ).
thf(3044,plain,
! [SV759: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ SV759 ) )
= $true )
| ( ( ~ ! [SY3941: $i] :
( ~ ( SV40 @ SY3941 )
| ( SV759 = SY3941 ) ) )
= $true )
| ( ( ~ ! [SY2411: $i] :
~ ( SV40 @ SY2411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2792]) ).
thf(3045,plain,
! [SV41: $i,SV611: $i,SV351: $i,SV853: $i] :
( ( ( in @ SV853 @ SV351 )
= $false )
| ( ( ( kpair @ SV611 @ SV853 )
= ( kpair @ SV611 @ SV853 ) )
= $true )
| ( ( in @ SV611 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2793]) ).
thf(3046,plain,
! [SV760: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV760 ) )
= $true )
| ( ( ~ ! [SY3942: $i] :
( ~ ( SV42 @ SY3942 )
| ( SV760 = SY3942 ) ) )
= $true )
| ( ( SV42
@ ( descr
@ ^ [SY2417: $i] : ( SV42 @ SY2417 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2794]) ).
thf(3047,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( in @ ( sK9_SY3238 @ SV353 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2795]) ).
thf(3048,plain,
! [SV44: $i,SV353: $i > $o] :
( ( ( ~ ( in @ ( sK36_SY3943 @ SV353 @ SV44 ) @ SV44 ) )
= $false )
| ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) )
| ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2796]) ).
thf(3049,plain,
! [SV44: $i,SV353: $i > $o] :
( ( ( ~ ( SV353 @ ( sK9_SY3238 @ SV353 @ SV44 ) )
| ~ ( SV353 @ ( sK36_SY3943 @ SV353 @ SV44 ) )
| ( ( sK9_SY3238 @ SV353 @ SV44 )
= ( sK36_SY3943 @ SV353 @ SV44 ) ) )
= $false )
| ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) )
| ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2796]) ).
thf(3050,plain,
! [SV612: $i,SV354: $i,SV45: $i,SV854: $i] :
( ( ( in @ SV854 @ ( funcSet @ SV45 @ SV354 ) )
= $false )
| ( ( ~ ! [SY4050: $i] :
( ~ ( in @ SY4050 @ SV45 )
| ( ( ap @ SV45 @ SV354 @ SV612 @ SY4050 )
= ( ap @ SV45 @ SV354 @ SV854 @ SY4050 ) ) )
| ( SV612 = SV854 ) )
= $true )
| ( ( in @ SV612 @ ( funcSet @ SV45 @ SV354 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2797]) ).
thf(3051,plain,
! [SV614: $i,SV356: $i,SV47: $i,SV855: $i] :
( ( ( in @ SV855 @ SV47 )
= $false )
| ( ( in @ ( kpair @ SV855 @ ( ap @ SV47 @ SV356 @ SV614 @ SV855 ) ) @ SV614 )
= $true )
| ( ( in @ SV614 @ ( funcSet @ SV47 @ SV356 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2798]) ).
thf(3052,plain,
! [SV616: $i,SV358: $i,SV49: $i,SV856: $i] :
( ( ( in @ SV856 @ SV49 )
= $false )
| ( ( in @ ( ap @ SV49 @ SV358 @ SV616 @ SV856 ) @ SV358 )
= $true )
| ( ( in @ SV616 @ ( funcSet @ SV49 @ SV358 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2799]) ).
thf(3053,plain,
! [SV359: $i,SV50: $i,SV857: $i,SV761: $i] :
( ( ( SV761 = SV857 )
= $false )
| ( ( ( setadjoin @ SV50 @ SV761 )
= ( setadjoin @ SV359 @ SV857 ) )
= $true )
| ( ( SV50 = SV359 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2800]) ).
thf(3054,plain,
! [SV762: $i,SV361: $i,SV52: $i,SV923: $i] :
( ( ( ~ ( in @ SV923 @ ( powerset @ SV52 ) )
| ! [SY4098: $i] :
( ~ ( in @ SY4098 @ SV52 )
| ~ ( in @ SY4098 @ ( binintersect @ SV361 @ SV762 ) )
| ( in @ SY4098 @ ( binunion @ SV762 @ SV923 ) ) ) )
= $true )
| ( ( in @ SV762 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2801]) ).
thf(3055,plain,
! [SV54: $i,SV618: $i > $i,SV363: $i] :
( ( ( in @ ( sK22_SY3742 @ SV363 @ SV618 @ SV54 ) @ SV54 )
= $true )
| ( ( in
@ ( lam @ SV54 @ SV363
@ ^ [SY3743: $i] : ( SV618 @ SY3743 ) )
@ ( funcSet @ SV54 @ SV363 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2802]) ).
thf(3056,plain,
! [SV763: $i,SV55: $i,SV364: $i] :
( ( ( ~ ( subset @ SV364 @ ( setminus @ SV55 @ SV763 ) ) )
= $true )
| ( ( subset @ SV763 @ ( setminus @ SV55 @ SV364 ) )
= $true )
| ( ( in @ SV763 @ ( powerset @ SV55 ) )
= $false )
| ( ( in @ SV364 @ ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2804]) ).
thf(3057,plain,
! [SV764: $i,SV365: $i,SV56: $i,SV924: $i] :
( ( ( ~ ( in @ SV924 @ ( powerset @ SV56 ) )
| ! [SY4099: $i] :
( ~ ( in @ SY4099 @ ( powerset @ SV56 ) )
| ( ( setminus @ SV56 @ ( binintersect @ ( binunion @ SV365 @ SV764 ) @ ( binunion @ SV924 @ SY4099 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV56 @ SV365 ) @ ( setminus @ SV56 @ SV764 ) ) @ ( binintersect @ ( setminus @ SV56 @ SV924 ) @ ( setminus @ SV56 @ SY4099 ) ) ) ) ) )
= $true )
| ( ( in @ SV764 @ ( powerset @ SV56 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV56 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2805]) ).
thf(3058,plain,
! [SV57: $i,SV366: $i] :
( ( ( ! [SY3265: $i] :
~ ~ ( ~ ( in @ SV366 @ SY3265 )
| ~ ( in @ SY3265 @ SV57 ) ) )
= $false )
| ( ( in @ SV366 @ ( setunion @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2806]) ).
thf(3059,plain,
! [SV57: $i,SV366: $i] :
( ( ( ! [SY3266: $i] :
~ ~ ( ~ ( in @ SV366 @ SY3266 )
| ~ ( in @ SY3266 @ SV57 ) ) )
= $true )
| ( ( in @ SV366 @ ( setunion @ SV57 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2807]) ).
thf(3060,plain,
! [SV765: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV765 ) )
= $true )
| ( ( ~ ! [SY3949: $i] :
( ~ ( SV58 @ SY3949 )
| ( SV765 = SY3949 ) ) )
= $true )
| ( ( ! [SY2464: $i,SY2465: $i] :
( ~ ( SV58 @ SY2464 )
| ~ ( SV58 @ SY2465 )
| ( SY2464 = SY2465 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2808]) ).
thf(3061,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ( ~ ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
| ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 ) )
| ~ ( ( ( sK37_SY3950 @ SV766 @ SV59 )
!= SV766 )
| ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) ) ) )
= $true )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2809]) ).
thf(3062,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ~ ( SV60 @ SV767 ) )
= $true )
| ( ( ~ ! [SY3951: $i] :
( ~ ( SV60 @ SY3951 )
| ( SV767 = SY3951 ) ) )
= $true )
| ( ( ~ ! [SY2472: $i] :
~ ~ ( ~ ( SV60 @ SY2472 )
| ~ ! [SY2473: $i] :
( ~ ( SV60 @ SY2473 )
| ( SY2472 = SY2473 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2810]) ).
thf(3063,plain,
! [SV367: $i > $o,SV61: $i,SV858: $i] :
( ( ( in @ SV858 @ SV61 )
= $false )
| ( ( SV367 @ SV858 )
= $true )
| ( ( ~ ! [SY3268: $i] :
~ ~ ( ~ ( in @ SY3268 @ SV61 )
| ~ ~ ( SV367 @ SY3268 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2811]) ).
thf(3064,plain,
! [SV619: $i,SV369: $i,SV63: $i,SV859: $i] :
( ( ( in @ SV859 @ SV63 )
= $false )
| ( ( in @ ( ap @ SV63 @ SV369 @ SV619 @ SV859 ) @ SV369 )
= $true )
| ( ( func @ SV63 @ SV369 @ SV619 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2812]) ).
thf(3065,plain,
! [SV64: $i,SV620: $i > $i,SV370: $i] :
( ( ( in @ ( sK23_SY3745 @ SV370 @ SV620 @ SV64 ) @ SV64 )
= $true )
| ( ( ( lam @ SV64 @ SV370
@ ^ [SY3746: $i] : ( SV620 @ SY3746 ) )
= ( lam @ SV64 @ SV370
@ ^ [SY3747: $i] : ( SV620 @ SY3747 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2813]) ).
thf(3066,plain,
! [SV65: $i,SV371: $i] :
( ( ( ~ ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 )
| ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 )
| ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 ) ) )
= $true )
| ( ( SV65 = SV371 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2815]) ).
thf(3067,plain,
! [SV768: $i,SV68: $i,SV372: $i] :
( ( ( ~ ( subset @ SV372 @ ( setminus @ SV68 @ SV768 ) ) )
= $true )
| ( ( ! [SY3952: $i] :
( ~ ( in @ SY3952 @ SV68 )
| ~ ( in @ SY3952 @ SV768 )
| ( in @ SY3952 @ ( setminus @ SV68 @ SV372 ) ) ) )
= $true )
| ( ( in @ SV768 @ ( powerset @ SV68 ) )
= $false )
| ( ( in @ SV372 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2816]) ).
thf(3068,plain,
! [SV769: $i,SV373: $i,SV69: $i,SV925: $i] :
( ( ( ~ ( in @ SV925 @ SV69 )
| ~ ( in @ SV925 @ ( setminus @ SV69 @ ( binintersect @ SV373 @ SV769 ) ) )
| ( in @ SV925 @ ( binunion @ ( setminus @ SV69 @ SV373 ) @ ( setminus @ SV69 @ SV769 ) ) ) )
= $true )
| ( ( in @ SV769 @ ( powerset @ SV69 ) )
= $false )
| ( ( in @ SV373 @ ( powerset @ SV69 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2817]) ).
thf(3069,plain,
! [SV376: $i,SV860: $o,SV72: $i,SV621: $i] :
( ( ( ( SV621 != SV72 )
| SV860 )
= $false )
| ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| SV860 )
| SV860 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2819]) ).
thf(3070,plain,
! [SV376: $i,SV72: $i,SV621: $i] :
( ( ( ( SV621 != SV72 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| $true )
| $true )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2820]) ).
thf(3071,plain,
! [SV376: $i,SV72: $i,SV621: $i] :
( ( ( ( SV621 != SV72 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| $false )
| $false )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2821]) ).
thf(3072,plain,
! [SV772: $i,SV379: $i,SV75: $i,SV926: $i] :
( ( ( ~ ( in @ SV926 @ SV75 )
| ~ ( in @ SV926 @ ( setminus @ SV75 @ ( binunion @ SV379 @ SV772 ) ) )
| ( in @ SV926 @ ( setminus @ SV75 @ SV772 ) ) )
= $true )
| ( ( in @ SV772 @ ( powerset @ SV75 ) )
= $false )
| ( ( in @ SV379 @ ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2823]) ).
thf(3073,plain,
! [SV380: $i > $i,SV76: $i,SV622: $i] :
( ( ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3287: $i] : ( SV380 @ SY3287 ) ) )
= $false )
| ( ( ~ ! [SY3750: $i] :
~ ~ ( ~ ( in @ SY3750 @ SV76 )
| ( SV622
!= ( SV380 @ SY3750 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2824]) ).
thf(3074,plain,
! [SV380: $i > $i,SV622: $i,SV76: $i] :
( ( ( ~ ! [SY3751: $i] :
~ ~ ( ~ ( in @ SY3751 @ SV76 )
| ( SV622
!= ( SV380 @ SY3751 ) ) ) )
= $false )
| ( ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3290: $i] : ( SV380 @ SY3290 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2825]) ).
thf(3075,plain,
! [SV381: $i > $i,SV623: $i,SV77: $i,SV918: $i] :
( ( ( ~ ( ~ ( in @ SV918 @ SV77 )
| ( SV623
!= ( SV381 @ SV918 ) ) ) )
= $false )
| ( ( in @ SV623
@ ( image1 @ SV77
@ ^ [SY3293: $i] : ( SV381 @ SY3293 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2826]) ).
thf(3076,plain,
! [SV773: $i,SV382: $i,SV78: $i,SV927: $i] :
( ( ( ~ ( in @ SV927 @ SV78 )
| ! [SY4100: $i] :
( ~ ( in @ SY4100 @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ SY4100 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
| ~ ! [SY4101: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY4101 @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ SY4101 ) @ SV382 ) )
| ~ ( in @ ( kpair @ SY4101 @ SY4100 ) @ SV773 ) ) ) )
= $true )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2827]) ).
thf(3077,plain,
! [SV384: $i,SV80: $i,SV625: $i] :
( ( ( in @ SV625 @ ( setadjoin @ SV80 @ SV384 ) )
= $false )
| ( ( ( SV625 = SV80 )
| ( in @ SV625 @ SV384 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2828]) ).
thf(3078,plain,
! [SV384: $i,SV80: $i,SV625: $i] :
( ( ( ( SV625 = SV80 )
| ( in @ SV625 @ SV384 ) )
= $false )
| ( ( in @ SV625 @ ( setadjoin @ SV80 @ SV384 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2829]) ).
thf(3079,plain,
! [SV774: $i,SV386: $i,SV82: $i,SV928: $i] :
( ( ( ~ ( in @ SV928 @ SV82 )
| ! [SY4102: $i] :
( ~ ( in @ SY4102 @ SV82 )
| ~ ( in @ ( kpair @ SV928 @ SY4102 ) @ ( binunion @ SV386 @ SV774 ) )
| ( in @ ( kpair @ SV928 @ SY4102 ) @ SV386 )
| ( in @ ( kpair @ SV928 @ SY4102 ) @ SV774 ) ) )
= $true )
| ( ( breln1 @ SV82 @ SV774 )
= $false )
| ( ( breln1 @ SV82 @ SV386 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(3080,plain,
! [SV776: $i,SV389: $i,SV86: $i,SV929: $i] :
( ( ( ~ ( in @ SV929 @ SV86 )
| ~ ( subset @ SV389 @ ( setminus @ SV86 @ SV776 ) )
| ~ ( in @ SV929 @ SV776 )
| ~ ( in @ SV929 @ SV389 ) )
= $true )
| ( ( in @ SV776 @ ( powerset @ SV86 ) )
= $false )
| ( ( in @ SV389 @ ( powerset @ SV86 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(3081,plain,
! [SV777: $i,SV390: $i,SV87: $i,SV930: $i] :
( ( ( ~ ( in @ SV930 @ SV87 )
| ~ ( subset @ SV390 @ SV777 )
| ~ ~ ( in @ SV930 @ SV777 )
| ~ ( in @ SV930 @ SV390 ) )
= $true )
| ( ( in @ SV777 @ ( powerset @ SV87 ) )
= $false )
| ( ( in @ SV390 @ ( powerset @ SV87 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2833]) ).
thf(3082,plain,
! [SV779: $i,SV393: $i,SV90: $i,SV931: $i] :
( ( ( ~ ( in @ SV931 @ ( powerset @ SV90 ) )
| ! [SY4103: $i] :
( ~ ( in @ SY4103 @ SV90 )
| ~ ( in @ SY4103 @ ( binintersect @ SV393 @ SV779 ) )
| ( in @ SY4103 @ ( binintersect @ ( binunion @ SV393 @ SV931 ) @ ( binunion @ SV779 @ SV931 ) ) ) ) )
= $true )
| ( ( in @ SV779 @ ( powerset @ SV90 ) )
= $false )
| ( ( in @ SV393 @ ( powerset @ SV90 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2835]) ).
thf(3083,plain,
! [SV92: $i,SV394: $i,SV627: $i] :
( ( ( in @ SV627 @ SV394 )
= $true )
| ( ( in @ SV627 @ ( setminus @ SV92 @ SV394 ) )
= $true )
| ( ( in @ SV627 @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2836]) ).
thf(3084,plain,
! [SV628: $i,SV396: $i,SV95: $i,SV861: $i] :
( ( ( in @ SV861 @ SV95 )
= $false )
| ( ( ( ap @ SV95 @ SV396 @ SV628 @ SV861 )
= ( ap @ SV95 @ SV396 @ SV628 @ SV861 ) )
= $true )
| ( ( in @ SV628 @ ( funcSet @ SV95 @ SV396 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2837]) ).
thf(3085,plain,
! [SV397: $i,SV96: $i,SV629: $i] :
( ( ( in @ SV629 @ SV96 )
= $false )
| ( ( in @ SV629 @ SV397 )
= $true )
| ( ( in @ SV629 @ ( setminus @ SV96 @ SV397 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2838]) ).
thf(3086,plain,
! [SV780: $i,SV400: $i,SV99: $i,SV932: $i] :
( ( ( ~ ( in @ SV932 @ SV99 )
| ~ ( in @ SV932 @ ( setminus @ SV99 @ ( binunion @ SV400 @ SV780 ) ) )
| ( in @ SV932 @ ( setminus @ SV99 @ SV400 ) ) )
= $true )
| ( ( in @ SV780 @ ( powerset @ SV99 ) )
= $false )
| ( ( in @ SV400 @ ( powerset @ SV99 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2839]) ).
thf(3087,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ! [SY2563: $i,SY2564: $i] :
( ~ ( SV100 @ SY2563 )
| ~ ( SV100 @ SY2564 )
| ( SY2563 = SY2564 ) ) )
= $false )
| ( ( ~ ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2840]) ).
thf(3088,plain,
! [SV102: $i,SV402: $i,SV631: $i] :
( ( ( ~ ( in @ SV631 @ SV402 ) )
= $false )
| ( ( ~ ( in @ SV631 @ SV102 ) )
= $true )
| ( ( in @ SV631 @ ( setminus @ SV102 @ SV402 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2841]) ).
thf(3089,plain,
! [SV404: $i > $o,SV104: $i,SV862: $i] :
( ( ( ~ ( in @ SV862 @ SV104 )
| ~ ~ ( SV404 @ SV862 ) )
= $true )
| ( ( ~ ! [SY3324: $i] :
( ~ ( in @ SY3324 @ SV104 )
| ( SV404 @ SY3324 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2842]) ).
thf(3090,plain,
! [SV106: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK44_SY2577 @ SV106 ) @ omega )
| ~ ( in @ ( sK44_SY2577 @ SV106 ) @ SV106 ) )
| ( in @ ( setadjoin @ ( sK44_SY2577 @ SV106 ) @ ( sK44_SY2577 @ SV106 ) ) @ SV106 ) )
= $false )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( ! [SY2578: $i] :
( ~ ( in @ SY2578 @ omega )
| ( in @ SY2578 @ SV106 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2843]) ).
thf(3091,plain,
! [SV633: $i,SV406: $i,SV108: $i,SV863: $i] :
( ( ( in @ SV863 @ SV108 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV406
@ ^ [SY4051: $i] : ( in @ ( kpair @ SV863 @ SY4051 ) @ SV633 ) ) )
= $true )
| ( ( func @ SV108 @ SV406 @ SV633 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2844]) ).
thf(3092,plain,
! [SV782: $i,SV407: $i,SV109: $i] :
( ( ( ~ ! [SY3965: $i] :
( ~ ( in @ SY3965 @ SV109 )
| ~ ( in @ SY3965 @ SV407 )
| ( in @ SY3965 @ SV782 ) ) )
= $true )
| ( ( subset @ SV407 @ SV782 )
= $true )
| ( ( in @ SV782 @ ( powerset @ SV109 ) )
= $false )
| ( ( in @ SV407 @ ( powerset @ SV109 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2845]) ).
thf(3093,plain,
! [SV783: $i,SV408: $i,SV110: $i,SV933: $i] :
( ( ( ~ ( in @ SV933 @ SV110 )
| ~ ~ ( in @ SV933 @ SV408 )
| ~ ( in @ SV933 @ ( binintersect @ SV408 @ SV783 ) ) )
= $true )
| ( ( in @ SV783 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV408 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2846]) ).
thf(3094,plain,
! [SV112: $i,SV635: $i,SV410: $i,SV864: $i] :
( ( ( in @ SV864 @ SV410 )
= $false )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV635 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV635 @ ( setadjoin @ SV864 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV112 @ SV410 ) ) )
= $true )
| ( ( in @ SV635 @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2847]) ).
thf(3095,plain,
! [SV784: $i,SV411: $i,SV113: $i,SV934: $i] :
( ( ( ~ ( in @ SV934 @ SV113 )
| ~ ( in @ SV934 @ ( setminus @ SV113 @ SV411 ) )
| ( in @ SV934 @ ( setminus @ SV113 @ ( binintersect @ SV411 @ SV784 ) ) ) )
= $true )
| ( ( in @ SV784 @ ( powerset @ SV113 ) )
= $false )
| ( ( in @ SV411 @ ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2848]) ).
thf(3096,plain,
! [SV114: $i,SV412: $i,SV785: $i] :
( ( ( ~ ( in @ SV785 @ SV412 ) )
= $true )
| ( ( ~ ( in @ SV785 @ ( setminus @ SV114 @ SV412 ) ) )
= $true )
| ( ( in @ SV785 @ SV114 )
= $false )
| ( ( in @ SV412 @ ( powerset @ SV114 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2849]) ).
thf(3097,plain,
! [SV639: $i,SV416: $i > $o,SV118: $i] :
( ( ( ~ ! [SY3768: $i] :
( ~ ( in @ SY3768 @ SV118 )
| ~ ( SV416 @ SY3768 )
| ( SY3768 = SV639 ) ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY3351: $i] : ( SV416 @ SY3351 ) )
= $true )
| ( ( SV416 @ SV639 )
= $false )
| ( ( in @ SV639 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2852]) ).
thf(3098,plain,
! [SV120: $i,SV418: $i,SV640: $i] :
( ( ( ~ ( in @ SV640 @ SV418 ) )
= $false )
| ( ( ~ ( in @ SV640 @ ( symdiff @ SV120 @ SV418 ) ) )
= $true )
| ( ( in @ SV640 @ SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2853]) ).
thf(3099,plain,
! [SV121: $i,SV641: $i > $i,SV419: $i] :
( ( ( in @ ( sK24_SY3770 @ SV419 @ SV641 @ SV121 ) @ SV121 )
= $true )
| ( ( ! [SY3771: $i] :
( ~ ( in @ SY3771 @ SV121 )
| ( ( ap @ SV121 @ SV419
@ ( lam @ SV121 @ SV419
@ ^ [SY3772: $i] : ( SV641 @ SY3772 ) )
@ SY3771 )
= ( SV641 @ SY3771 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2854]) ).
thf(3100,plain,
! [SV641: $i > $i,SV419: $i,SV121: $i,SV935: $i] :
( ( ( ~ ( in @ SV935 @ SV121 )
| ( ( ap @ SV121 @ SV419
@ ( lam @ SV121 @ SV419
@ ^ [SY3772: $i] : ( SV641 @ SY3772 ) )
@ SV935 )
= ( SV641 @ SV935 ) ) )
= $true )
| ( ( in @ ( SV641 @ ( sK24_SY3770 @ SV419 @ SV641 @ SV121 ) ) @ SV419 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2855]) ).
thf(3101,plain,
! [SV865: $i > $o,SV788: $i > $o,SV420: $i,SV122: $i] :
( ( ( ! [SY4052: $i] :
( ~ ( in @ SY4052 @ SV122 )
| ! [SY4053: $i] :
( ~ ( in @ SY4053 @ SV420 )
| ( SY4052 != SY4053 )
| ~ ( ~ ( ~ ( SV788 @ SY4052 )
| ( SV865 @ SY4053 ) )
| ~ ( ~ ( SV865 @ SY4053 )
| ( SV788 @ SY4052 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2856]) ).
thf(3102,plain,
! [SV789: $i,SV421: $i > $o,SV123: $i,SV936: $i] :
( ( ( ~ ( in @ SV936 @ SV123 )
| ~ ( SV421 @ SV789 )
| ~ ( SV421 @ SV936 )
| ( SV789 = SV936 ) )
= $true )
| ( ( in @ SV789 @ SV123 )
= $false )
| ( ( ex1 @ SV123
@ ^ [SY3363: $i] : ( SV421 @ SY3363 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2857]) ).
thf(3103,plain,
! [SV423: $i,SV790: $i,SV125: $i,SV937: $i] :
( ( ( ~ ( in @ SV937 @ SV125 )
| ! [SY4105: $i] :
( ~ ( in @ SY4105 @ SV125 )
| ~ ( in @ ( kpair @ SV937 @ SY4105 ) @ SV790 )
| ( in @ ( kpair @ SV937 @ SY4105 ) @ ( binunion @ SV423 @ SV790 ) ) ) )
= $true )
| ( ( breln1 @ SV125 @ SV790 )
= $false )
| ( ( breln1 @ SV125 @ SV423 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2858]) ).
thf(3104,plain,
! [SV642: $i,SV424: $o,SV126: $i,SV866: $i] :
( ( ( in @ SV866 @ SV126 )
= $false )
| ( ( ~ ~ SV424
| ( in @ SV866
@ ( dsetconstr @ SV126
@ ^ [SY4056: $i] :
( ~ ( ~ SV424
| ( SY4056 != SV642 ) )
| ~ ( ~ ~ SV424
| ( SY4056 != SV866 ) ) ) ) ) )
= $true )
| ( ( in @ SV642 @ SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2859]) ).
thf(3105,plain,
! [SV643: $i,SV126: $i,SV867: $i] :
( ( ( in @ SV867 @ SV126 )
= $false )
| ( ( ~ ~ $true
| ( in @ SV867
@ ( dsetconstr @ SV126
@ ^ [SY4057: $i] :
( ~ ( ~ $true
| ( SY4057 != SV643 ) )
| ~ ( ~ ~ $true
| ( SY4057 != SV867 ) ) ) ) ) )
= $true )
| ( ( in @ SV643 @ SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2860]) ).
thf(3106,plain,
! [SV644: $i,SV126: $i,SV868: $i] :
( ( ( in @ SV868 @ SV126 )
= $false )
| ( ( ~ ~ $false
| ( in @ SV868
@ ( dsetconstr @ SV126
@ ^ [SY4058: $i] :
( ~ ( ~ $false
| ( SY4058 != SV644 ) )
| ~ ( ~ ~ $false
| ( SY4058 != SV868 ) ) ) ) ) )
= $true )
| ( ( in @ SV644 @ SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2861]) ).
thf(3107,plain,
! [SV426: $i,SV128: $i,SV646: $i] :
( ( ( in @ SV646 @ ( symdiff @ SV128 @ SV426 ) )
= $false )
| ( ( in @ SV646 @ SV426 )
= $false )
| ( ( in @ SV646 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2862]) ).
thf(3108,plain,
! [SV130: $i,SV427: $i,SV938: $i] :
( ( ( ~ ( in @ SV938 @ SV427 )
| ( in @ SV938 @ SV130 ) )
= $true )
| ( ( in @ SV427 @ ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(3109,plain,
! [SV427: $i,SV130: $i] :
( ( ( ~ ( in @ ( sK45_SY3375 @ SV130 @ SV427 ) @ SV427 )
| ( in @ ( sK45_SY3375 @ SV130 @ SV427 ) @ SV130 ) )
= $false )
| ( ( in @ SV427 @ ( powerset @ SV130 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2865]) ).
thf(3110,plain,
! [SV792: $i,SV428: $i,SV131: $i,SV939: $i] :
( ( ( ~ ( in @ SV939 @ SV131 )
| ! [SY4106: $i] :
( ~ ( in @ SY4106 @ SV131 )
| ! [SY4107: $i] :
( ~ ( in @ SY4107 @ SV131 )
| ~ ( in @ ( kpair @ SV939 @ SY4107 ) @ SV428 )
| ~ ( in @ ( kpair @ SY4107 @ SY4106 ) @ SV792 )
| ( in @ ( kpair @ SV939 @ SY4106 ) @ ( breln1compset @ SV131 @ SV428 @ SV792 ) ) ) ) )
= $true )
| ( ( breln1 @ SV131 @ SV792 )
= $false )
| ( ( breln1 @ SV131 @ SV428 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(3111,plain,
! [SV794: $i,SV432: $i,SV135: $i] :
( ( ( ~ ! [SY3983: $i] :
( ~ ( in @ SY3983 @ SV135 )
| ! [SY3984: $i] :
( ~ ( in @ SY3984 @ SV135 )
| ~ ( in @ ( kpair @ SY3983 @ SY3984 ) @ SV432 )
| ( in @ ( kpair @ SY3983 @ SY3984 ) @ SV794 ) ) ) )
= $true )
| ( ( subset @ SV432 @ SV794 )
= $true )
| ( ( breln1 @ SV135 @ SV794 )
= $false )
| ( ( breln1 @ SV135 @ SV432 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2868]) ).
thf(3112,plain,
! [SV136: $i] :
( ( ( ~ ( in @ ( sK25_SY2669 @ SV136 ) @ SV136 )
| ( ( binintersect @ ( sK25_SY2669 @ SV136 ) @ SV136 )
!= emptyset ) )
= $false )
| ( ( SV136 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2869]) ).
thf(3113,plain,
! [SV434: $i,SV138: $i,SV869: $i,SV795: $i] :
( ( ( SV795 = SV869 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV795 @ SV138 )
| ( in @ SV869 @ SV434 ) )
| ~ ( ~ ( in @ SV869 @ SV434 )
| ( in @ SV795 @ SV138 ) ) ) )
= $true )
| ( ( SV138 = SV434 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2870]) ).
thf(3114,plain,
! [SV796: $i,SV435: $i,SV139: $i,SV940: $i] :
( ( ( ~ ( in @ SV940 @ ( powerset @ SV139 ) )
| ~ ( subset @ SV435 @ SV940 )
| ( subset @ ( binintersect @ SV435 @ SV796 ) @ SV940 ) )
= $true )
| ( ( in @ SV796 @ ( powerset @ SV139 ) )
= $false )
| ( ( in @ SV435 @ ( powerset @ SV139 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2871]) ).
thf(3115,plain,
! [SV650: $i,SV870: $i,SV436: $i,SV140: $i] :
( ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( ~ ! [SY4059: $i] :
( ~ ( in @ SY4059 @ SV140 )
| ! [SY4060: $i] :
( ~ ( in @ SY4060 @ SV436 )
| ~ ( in @ ( kpair @ SY4059 @ SY4060 ) @ SV650 )
| ( in @ ( kpair @ SY4059 @ SY4060 ) @ SV870 ) ) )
| ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) )
| ( SV650 = SV870 ) )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2872]) ).
thf(3116,plain,
! [SV141: $i,SV651: $i,SV437: $i,SV871: $i] :
( ( ( in @ SV871 @ SV437 )
= $false )
| ( ( in @ ( kpair @ SV651 @ SV871 ) @ ( cartprod @ SV141 @ SV437 ) )
= $true )
| ( ( in @ SV651 @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2873]) ).
thf(3117,plain,
! [SV142: $i,SV652: $i,SV438: $i,SV872: $i] :
( ( ( in @ SV872 @ SV438 )
= $false )
| ( ( in @ ( kpair @ SV652 @ SV872 ) @ ( powerset @ ( powerset @ ( binunion @ SV142 @ SV438 ) ) ) )
= $true )
| ( ( in @ SV652 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(3118,plain,
! [SV144: $i,SV654: $i > $i,SV440: $i] :
( ( ( in @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) @ SV144 )
= $true )
| ( ( ! [SY3787: $i] :
( ~ ( in @ SY3787 @ ( funcSet @ SV440 @ SV144 ) )
| ~ ! [SY3788: $i] :
( ~ ( in @ SY3788 @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SY3787 @ ( SV654 @ SY3788 ) )
= SY3788 ) )
| ( surjective @ SV440 @ SV144 @ SY3787 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2875]) ).
thf(3119,plain,
! [SV654: $i > $i,SV144: $i,SV440: $i,SV941: $i] :
( ( ( ~ ( in @ SV941 @ ( funcSet @ SV440 @ SV144 ) )
| ~ ! [SY4108: $i] :
( ~ ( in @ SY4108 @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SV941 @ ( SV654 @ SY4108 ) )
= SY4108 ) )
| ( surjective @ SV440 @ SV144 @ SV941 ) )
= $true )
| ( ( in @ ( SV654 @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) ) @ SV440 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2876]) ).
thf(3120,plain,
! [SV145: $i,SV441: $i,SV797: $i] :
( ( ( ~ ( in @ SV797 @ SV441 ) )
= $true )
| ( ( in @ SV797 @ ( setminus @ SV145 @ ( setminus @ SV145 @ SV441 ) ) )
= $true )
| ( ( in @ SV797 @ SV145 )
= $false )
| ( ( in @ SV441 @ ( powerset @ SV145 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2877]) ).
thf(3121,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( in @ ( sK11_SY3407 @ SV442 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2878]) ).
thf(3122,plain,
! [SV146: $i,SV442: $i > $o] :
( ( ( ~ ( in @ ( sK38_SY3987 @ SV442 @ SV146 ) @ SV146 ) )
= $false )
| ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) )
| ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2879]) ).
thf(3123,plain,
! [SV146: $i,SV442: $i > $o] :
( ( ( ~ ( SV442 @ ( sK11_SY3407 @ SV442 @ SV146 ) )
| ~ ( SV442 @ ( sK38_SY3987 @ SV442 @ SV146 ) )
| ( ( sK11_SY3407 @ SV442 @ SV146 )
= ( sK38_SY3987 @ SV442 @ SV146 ) ) )
= $false )
| ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) )
| ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2879]) ).
thf(3124,plain,
! [SV798: $i,SV443: $i,SV147: $i,SV942: $i] :
( ( ( ~ ( in @ SV942 @ SV147 )
| ~ ( in @ SV942 @ ( setminus @ SV147 @ SV443 ) )
| ~ ( in @ SV942 @ ( binintersect @ SV443 @ SV798 ) ) )
= $true )
| ( ( in @ SV798 @ ( powerset @ SV147 ) )
= $false )
| ( ( in @ SV443 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2880]) ).
thf(3125,plain,
! [SV799: $i,SV444: $i,SV148: $i,SV943: $i] :
( ( ( ~ ( in @ SV943 @ ( powerset @ SV148 ) )
| ! [SY4109: $i] :
( ~ ( in @ SY4109 @ SV148 )
| ~ ( in @ SY4109 @ ( binintersect @ SV444 @ SV799 ) )
| ( in @ SY4109 @ ( binunion @ SV444 @ SV943 ) ) ) )
= $true )
| ( ( in @ SV799 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV444 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(3126,plain,
! [SV149: $i,SV445: $i > $o] :
( ( ( ~ ( in @ ( sK27_SY3417 @ SV445 @ SV149 ) @ SV149 )
| ~ ( SV445 @ ( sK27_SY3417 @ SV445 @ SV149 ) ) )
= $false )
| ( ( ex1 @ SV149
@ ^ [SY3416: $i] : ( SV445 @ SY3416 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2882]) ).
thf(3127,plain,
! [SV800: $i,SV446: $i,SV944: $i,SV150: $i] :
( ( ( ~ ( breln1 @ SV150 @ SV944 )
| ( ( breln1compset @ SV150 @ ( binunion @ SV446 @ SV800 ) @ SV944 )
= ( binunion @ ( breln1compset @ SV150 @ SV446 @ SV944 ) @ ( breln1compset @ SV150 @ SV800 @ SV944 ) ) ) )
= $true )
| ( ( breln1 @ SV150 @ SV800 )
= $false )
| ( ( breln1 @ SV150 @ SV446 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2883]) ).
thf(3128,plain,
! [SV152: $i > $o,SV448: $i > $o] :
( ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2885]) ).
thf(3129,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ( ~ ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
| ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) ) )
| ~ ( ~ ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
| ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2886]) ).
thf(3130,plain,
! [SV657: $i,SV451: $o,SV155: $i,SV873: $i] :
( ( ( in @ SV873 @ SV155 )
= $false )
| ( ( ~ ~ SV451
| ( ( dsetconstr @ SV155
@ ^ [SY4063: $i] :
( ~ ( ~ SV451
| ( SY4063 != SV657 ) )
| ~ ( ~ ~ SV451
| ( SY4063 != SV873 ) ) ) )
= ( setadjoin @ SV873 @ emptyset ) ) )
= $true )
| ( ( in @ SV657 @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2887]) ).
thf(3131,plain,
! [SV658: $i,SV155: $i,SV874: $i] :
( ( ( in @ SV874 @ SV155 )
= $false )
| ( ( ~ ~ $true
| ( ( dsetconstr @ SV155
@ ^ [SY4064: $i] :
( ~ ( ~ $true
| ( SY4064 != SV658 ) )
| ~ ( ~ ~ $true
| ( SY4064 != SV874 ) ) ) )
= ( setadjoin @ SV874 @ emptyset ) ) )
= $true )
| ( ( in @ SV658 @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2888]) ).
thf(3132,plain,
! [SV659: $i,SV155: $i,SV875: $i] :
( ( ( in @ SV875 @ SV155 )
= $false )
| ( ( ~ ~ $false
| ( ( dsetconstr @ SV155
@ ^ [SY4065: $i] :
( ~ ( ~ $false
| ( SY4065 != SV659 ) )
| ~ ( ~ ~ $false
| ( SY4065 != SV875 ) ) ) )
= ( setadjoin @ SV875 @ emptyset ) ) )
= $true )
| ( ( in @ SV659 @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2889]) ).
thf(3133,plain,
! [SV453: $i,SV802: $i,SV157: $i,SV945: $i] :
( ( ( ~ ( in @ SV945 @ SV157 )
| ~ ( in @ ( kpair @ SV802 @ SV945 ) @ SV453 )
| ( in @ ( kpair @ SV945 @ SV802 ) @ ( breln1invset @ SV157 @ SV453 ) ) )
= $true )
| ( ( in @ SV802 @ SV157 )
= $false )
| ( ( breln1 @ SV157 @ SV453 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(3134,plain,
! [SV662: $i,SV455: $i > $o,SV159: $i] :
( ( ( ( dsetconstr @ SV159
@ ^ [SY3442: $i] : ( SV455 @ SY3442 ) )
= emptyset )
= $false )
| ( ( SV455 @ SV662 )
= $false )
| ( ( in @ SV662 @ SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2893]) ).
thf(3135,plain,
! [SV459: $i,SV804: $i,SV163: $i,SV946: $i] :
( ( ( ~ ( in @ SV946 @ ( powerset @ SV163 ) )
| ~ ( subset @ SV804 @ SV946 )
| ( subset @ ( binintersect @ SV459 @ SV804 ) @ SV946 ) )
= $true )
| ( ( in @ SV804 @ ( powerset @ SV163 ) )
= $false )
| ( ( in @ SV459 @ ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2896]) ).
thf(3136,plain,
! [SV463: $i,SV167: $i,SV876: $i,SV805: $i] :
( ( ( SV805 = SV876 )
= $false )
| ( ( ~ ( in @ SV805 @ SV167 )
| ( in @ SV876 @ SV463 ) )
= $true )
| ( ( SV167 = SV463 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2898]) ).
thf(3137,plain,
! [SV666: $i,SV877: $i,SV464: $i,SV168: $i] :
( ( ( breln @ SV168 @ SV464 @ SV877 )
= $false )
| ( ( ~ ! [SY4066: $i] :
( ~ ( in @ SY4066 @ SV168 )
| ! [SY4067: $i] :
( ~ ( in @ SY4067 @ SV464 )
| ~ ( in @ ( kpair @ SY4066 @ SY4067 ) @ SV666 )
| ( in @ ( kpair @ SY4066 @ SY4067 ) @ SV877 ) ) )
| ( subset @ SV666 @ SV877 ) )
= $true )
| ( ( breln @ SV168 @ SV464 @ SV666 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2899]) ).
thf(3138,plain,
! [SV806: $i,SV465: $i,SV947: $i,SV169: $i] :
( ( ( ~ ( breln1 @ SV169 @ SV947 )
| ( ( breln1compset @ SV169 @ ( binunion @ SV465 @ SV806 ) @ SV947 )
= ( binunion @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SV947 ) @ ( breln1invset @ SV169 @ SV806 ) ) ) @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SV947 ) @ ( breln1invset @ SV169 @ SV465 ) ) ) ) ) )
= $true )
| ( ( breln1 @ SV169 @ SV806 )
= $false )
| ( ( breln1 @ SV169 @ SV465 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(3139,plain,
! [SV171: $i,SV807: $i,SV466: $i,SV948: $i] :
( ( ( ~ ( in @ SV948 @ ( binintersect @ SV466 @ SV807 ) )
| ( in @ SV948 @ SV171 ) )
= $true )
| ( ( in @ SV807 @ ( powerset @ SV171 ) )
= $false )
| ( ( in @ SV466 @ ( powerset @ SV171 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2901]) ).
thf(3140,plain,
! [SV808: $i,SV173: $i,SV468: $i] :
( ( ( ~ ( subset @ SV468 @ ( setminus @ SV173 @ SV808 ) ) )
= $true )
| ( ( subset @ SV808 @ ( setminus @ SV173 @ SV468 ) )
= $true )
| ( ( in @ SV808 @ ( powerset @ SV173 ) )
= $false )
| ( ( in @ SV468 @ ( powerset @ SV173 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2902]) ).
thf(3141,plain,
! [SV175: $i,SV470: $i > $i] :
( ( ! [SY3923: $i] :
~ ( ~ ( ~ ( in @ SY3923 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
| ~ ! [SY3464: $i] :
~ ~ ( ~ ( in @ SY3464 @ SV175 )
| ( SY3923
!= ( SV470 @ SY3464 ) ) ) )
| ~ ( ~ ~ ! [SY3465: $i] :
~ ~ ( ~ ( in @ SY3465 @ SV175 )
| ( SY3923
!= ( SV470 @ SY3465 ) ) )
| ( in @ SY3923 @ ( sK3_SY3462 @ SV470 @ SV175 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2903]) ).
thf(3142,plain,
! [SV470: $i > $i,SV175: $i] :
( ( ! [SY3926: $i] :
( ~ ! [SY3467: $i] :
~ ( ~ ( ~ ( in @ SY3467 @ SY3926 )
| ~ ! [SY3468: $i] :
~ ~ ( ~ ( in @ SY3468 @ SV175 )
| ( SY3467
!= ( SV470 @ SY3468 ) ) ) )
| ~ ( ~ ~ ! [SY3469: $i] :
~ ~ ( ~ ( in @ SY3469 @ SV175 )
| ( SY3467
!= ( SV470 @ SY3469 ) ) )
| ( in @ SY3467 @ SY3926 ) ) )
| ( ( sK3_SY3462 @ SV470 @ SV175 )
= SY3926 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2904]) ).
thf(3143,plain,
! [SV180: $i,SV475: $i,SV670: $i > $i > $o] :
( ( ( in @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV180 )
= $true )
| ( ( ! [SY3807: $i] :
( ~ ( in @ SY3807 @ ( breln1Set @ SV475 ) )
| ~ ( reflwellordering @ SV475 @ SY3807 )
| ! [SY3808: $i] :
( ~ ( in @ SY3808 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY3809: $i] :
~ ( ~ ( SV670 @ SY3808 @ SY3809 )
| ~ ! [SY3810: $i] :
( ~ ( in @ SY3810 @ SV475 )
| ~ ( SV670 @ SY3808 @ SY3810 )
| ( in @ ( kpair @ SY3809 @ SY3810 ) @ SY3807 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2908]) ).
thf(3144,plain,
! [SV180: $i,SV670: $i > $i > $o,SV475: $i] :
( ( ( ! [SY4068: $i] :
~ ~ ( ~ ( in @ SY4068 @ SV475 )
| ~ ( SV670 @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SY4068 ) ) )
= $true )
| ( ( ! [SY3807: $i] :
( ~ ( in @ SY3807 @ ( breln1Set @ SV475 ) )
| ~ ( reflwellordering @ SV475 @ SY3807 )
| ! [SY3808: $i] :
( ~ ( in @ SY3808 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY3809: $i] :
~ ( ~ ( SV670 @ SY3808 @ SY3809 )
| ~ ! [SY3810: $i] :
( ~ ( in @ SY3810 @ SV475 )
| ~ ( SV670 @ SY3808 @ SY3810 )
| ( in @ ( kpair @ SY3809 @ SY3810 ) @ SY3807 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2909]) ).
thf(3145,plain,
! [SV181: $i,SV671: $i,SV476: $i,SV878: $i] :
( ( ( in @ SV878 @ SV476 )
= $false )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV671 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV671 @ ( setadjoin @ SV878 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV181 @ SV476 ) ) ) )
= $true )
| ( ( in @ SV671 @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2910]) ).
thf(3146,plain,
! [SV182: $i,SV672: $i > $i,SV477: $i] :
( ( ( in @ ( sK30_SY3812 @ SV477 @ SV672 @ SV182 ) @ SV182 )
= $true )
| ( ( ! [SY3813: $i] :
( ~ ( in @ SY3813 @ SV182 )
| ( ( ap @ SV182 @ SV477
@ ( lam @ SV182 @ SV477
@ ^ [SY3814: $i] : ( SV672 @ SY3814 ) )
@ SY3813 )
= ( SV672 @ SY3813 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2911]) ).
thf(3147,plain,
! [SV672: $i > $i,SV477: $i,SV182: $i,SV949: $i] :
( ( ( ~ ( in @ SV949 @ SV182 )
| ( ( ap @ SV182 @ SV477
@ ( lam @ SV182 @ SV477
@ ^ [SY3814: $i] : ( SV672 @ SY3814 ) )
@ SV949 )
= ( SV672 @ SV949 ) ) )
= $true )
| ( ( in @ ( SV672 @ ( sK30_SY3812 @ SV477 @ SV672 @ SV182 ) ) @ SV477 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2912]) ).
thf(3148,plain,
! [SV183: $i,SV478: $i,SV673: $i] :
( ( ( in @ SV673 @ SV478 )
= $true )
| ( ( ~ ( subset @ SV183 @ SV478 ) )
= $true )
| ( ( in @ SV673 @ SV183 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2913]) ).
thf(3149,plain,
! [SV184: $i,SV479: $i,SV674: $i] :
( ( ( in @ SV674 @ SV479 )
= $true )
| ( ( SV184 != SV479 )
= $true )
| ( ( in @ SV674 @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2914]) ).
thf(3150,plain,
! [SV812: $i,SV481: $i,SV186: $i,SV950: $i] :
( ( ( ~ ( in @ SV950 @ SV186 )
| ~ ( in @ SV481 @ ( powerset @ SV812 ) )
| ~ ( in @ SV950 @ SV481 )
| ( in @ SV950 @ SV812 ) )
= $true )
| ( ( in @ SV812 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV481 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2916]) ).
thf(3151,plain,
! [SV483: $i > $o,SV188: $i,SV675: $i] :
( ( ( ~ ( in @ SV675
@ ( dsetconstr @ SV188
@ ^ [SY3494: $i] : ( SV483 @ SY3494 ) ) )
| ( SV483 @ SV675 ) )
= $true )
| ( ( in @ SV675 @ SV188 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2917]) ).
thf(3152,plain,
! [SV188: $i,SV675: $i,SV483: $i > $o] :
( ( ( ~ ( SV483 @ SV675 )
| ( in @ SV675
@ ( dsetconstr @ SV188
@ ^ [SY3495: $i] : ( SV483 @ SY3495 ) ) ) )
= $true )
| ( ( in @ SV675 @ SV188 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2918]) ).
thf(3153,plain,
! [SV484: $i > $o,SV189: $i,SV879: $i] :
( ( ( in @ SV879 @ SV189 )
= $false )
| ( ( SV484 @ SV879 )
= $true )
| ( ( ~ ! [SY3497: $i] :
~ ~ ( ~ ( in @ SY3497 @ SV189 )
| ~ ~ ( SV484 @ SY3497 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2919]) ).
thf(3154,plain,
! [SV190: $i,SV813: $o,SV485: $i] :
( ( ( ~ ( in @ SV485 @ ( sK46_SY4001 @ SV813 @ SV190 @ SV485 ) )
| ~ ( in @ ( sK46_SY4001 @ SV813 @ SV190 @ SV485 ) @ SV190 )
| SV813 )
= $false )
| ( SV813 = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2920]) ).
thf(3155,plain,
! [SV190: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ ( sK47_SX0 @ SV190 @ SV485 ) )
| ~ ( in @ ( sK47_SX0 @ SV190 @ SV485 ) @ SV190 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2921]) ).
thf(3156,plain,
! [SV190: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ ( sK48_SX0 @ SV190 @ SV485 ) )
| ~ ( in @ ( sK48_SX0 @ SV190 @ SV485 ) @ SV190 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2922]) ).
thf(3157,plain,
! [SV676: $i,SV486: $i,SV191: $i,SV880: $i] :
( ( ( in @ SV880 @ SV191 )
= $false )
| ( ( ! [SY4069: $i] :
( ~ ( in @ SY4069 @ SV486 )
| ~ ( in @ ( kpair @ SV880 @ SY4069 ) @ SV676 )
| ( ( ap @ SV191 @ SV486 @ SV676 @ SV880 )
= SY4069 ) ) )
= $true )
| ( ( in @ SV676 @ ( funcSet @ SV191 @ SV486 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2923]) ).
thf(3158,plain,
! [SV193: $i,SV488: $i > $i,SV881: $i] :
( ( ~ ( ~ ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
| ~ ! [SY4070: $i] :
~ ~ ( ~ ( in @ SY4070 @ SV193 )
| ( SV881
!= ( SV488 @ SY4070 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2925]) ).
thf(3159,plain,
! [SV488: $i > $i,SV881: $i,SV193: $i] :
( ( ~ ( ~ ~ ! [SY4071: $i] :
~ ~ ( ~ ( in @ SY4071 @ SV193 )
| ( SV881
!= ( SV488 @ SY4071 ) ) )
| ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2925]) ).
thf(3160,plain,
! [SV489: $i,SV194: $i,SV814: $i] :
( ( ( ~ ~ ( in @ SV814 @ ( setminus @ SV194 @ SV489 ) ) )
= $true )
| ( ( in @ SV814 @ SV489 )
= $true )
| ( ( in @ SV814 @ SV194 )
= $false )
| ( ( in @ SV489 @ ( powerset @ SV194 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2926]) ).
thf(3161,plain,
! [SV919: $i] :
( ( ( ~ ( in @ SV919 @ sK5_SY3512 ) )
= $true )
| ( ( subset @ SV919 @ sK5_SY3512 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2928]) ).
thf(3162,plain,
( ( in @ sK31_SY3934 @ ( binintersect @ sK1_SX0 @ sK5_SY3512 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2929]) ).
thf(3163,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ SV816 ) )
= $true )
| ( ( ~ ! [SY4002: $i] :
( ~ ( SV196 @ SY4002 )
| ( SV816 = SY4002 ) ) )
= $true )
| ( ( ~ ! [SY2855: $i] :
~ ~ ( ~ ( SV196 @ SY2855 )
| ~ ! [SY2856: $i] :
( ~ ( SV196 @ SY2856 )
| ( SY2855 = SY2856 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2931]) ).
thf(3164,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2932]) ).
thf(3165,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
| ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) ) )
| ~ ( ~ ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
| ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2933]) ).
thf(3166,plain,
! [SV199: $i,SV492: $i,SV679: $i] :
( ( ( ~ ( ~ ( in @ ( sK39_SY3820 @ SV679 @ SV492 @ SV199 ) @ SV199 )
| ~ ~ ! [SY4093: $i] :
~ ~ ( ~ ( in @ SY4093 @ SV492 )
| ( SV679
!= ( kpair @ ( sK39_SY3820 @ SV679 @ SV492 @ SV199 ) @ SY4093 ) ) ) ) )
= $true )
| ( ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2934]) ).
thf(3167,plain,
! [SV817: $i,SV493: $i,SV200: $i,SV951: $i] :
( ( ( ~ ( in @ SV951 @ SV200 )
| ~ ~ ( in @ SV951 @ ( binunion @ SV493 @ SV817 ) )
| ~ ( in @ SV951 @ SV817 ) )
= $true )
| ( ( in @ SV817 @ ( powerset @ SV200 ) )
= $false )
| ( ( in @ SV493 @ ( powerset @ SV200 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2935]) ).
thf(3168,plain,
! [SV680: $i,SV495: $o,SV202: $i,SV882: $i] :
( ( ( in @ SV882 @ SV202 )
= $false )
| ( ( in @ ( if @ SV202 @ SV495 @ SV680 @ SV882 ) @ SV202 )
= $true )
| ( ( in @ SV680 @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2936]) ).
thf(3169,plain,
! [SV681: $i,SV202: $i,SV883: $i] :
( ( ( in @ SV883 @ SV202 )
= $false )
| ( ( in @ ( if @ SV202 @ $true @ SV681 @ SV883 ) @ SV202 )
= $true )
| ( ( in @ SV681 @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2937]) ).
thf(3170,plain,
! [SV682: $i,SV202: $i,SV884: $i] :
( ( ( in @ SV884 @ SV202 )
= $false )
| ( ( in @ ( if @ SV202 @ $false @ SV682 @ SV884 ) @ SV202 )
= $true )
| ( ( in @ SV682 @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2938]) ).
thf(3171,plain,
! [SV885: $o,SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV203 )
| ~ ~ ( in @ SV683 @ SV496 )
| SV885 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SV885 )
| SV885 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2939]) ).
thf(3172,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV203 )
| ~ ~ ( in @ SV683 @ SV496 )
| $true )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $true )
| $true )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2940]) ).
thf(3173,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV203 )
| ~ ~ ( in @ SV683 @ SV496 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $false )
| $false )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2941]) ).
thf(3174,plain,
! [SV204: $i,SV684: $i > $i,SV497: $i] :
( ( ( in @ ( sK33_SY3826 @ SV497 @ SV684 @ SV204 ) @ SV204 )
= $true )
| ( ( func @ SV204 @ SV497
@ ( lam @ SV204 @ SV497
@ ^ [SY3827: $i] : ( SV684 @ SY3827 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2942]) ).
thf(3175,plain,
! [SV686: $i,SV499: $o,SV206: $i,SV886: $i] :
( ( ( in @ SV886 @ SV206 )
= $false )
| ( ( in @ ( if @ SV206 @ SV499 @ SV686 @ SV886 ) @ ( setadjoin @ SV686 @ ( setadjoin @ SV886 @ emptyset ) ) )
= $true )
| ( ( in @ SV686 @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2944]) ).
thf(3176,plain,
! [SV687: $i,SV206: $i,SV887: $i] :
( ( ( in @ SV887 @ SV206 )
= $false )
| ( ( in @ ( if @ SV206 @ $true @ SV687 @ SV887 ) @ ( setadjoin @ SV687 @ ( setadjoin @ SV887 @ emptyset ) ) )
= $true )
| ( ( in @ SV687 @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2945]) ).
thf(3177,plain,
! [SV688: $i,SV206: $i,SV888: $i] :
( ( ( in @ SV888 @ SV206 )
= $false )
| ( ( in @ ( if @ SV206 @ $false @ SV688 @ SV888 ) @ ( setadjoin @ SV688 @ ( setadjoin @ SV888 @ emptyset ) ) )
= $true )
| ( ( in @ SV688 @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2946]) ).
thf(3178,plain,
! [SV207: $i,SV500: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK40_SY3540 @ SV500 @ SV207 ) @ SV207 )
| ~ ( SV500 @ ( sK40_SY3540 @ SV500 @ SV207 ) ) ) )
= $true )
| ( ( ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SV207 )
| ~ ( SV500 @ SY3541 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2947]) ).
thf(3179,plain,
! [SV952: $o,SV818: $i,SV501: $i,SV208: $i] :
( ( ( ! [SY4111: $i] :
( ~ ( in @ SY4111 @ SV208 )
| ~ ( in @ SY4111 @ ( binunion @ SV501 @ SV818 ) )
| ~ ( ~ ( in @ SY4111 @ SV501 )
| SV952 )
| ~ ( ~ ( in @ SY4111 @ SV818 )
| SV952 )
| SV952 ) )
= $true )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2948]) ).
thf(3180,plain,
! [SV818: $i,SV501: $i,SV208: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV208 )
| ~ ( in @ SX0 @ ( binunion @ SV501 @ SV818 ) )
| ~ ( ~ ( in @ SX0 @ SV501 )
| $true )
| ~ ( ~ ( in @ SX0 @ SV818 )
| $true )
| $true ) )
= $true )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2948]) ).
thf(3181,plain,
! [SV818: $i,SV501: $i,SV208: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV208 )
| ~ ( in @ SX0 @ ( binunion @ SV501 @ SV818 ) )
| ~ ( ~ ( in @ SX0 @ SV501 )
| $false )
| ~ ( ~ ( in @ SX0 @ SV818 )
| $false )
| $false ) )
= $true )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2948]) ).
thf(3182,plain,
! [SV889: $i > $o,SV689: $i,SV502: $i,SV209: $i] :
( ( ( ! [SY4072: $i] :
( ~ ( in @ SY4072 @ SV209 )
| ! [SY4073: $i] :
( ~ ( in @ SY4073 @ SV502 )
| ~ ( in @ ( kpair @ SY4072 @ SY4073 ) @ SV689 )
| ( SV889 @ ( kpair @ SY4072 @ SY4073 ) ) ) ) )
= $false )
| ( ( ! [SY4074: $i] :
( ~ ( in @ SY4074 @ SV689 )
| ( SV889 @ SY4074 ) ) )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2949]) ).
thf(3183,plain,
! [SV690: $i,SV503: $o,SV210: $i,SV890: $i] :
( ( ( in @ SV890 @ SV210 )
= $false )
| ( ( ~ SV503
| ( in @ SV690
@ ( dsetconstr @ SV210
@ ^ [SY4075: $i] :
( ~ ( ~ SV503
| ( SY4075 != SV690 ) )
| ~ ( ~ ~ SV503
| ( SY4075 != SV890 ) ) ) ) ) )
= $true )
| ( ( in @ SV690 @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2950]) ).
thf(3184,plain,
! [SV691: $i,SV210: $i,SV891: $i] :
( ( ( in @ SV891 @ SV210 )
= $false )
| ( ( ~ $true
| ( in @ SV691
@ ( dsetconstr @ SV210
@ ^ [SY4076: $i] :
( ~ ( ~ $true
| ( SY4076 != SV691 ) )
| ~ ( ~ ~ $true
| ( SY4076 != SV891 ) ) ) ) ) )
= $true )
| ( ( in @ SV691 @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2951]) ).
thf(3185,plain,
! [SV692: $i,SV210: $i,SV892: $i] :
( ( ( in @ SV892 @ SV210 )
= $false )
| ( ( ~ $false
| ( in @ SV692
@ ( dsetconstr @ SV210
@ ^ [SY4077: $i] :
( ~ ( ~ $false
| ( SY4077 != SV692 ) )
| ~ ( ~ ~ $false
| ( SY4077 != SV892 ) ) ) ) ) )
= $true )
| ( ( in @ SV692 @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2952]) ).
thf(3186,plain,
! [SV212: $i,SV504: $i,SV693: $i] :
( ( ( in @ SV693 @ SV504 )
= $true )
| ( ( ~ ( in @ SV693 @ SV212 ) )
= $true )
| ( ( subset @ SV212 @ SV504 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2953]) ).
thf(3187,plain,
! [SV819: $i,SV508: $i,SV216: $i,SV953: $i] :
( ( ( ~ ( in @ SV953 @ SV216 )
| ! [SY4112: $i] :
( ~ ( in @ SY4112 @ SV216 )
| ~ ( in @ ( kpair @ SV953 @ SY4112 ) @ ( binunion @ SV508 @ SV819 ) )
| ! [SY4113: $o] :
( ~ ( ~ ( in @ ( kpair @ SV953 @ SY4112 ) @ SV508 )
| SY4113 )
| ~ ( ~ ( in @ ( kpair @ SV953 @ SY4112 ) @ SV819 )
| SY4113 )
| SY4113 ) ) )
= $true )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2954]) ).
thf(3188,plain,
! [SV820: $i,SV509: $i,SV217: $i,SV954: $i] :
( ( ( ~ ( in @ SV954 @ SV217 )
| ~ ( in @ SV954 @ ( setminus @ SV217 @ ( binunion @ SV509 @ SV820 ) ) )
| ( in @ SV954 @ ( binintersect @ ( setminus @ SV217 @ SV509 ) @ ( setminus @ SV217 @ SV820 ) ) ) )
= $true )
| ( ( in @ SV820 @ ( powerset @ SV217 ) )
= $false )
| ( ( in @ SV509 @ ( powerset @ SV217 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2955]) ).
thf(3189,plain,
! [SV218: $i,SV696: $i,SV510: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK41_SY3843 @ SV510 @ SV696 @ SV218 ) @ SV218 )
| ( SV696
!= ( SV510 @ ( sK41_SY3843 @ SV510 @ SV696 @ SV218 ) ) ) ) )
= $true )
| ( ( in @ SV696
@ ( image1 @ SV218
@ ^ [SY3564: $i] : ( SV510 @ SY3564 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2956]) ).
thf(3190,plain,
! [SV699: $i,SV514: $o,SV223: $i,SV893: $i] :
( ( ( in @ SV893 @ SV223 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY4078: $i] :
( ~ ( ~ SV514
| ( SY4078 != SV699 ) )
| ~ ( ~ ~ SV514
| ( SY4078 != SV893 ) ) ) ) )
= $true )
| ( ( in @ SV699 @ SV223 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2957]) ).
thf(3191,plain,
! [SV700: $i,SV223: $i,SV894: $i] :
( ( ( in @ SV894 @ SV223 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY4079: $i] :
( ~ ( ~ $true
| ( SY4079 != SV700 ) )
| ~ ( ~ ~ $true
| ( SY4079 != SV894 ) ) ) ) )
= $true )
| ( ( in @ SV700 @ SV223 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2958]) ).
thf(3192,plain,
! [SV701: $i,SV223: $i,SV895: $i] :
( ( ( in @ SV895 @ SV223 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV223
@ ^ [SY4080: $i] :
( ~ ( ~ $false
| ( SY4080 != SV701 ) )
| ~ ( ~ ~ $false
| ( SY4080 != SV895 ) ) ) ) )
= $true )
| ( ( in @ SV701 @ SV223 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2959]) ).
thf(3193,plain,
! [SV224: $i,SV821: $i,SV515: $i] :
( ( ( ~ ( subset @ SV515 @ SV821 ) )
= $true )
| ( ( subset @ ( setminus @ SV224 @ SV821 ) @ ( setminus @ SV224 @ SV515 ) )
= $true )
| ( ( in @ SV821 @ ( powerset @ SV224 ) )
= $false )
| ( ( in @ SV515 @ ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2960]) ).
thf(3194,plain,
! [SV226: $i] :
( ( ~ ~ ( ~ ! [SY3851: $i] :
( ~ ( in @ SY3851 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY2945: $i] :
( ~ ( in @ SY2945 @ SY3851 )
| ( in @ SY2945 @ SV226 ) ) )
| ~ ! [SY3853: $i,SY3854: $i] :
( ~ ~ ( ~ ( in @ SY3853 @ SV226 )
| ~ ( in @ SY3854 @ SV226 ) )
| ~ ! [SY3855: $i] :
( ~ ( in @ SY3855 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SY3853 @ SY3855 )
| ( in @ SY3854 @ SY3855 ) )
| ~ ( ~ ( in @ SY3854 @ SY3855 )
| ( in @ SY3853 @ SY3855 ) ) ) )
| ( SY3853 = SY3854 ) ) )
| ~ ! [SY3856: $i,SY3857: $i] :
( ~ ~ ( ~ ( in @ SY3856 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY3857 @ ( sK2_SY2943 @ SV226 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3856 )
| ( in @ SX4 @ SY3857 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3857 )
| ( in @ SX4 @ SY3856 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(3195,plain,
! [SV226: $i,SV955: $i] :
( ( ~ ~ ( ~ ! [SY4114: $i] :
( ~ ( in @ SY4114 @ SV955 )
| ( in @ SY4114 @ SV226 ) )
| ~ ~ ! [SY4115: $i] :
~ ( in @ SY4115 @ SV955 ) )
| ~ ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2962]) ).
thf(3196,plain,
! [SV703: $i > $i > $o,SV227: $i,SV752: $i,SV517: $i,SV920: $i] :
( ( ( ~ ( in @ SV920 @ SV517 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV752 @ SV920 )
@ ( dpsetconstr @ SV227 @ SV517
@ ^ [SY3870: $i,SY3871: $i] : ( SV703 @ SY3870 @ SY3871 ) ) )
| ( SV703 @ SV752 @ SV920 ) )
= $true )
| ( ( in @ SV752 @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2963]) ).
thf(3197,plain,
! [SV822: $i,SV519: $i,SV229: $i,SV956: $i] :
( ( ( ~ ( in @ SV956 @ SV229 )
| ~ ~ ( in @ SV956 @ ( binunion @ SV519 @ SV822 ) )
| ~ ( in @ SV956 @ SV519 ) )
= $true )
| ( ( in @ SV822 @ ( powerset @ SV229 ) )
= $false )
| ( ( in @ SV519 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2965]) ).
thf(3198,plain,
! [SV230: $i > $i > $o,SV520: $i] :
( ( ( ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2966]) ).
thf(3199,plain,
! [SV957: $i,SV520: $i,SV230: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
| ~ ! [SY4121: $i] :
( ~ ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SY4121 )
| ( SV957 = SY4121 ) ) ) )
= $true )
| ( ( ~ ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2967]) ).
thf(3200,plain,
! [SV705: $i,SV896: $i,SV521: $i,SV231: $i] :
( ( ( func @ SV231 @ SV521 @ SV896 )
= $false )
| ( ( ~ ! [SY4081: $i] :
( ~ ( in @ SY4081 @ SV231 )
| ( ( ap @ SV231 @ SV521 @ SV705 @ SY4081 )
= ( ap @ SV231 @ SV521 @ SV896 @ SY4081 ) ) )
| ( SV705 = SV896 ) )
= $true )
| ( ( func @ SV231 @ SV521 @ SV705 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2968]) ).
thf(3201,plain,
! [SV706: $i,SV522: $o,SV232: $i,SV897: $i] :
( ( ( in @ SV897 @ SV232 )
= $false )
| ( ( ~ SV522
| ( ( if @ SV232 @ SV522 @ SV706 @ SV897 )
= SV706 ) )
= $true )
| ( ( in @ SV706 @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2969]) ).
thf(3202,plain,
! [SV707: $i,SV232: $i,SV898: $i] :
( ( ( in @ SV898 @ SV232 )
= $false )
| ( ( ~ $true
| ( ( if @ SV232 @ $true @ SV707 @ SV898 )
= SV707 ) )
= $true )
| ( ( in @ SV707 @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2970]) ).
thf(3203,plain,
! [SV708: $i,SV232: $i,SV899: $i] :
( ( ( in @ SV899 @ SV232 )
= $false )
| ( ( ~ $false
| ( ( if @ SV232 @ $false @ SV708 @ SV899 )
= SV708 ) )
= $true )
| ( ( in @ SV708 @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2971]) ).
thf(3204,plain,
! [SV233: $i,SV523: $i,SV823: $i > $o] :
( ( ( ~ ( in @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ SV233 )
| ! [SY4122: $i] :
( ~ ( in @ SY4122 @ SV233 )
| ~ ( in @ ( kpair @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ SY4122 ) @ SV523 )
| ( SV823 @ ( kpair @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ SY4122 ) ) ) )
= $false )
| ( ( ! [SY4016: $i] :
( ~ ( in @ SY4016 @ SV523 )
| ( SV823 @ SY4016 ) ) )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2972]) ).
thf(3205,plain,
! [SV235: $i,SV525: $i] :
( ( ( ~ ( in @ ( sK34_SY3599 @ SV525 @ SV235 ) @ SV235 )
| ~ ( in @ SV525 @ ( sK34_SY3599 @ SV525 @ SV235 ) ) )
= $false )
| ( ( in @ SV525 @ ( setunion @ SV235 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2974]) ).
thf(3206,plain,
! [SV711: $i,SV529: $i,SV240: $i,SV900: $i] :
( ( ( in @ SV900 @ SV240 )
= $false )
| ( ( in @ ( kpair @ SV900 @ ( ap @ SV240 @ SV529 @ SV711 @ SV900 ) ) @ SV711 )
= $true )
| ( ( func @ SV240 @ SV529 @ SV711 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2975]) ).
thf(3207,plain,
! [SV825: $i,SV531: $i,SV243: $i,SV958: $i] :
( ( ( ~ ( in @ SV958 @ ( powerset @ SV243 ) )
| ( in @ ( binintersect @ SV531 @ SV825 ) @ ( powerset @ ( binintersect @ ( binunion @ SV531 @ SV958 ) @ ( binunion @ SV825 @ SV958 ) ) ) ) )
= $true )
| ( ( in @ SV825 @ ( powerset @ SV243 ) )
= $false )
| ( ( in @ SV531 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2978]) ).
thf(3208,plain,
! [SV532: $i,SV244: $i,SV826: $i] :
( ( ( ~ ( in @ SV826 @ ( setminus @ SV244 @ ( setminus @ SV244 @ SV532 ) ) ) )
= $true )
| ( ( in @ SV826 @ SV532 )
= $true )
| ( ( in @ SV826 @ SV244 )
= $false )
| ( ( in @ SV532 @ ( powerset @ SV244 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2979]) ).
thf(3209,plain,
! [SV533: $i > $o,SV245: $i,SV901: $i] :
( ( ( ~ ( in @ SV901 @ SV245 )
| ~ ( SV533 @ SV901 ) )
= $true )
| ( ( ( ( dsetconstr @ SV245
@ ^ [SY3609: $i] : ( SV533 @ SY3609 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2980]) ).
thf(3210,plain,
! [SV712: $i,SV534: $i,SV246: $i,SV902: $i] :
( ( ( in @ SV902 @ SV246 )
= $false )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV534
@ ^ [SY4082: $i] : ( in @ ( kpair @ SV902 @ SY4082 ) @ SV712 ) ) )
@ SV534 )
= $true )
| ( ( func @ SV246 @ SV534 @ SV712 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2981]) ).
thf(3211,plain,
! [SV535: $i,SV827: $i,SV247: $i,SV959: $i] :
( ( ( ~ ( in @ SV959 @ SV247 )
| ~ ( in @ ( kpair @ SV959 @ SV827 ) @ ( breln1invset @ SV247 @ SV535 ) )
| ( in @ ( kpair @ SV827 @ SV959 ) @ SV535 ) )
= $true )
| ( ( in @ SV827 @ SV247 )
= $false )
| ( ( breln1 @ SV247 @ SV535 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2982]) ).
thf(3212,plain,
! [SV249: $i,SV921: $i] :
( ( ( ~ ( in @ SV921 @ SV249 ) )
= $true )
| ( ( subset @ SV921 @ SV249 )
= $true )
| ( ( in @ ( sK7_SY3023 @ SV249 ) @ SV249 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2983]) ).
thf(3213,plain,
! [SV249: $i,SV903: $i] :
( ( ( in @ SV903 @ SV249 )
= $false )
| ( ( subset @ SV903 @ SV249 )
= $true )
| ( ( subset @ ( sK7_SY3023 @ SV249 ) @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2984]) ).
thf(3214,plain,
! [SV828: $i,SV538: $i,SV251: $i,SV960: $i] :
( ( ( ~ ( in @ SV960 @ SV251 )
| ~ ~ ( in @ SV960 @ SV538 )
| ~ ~ ( in @ SV960 @ SV828 )
| ~ ( in @ SV960 @ ( binunion @ SV538 @ SV828 ) ) )
= $true )
| ( ( in @ SV828 @ ( powerset @ SV251 ) )
= $false )
| ( ( in @ SV538 @ ( powerset @ SV251 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2985]) ).
thf(3215,plain,
! [SV714: $i,SV539: $o,SV252: $i,SV904: $i] :
( ( ( in @ SV904 @ SV252 )
= $false )
| ( ( ~ SV539
| ( ( dsetconstr @ SV252
@ ^ [SY4083: $i] :
( ~ ( ~ SV539
| ( SY4083 != SV714 ) )
| ~ ( ~ ~ SV539
| ( SY4083 != SV904 ) ) ) )
= ( setadjoin @ SV714 @ emptyset ) ) )
= $true )
| ( ( in @ SV714 @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2986]) ).
thf(3216,plain,
! [SV715: $i,SV252: $i,SV905: $i] :
( ( ( in @ SV905 @ SV252 )
= $false )
| ( ( ~ $true
| ( ( dsetconstr @ SV252
@ ^ [SY4084: $i] :
( ~ ( ~ $true
| ( SY4084 != SV715 ) )
| ~ ( ~ ~ $true
| ( SY4084 != SV905 ) ) ) )
= ( setadjoin @ SV715 @ emptyset ) ) )
= $true )
| ( ( in @ SV715 @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2987]) ).
thf(3217,plain,
! [SV716: $i,SV252: $i,SV906: $i] :
( ( ( in @ SV906 @ SV252 )
= $false )
| ( ( ~ $false
| ( ( dsetconstr @ SV252
@ ^ [SY4085: $i] :
( ~ ( ~ $false
| ( SY4085 != SV716 ) )
| ~ ( ~ ~ $false
| ( SY4085 != SV906 ) ) ) )
= ( setadjoin @ SV716 @ emptyset ) ) )
= $true )
| ( ( in @ SV716 @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2988]) ).
thf(3218,plain,
! [SV717: $i,SV541: $i,SV254: $i,SV907: $i] :
( ( ( in @ SV907 @ SV254 )
= $false )
| ( ( ( ap @ SV254 @ SV541 @ SV717 @ SV907 )
= ( ap @ SV254 @ SV541 @ SV717 @ SV907 ) )
= $true )
| ( ( func @ SV254 @ SV541 @ SV717 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2989]) ).
thf(3219,plain,
! [SV256: $i,SV543: $i,SV753: $i,SV718: $i] :
( ( ( SV718 = SV753 )
= $false )
| ( ( SV543 = SV753 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV256 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV256 @ ( setadjoin @ SV543 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV718 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV718 @ ( setadjoin @ SV753 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2990]) ).
thf(3220,plain,
! [SV719: $i,SV548: $i,SV259: $i,SV908: $i] :
( ( ( in @ SV908 @ SV259 )
= $false )
| ( ( ! [SY4086: $i] :
( ~ ( in @ SY4086 @ SV548 )
| ~ ( in @ ( kpair @ SV908 @ SY4086 ) @ SV719 )
| ( ( ap @ SV259 @ SV548 @ SV719 @ SV908 )
= SY4086 ) ) )
= $true )
| ( ( func @ SV259 @ SV548 @ SV719 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2991]) ).
thf(3221,plain,
! [SV829: $i,SV549: $i,SV260: $i] :
( ( ( ~ ! [SY4020: $i] :
( ~ ( in @ SY4020 @ SV260 )
| ! [SY4021: $i] :
( ~ ( in @ SY4021 @ SV260 )
| ~ ( in @ ( kpair @ SY4020 @ SY4021 ) @ SV549 )
| ( in @ ( kpair @ SY4020 @ SY4021 ) @ SV829 ) ) ) )
= $true )
| ( ( ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) )
| ( SV549 = SV829 ) )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2992]) ).
thf(3222,plain,
! [SV830: $i,SV553: $i,SV264: $i,SV961: $i] :
( ( ( ~ ( in @ SV961 @ SV264 )
| ! [SY4123: $i] :
( ~ ( in @ SY4123 @ SV264 )
| ~ ( ( in @ ( kpair @ SV961 @ SY4123 ) @ SV553 )
| ( in @ ( kpair @ SV961 @ SY4123 ) @ SV830 ) )
| ( in @ ( kpair @ SV961 @ SY4123 ) @ ( binunion @ SV553 @ SV830 ) ) ) )
= $true )
| ( ( breln1 @ SV264 @ SV830 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2994]) ).
thf(3223,plain,
! [SV265: $i,SV722: $i,SV554: $i,SV909: $i] :
( ( ( in @ SV909 @ SV554 )
= $false )
| ( ( subset @ ( setadjoin @ SV722 @ ( setadjoin @ SV909 @ emptyset ) ) @ ( binunion @ SV265 @ SV554 ) )
= $true )
| ( ( in @ SV722 @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2995]) ).
thf(3224,plain,
! [SV271: $i,SV559: $i,SV833: $i > $o] :
( ( ( ~ ( in @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ SV271 )
| ! [SY4124: $i] :
( ~ ( in @ SY4124 @ SV271 )
| ~ ( in @ ( kpair @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ SY4124 ) @ SV559 )
| ( SV833 @ ( kpair @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ SY4124 ) ) ) )
= $false )
| ( ( ! [SY4028: $i] :
( ~ ( in @ SY4028 @ SV559 )
| ( SV833 @ SY4028 ) ) )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2998]) ).
thf(3225,plain,
! [SV272: $i,SV560: $i,SV725: $i] :
( ( ( in @ SV725 @ SV560 )
= $true )
| ( ( in @ SV725 @ ( symdiff @ SV272 @ SV560 ) )
= $true )
| ( ( in @ SV725 @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2999]) ).
thf(3226,plain,
! [SV273: $i,SV726: $i,SV561: $i,SV910: $i] :
( ( ( in @ SV910 @ SV561 )
= $false )
| ( ( ( kfst @ ( kpair @ SV726 @ SV910 ) )
= SV726 )
= $true )
| ( ( in @ SV726 @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3000]) ).
thf(3227,plain,
! [SV562: $i,SV834: $i,SV274: $i] :
( ( ( ~ ( subset @ ( setminus @ SV274 @ SV834 ) @ ( setminus @ SV274 @ SV562 ) ) )
= $true )
| ( ( subset @ SV562 @ SV834 )
= $true )
| ( ( in @ SV834 @ ( powerset @ SV274 ) )
= $false )
| ( ( in @ SV562 @ ( powerset @ SV274 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3001]) ).
thf(3228,plain,
! [SV563: $i > $o,SV275: $i] :
( ( ( ~ ! [SY3654: $i] :
~ ~ ( ~ ( in @ SY3654 @ SV275 )
| ~ ( SV563 @ SY3654 ) ) )
= $false )
| ( ( in @ ( sK16_SY3653 @ SV563 @ SV275 ) @ SV275 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3002]) ).
thf(3229,plain,
! [SV563: $i > $o,SV275: $i] :
( ( ( ~ ! [SY3654: $i] :
~ ~ ( ~ ( in @ SY3654 @ SV275 )
| ~ ( SV563 @ SY3654 ) ) )
= $false )
| ( ( SV563 @ ( sK16_SY3653 @ SV563 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3003]) ).
thf(3230,plain,
! [SV835: $i,SV565: $i,SV277: $i,SV962: $i] :
( ( ( ~ ( in @ SV962 @ SV277 )
| ~ ( in @ SV962 @ ( setminus @ SV277 @ ( binunion @ SV565 @ SV835 ) ) )
| ( in @ SV962 @ ( setminus @ SV277 @ SV565 ) ) )
= $true )
| ( ( in @ SV835 @ ( powerset @ SV277 ) )
= $false )
| ( ( in @ SV565 @ ( powerset @ SV277 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3004]) ).
thf(3231,plain,
! [SV278: $i,SV566: $i] :
( ( ( ~ ! [SY3658: $i] :
( ~ ( in @ SY3658 @ SV566 )
| ( in @ SY3658 @ SV278 ) ) )
= $true )
| ( ( SV278 = SV566 )
= $true )
| ( ( in @ ( sK17_SY3657 @ SV566 @ SV278 ) @ SV278 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3005]) ).
thf(3232,plain,
! [SV278: $i,SV566: $i] :
( ( ( ! [SY3658: $i] :
( ~ ( in @ SY3658 @ SV566 )
| ( in @ SY3658 @ SV278 ) ) )
= $false )
| ( ( SV278 = SV566 )
= $true )
| ( ( in @ ( sK17_SY3657 @ SV566 @ SV278 ) @ SV566 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3006]) ).
thf(3233,plain,
! [SV836: $i,SV568: $i,SV280: $i,SV963: $i] :
( ( ( ~ ( in @ SV963 @ SV280 )
| ! [SY4125: $i] :
( ~ ( in @ SY4125 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SY4125 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
| ! [SY4126: $o] :
( ~ ! [SY4127: $i] :
( ~ ( in @ SY4127 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SY4127 ) @ SV568 )
| ~ ( in @ ( kpair @ SY4127 @ SY4125 ) @ SV836 )
| SY4126 )
| SY4126 ) ) )
= $true )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3007]) ).
thf(3234,plain,
! [SV282: $i,SV570: $i,SV728: $i] :
( ( ( in @ SV728 @ SV570 )
= $false )
| ( ( in @ SV728 @ ( symdiff @ SV282 @ SV570 ) )
= $true )
| ( ( in @ SV728 @ SV282 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3008]) ).
thf(3235,plain,
! [SV284: $i,SV572: $i] :
( ( ( ~ ( ~ ( in @ ( sK42_SY3668 @ SV572 @ SV284 ) @ SV284 )
| ~ ( in @ ( sK42_SY3668 @ SV572 @ SV284 ) @ SV572 ) ) )
= $true )
| ( ( ( binintersect @ SV284 @ SV572 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3009]) ).
thf(3236,plain,
! [SV837: $i,SV288: $i > $o] :
( ( ( ~ ( SV288 @ SV837 ) )
= $true )
| ( ( ~ ! [SY4034: $i] :
( ~ ( SV288 @ SY4034 )
| ( SV837 = SY4034 ) ) )
= $true )
| ( ( ! [SY3119: $i,SY3120: $i] :
( ~ ( SV288 @ SY3119 )
| ~ ( SV288 @ SY3120 )
| ( SY3119 = SY3120 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3010]) ).
thf(3237,plain,
! [SV289: $i,SV575: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK43_SY3670 @ SV575 @ SV289 ) @ SV289 )
| ~ ( SV575 @ ( sK43_SY3670 @ SV575 @ SV289 ) ) ) )
= $true )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV289 )
| ~ ( SV575 @ SY3671 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3011]) ).
thf(3238,plain,
! [SV293: $i,SV755: $i,SV732: $i > $i > $o,SV579: $i,SV922: $i] :
( ( ( ~ ( in @ SV922 @ SV579 ) )
= $true )
| ( ( ~ ( SV732 @ SV755 @ SV922 )
| ( in @ ( kpair @ SV755 @ SV922 )
@ ( dpsetconstr @ SV293 @ SV579
@ ^ [SY3897: $i,SY3898: $i] : ( SV732 @ SY3897 @ SY3898 ) ) ) )
= $true )
| ( ( in @ SV755 @ SV293 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3014]) ).
thf(3239,plain,
! [SV583: $i,SV757: $o,SV298: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV298 )
| SV757 )
= $false )
| ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| SV757 )
| SV757 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3016]) ).
thf(3240,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV298 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| $true )
| $true )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3017]) ).
thf(3241,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV298 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| $false )
| $false )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3018]) ).
thf(3242,plain,
! [SV840: $i,SV584: $i,SV299: $i] :
( ( ( ~ ! [SY4035: $i] :
( ~ ( in @ SY4035 @ SV299 )
| ~ ( in @ SY4035 @ SV584 )
| ( in @ SY4035 @ SV840 ) ) )
= $true )
| ( ( ~ ! [SY4036: $i] :
( ~ ( in @ SY4036 @ SV299 )
| ~ ( in @ SY4036 @ SV840 )
| ( in @ SY4036 @ SV584 ) )
| ( SV584 = SV840 ) )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3019]) ).
thf(3243,plain,
! [SV841: $i,SV585: $i,SV300: $i,SV964: $i] :
( ( ( ~ ( in @ SV964 @ SV300 )
| ! [SY4128: $i] :
( ~ ( in @ SY4128 @ SV300 )
| ~ ( in @ ( kpair @ SV964 @ SY4128 ) @ SV585 )
| ( in @ ( kpair @ SV964 @ SY4128 ) @ ( binunion @ SV585 @ SV841 ) ) ) )
= $true )
| ( ( breln1 @ SV300 @ SV841 )
= $false )
| ( ( breln1 @ SV300 @ SV585 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3020]) ).
thf(3244,plain,
! [SV734: $i,SV911: $i,SV586: $i,SV301: $i] :
( ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( ~ ! [SY4087: $i] :
( ~ ( in @ SY4087 @ SV301 )
| ( ( ap @ SV301 @ SV586 @ SV734 @ SY4087 )
= ( ap @ SV301 @ SV586 @ SV911 @ SY4087 ) ) )
| ! [SY4088: $i] :
( ~ ( in @ SY4088 @ SV301 )
| ! [SY4089: $i] :
( ~ ( in @ SY4089 @ SV586 )
| ~ ( in @ ( kpair @ SY4088 @ SY4089 ) @ SV911 )
| ( in @ ( kpair @ SY4088 @ SY4089 ) @ SV734 ) ) ) )
= $true )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3021]) ).
thf(3245,plain,
! [SV842: $i,SV587: $i,SV302: $i,SV965: $i] :
( ( ( ~ ( in @ SV965 @ SV302 )
| ~ ( in @ SV965 @ ( binunion @ ( setminus @ SV302 @ SV587 ) @ ( setminus @ SV302 @ SV842 ) ) )
| ( in @ SV965 @ ( setminus @ SV302 @ ( binintersect @ SV587 @ SV842 ) ) ) )
= $true )
| ( ( in @ SV842 @ ( powerset @ SV302 ) )
= $false )
| ( ( in @ SV587 @ ( powerset @ SV302 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3022]) ).
thf(3246,plain,
! [SV843: $i,SV589: $i,SV305: $i,SV966: $i] :
( ( ( ~ ( in @ SV966 @ ( powerset @ SV305 ) )
| ( in @ ( binintersect @ SV589 @ SV843 ) @ ( powerset @ ( binintersect @ ( binunion @ SV589 @ SV966 ) @ ( binunion @ SV843 @ SV966 ) ) ) ) )
= $true )
| ( ( in @ SV843 @ ( powerset @ SV305 ) )
= $false )
| ( ( in @ SV589 @ ( powerset @ SV305 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3023]) ).
thf(3247,plain,
! [SV844: $i,SV590: $i,SV307: $i,SV967: $i] :
( ( ( ~ ( in @ SV967 @ SV307 )
| ~ ( in @ SV967 @ ( binintersect @ ( setminus @ SV307 @ SV590 ) @ ( setminus @ SV307 @ SV844 ) ) )
| ( in @ SV967 @ ( setminus @ SV307 @ ( binunion @ SV590 @ SV844 ) ) ) )
= $true )
| ( ( in @ SV844 @ ( powerset @ SV307 ) )
= $false )
| ( ( in @ SV590 @ ( powerset @ SV307 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3024]) ).
thf(3248,plain,
! [SV845: $i,SV591: $i,SV308: $i] :
( ( ( ~ ! [SY4042: $i] :
( ~ ( in @ SY4042 @ SV308 )
| ~ ( in @ SY4042 @ SV591 )
| ( in @ SY4042 @ SV845 ) ) )
= $true )
| ( ( in @ SV591 @ ( powerset @ SV845 ) )
= $true )
| ( ( in @ SV845 @ ( powerset @ SV308 ) )
= $false )
| ( ( in @ SV591 @ ( powerset @ SV308 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3025]) ).
thf(3249,plain,
! [SV846: $i,SV592: $i,SV309: $i,SV968: $i] :
( ( ( ~ ( in @ SV968 @ SV309 )
| ~ ( in @ SV968 @ ( setminus @ SV309 @ SV592 ) )
| ~ ( in @ SV968 @ ( setminus @ SV309 @ SV846 ) )
| ( in @ SV968 @ ( setminus @ SV309 @ ( binunion @ SV592 @ SV846 ) ) ) )
= $true )
| ( ( in @ SV846 @ ( powerset @ SV309 ) )
= $false )
| ( ( in @ SV592 @ ( powerset @ SV309 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3026]) ).
thf(3250,plain,
! [SV313: $i,SV736: $i,SV596: $i,SV912: $i] :
( ( ( in @ SV912 @ SV596 )
= $false )
| ( ( in @ ( setadjoin @ SV736 @ ( setadjoin @ SV912 @ emptyset ) ) @ ( powerset @ ( binunion @ SV313 @ SV596 ) ) )
= $true )
| ( ( in @ SV736 @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3027]) ).
thf(3251,plain,
! [SV314: $i,SV737: $i,SV597: $i,SV913: $i] :
( ( ( in @ SV913 @ SV597 )
= $false )
| ( ( ( ksnd @ ( kpair @ SV737 @ SV913 ) )
= SV913 )
= $true )
| ( ( in @ SV737 @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3028]) ).
thf(3252,plain,
! [SV847: $i,SV598: $i,SV315: $i,SV969: $i] :
( ( ( ~ ( in @ SV969 @ SV315 )
| ~ ( in @ SV969 @ ( setminus @ SV315 @ ( binunion @ SV598 @ SV847 ) ) )
| ~ ( in @ SV969 @ SV598 ) )
= $true )
| ( ( in @ SV847 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV598 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3029]) ).
thf(3253,plain,
! [SV848: $i,SV316: $i > $o] :
( ( ( ~ ( SV316 @ SV848 ) )
= $true )
| ( ( ~ ! [SY4045: $i] :
( ~ ( SV316 @ SY4045 )
| ( SV848 = SY4045 ) ) )
= $true )
| ( ( ~ ! [SY3190: $i] :
~ ! [SY3191: $i] :
~ ( ~ ( ~ ( SV316 @ SY3191 )
| ( SY3191 = SY3190 ) )
| ~ ( ( SY3191 != SY3190 )
| ( SV316 @ SY3191 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3030]) ).
thf(3254,plain,
! [SV849: $i,SV599: $i,SV317: $i,SV970: $i] :
( ( ( ~ ( in @ SV970 @ ( powerset @ SV317 ) )
| ! [SY4129: $i] :
( ~ ( in @ SY4129 @ ( powerset @ SV317 ) )
| ~ ( subset @ SV599 @ SV970 )
| ~ ( subset @ SV849 @ SY4129 )
| ( subset @ ( binintersect @ SV599 @ SV849 ) @ ( binintersect @ SV970 @ SY4129 ) ) ) )
= $true )
| ( ( in @ SV849 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3031]) ).
thf(3255,plain,
! [SV600: $i,SV850: $i,SV318: $i,SV971: $i] :
( ( ( ~ ( in @ SV971 @ SV318 )
| ~ ~ ( in @ SV971 @ SV850 )
| ~ ( in @ SV971 @ ( binintersect @ SV600 @ SV850 ) ) )
= $true )
| ( ( in @ SV850 @ ( powerset @ SV318 ) )
= $false )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3032]) ).
thf(3256,plain,
! [SV914: $i > $o,SV738: $i,SV601: $i,SV319: $i] :
( ( ( ! [SY4090: $i] :
( ~ ( in @ SY4090 @ SV319 )
| ! [SY4091: $i] :
( ~ ( in @ SY4091 @ SV601 )
| ~ ( in @ ( kpair @ SY4090 @ SY4091 ) @ SV738 )
| ( SV914 @ ( kpair @ SY4090 @ SY4091 ) ) ) ) )
= $false )
| ( ( ! [SY4092: $i] :
( ~ ( in @ SY4092 @ SV738 )
| ( SV914 @ SY4092 ) ) )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3033]) ).
thf(3257,plain,
! [SV739: $i,SV603: $o,SV321: $i,SV915: $i] :
( ( ( in @ SV915 @ SV321 )
= $false )
| ( ( ~ ~ SV603
| ( ( if @ SV321 @ SV603 @ SV739 @ SV915 )
= SV915 ) )
= $true )
| ( ( in @ SV739 @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3035]) ).
thf(3258,plain,
! [SV740: $i,SV321: $i,SV916: $i] :
( ( ( in @ SV916 @ SV321 )
= $false )
| ( ( ~ ~ $true
| ( ( if @ SV321 @ $true @ SV740 @ SV916 )
= SV916 ) )
= $true )
| ( ( in @ SV740 @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3036]) ).
thf(3259,plain,
! [SV741: $i,SV321: $i,SV917: $i] :
( ( ( in @ SV917 @ SV321 )
= $false )
| ( ( ~ ~ $false
| ( ( if @ SV321 @ $false @ SV741 @ SV917 )
= SV917 ) )
= $true )
| ( ( in @ SV741 @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3037]) ).
thf(3260,plain,
! [SV322: $i,SV851: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK51_SY3211 @ SV851 @ SV322 ) @ SV322 )
| ~ ~ ~ ! [SY4130: $i] :
~ ~ ( ~ ( in @ SY4130 @ ( sK51_SY3211 @ SV851 @ SV322 ) )
| ~ ( in @ SY4130 @ SV322 ) ) ) )
= $false )
| ( ( in @ SV851 @ SV322 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3038]) ).
thf(3261,plain,
! [SV852: $i,SV606: $i,SV325: $i,SV972: $i] :
( ( ( ~ ( in @ SV972 @ ( powerset @ SV325 ) )
| ~ ( subset @ SV606 @ SV852 )
| ~ ( subset @ SV606 @ SV972 )
| ( subset @ SV606 @ ( binintersect @ SV852 @ SV972 ) ) )
= $true )
| ( ( in @ SV852 @ ( powerset @ SV325 ) )
= $false )
| ( ( in @ SV606 @ ( powerset @ SV325 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3040]) ).
thf(3262,plain,
! [SV37: $i] :
( ( ( ~ ( in @ ( sK20_SY2402 @ SV37 ) @ SV37 ) )
= $false )
| ( ( SV37 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3041]) ).
thf(3263,plain,
! [SV37: $i] :
( ( ( ~ $true ) = $false )
| ( ( SV37 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3041]) ).
thf(3264,plain,
! [SV759: $i,SV40: $i > $o] :
( ( ( SV40 @ SV759 )
= $false )
| ( ( ~ ! [SY3941: $i] :
( ~ ( SV40 @ SY3941 )
| ( SV759 = SY3941 ) ) )
= $true )
| ( ( ~ ! [SY2411: $i] :
~ ( SV40 @ SY2411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3044]) ).
thf(3265,plain,
! [SV760: $i,SV42: $i > $o] :
( ( ( SV42 @ SV760 )
= $false )
| ( ( ~ ! [SY3942: $i] :
( ~ ( SV42 @ SY3942 )
| ( SV760 = SY3942 ) ) )
= $true )
| ( ( SV42
@ ( descr
@ ^ [SY2417: $i] : ( SV42 @ SY2417 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3046]) ).
thf(3266,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ( ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( in @ ( sK9_SY3238 @ SV353 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3047]) ).
thf(3267,plain,
! [SV44: $i,SV353: $i > $o] :
( ( ( in @ ( sK36_SY3943 @ SV353 @ SV44 ) @ SV44 )
= $true )
| ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) )
| ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3048]) ).
thf(3268,plain,
! [SV44: $i,SV353: $i > $o] :
( ( ( ~ ( SV353 @ ( sK9_SY3238 @ SV353 @ SV44 ) ) )
= $false )
| ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) )
| ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3049]) ).
thf(3269,plain,
! [SV44: $i,SV353: $i > $o] :
( ( ( ~ ( SV353 @ ( sK36_SY3943 @ SV353 @ SV44 ) )
| ( ( sK9_SY3238 @ SV353 @ SV44 )
= ( sK36_SY3943 @ SV353 @ SV44 ) ) )
= $false )
| ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) )
| ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3049]) ).
thf(3270,plain,
! [SV854: $i,SV612: $i,SV354: $i,SV45: $i] :
( ( ( ~ ! [SY4050: $i] :
( ~ ( in @ SY4050 @ SV45 )
| ( ( ap @ SV45 @ SV354 @ SV612 @ SY4050 )
= ( ap @ SV45 @ SV354 @ SV854 @ SY4050 ) ) ) )
= $true )
| ( ( SV612 = SV854 )
= $true )
| ( ( in @ SV854 @ ( funcSet @ SV45 @ SV354 ) )
= $false )
| ( ( in @ SV612 @ ( funcSet @ SV45 @ SV354 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3050]) ).
thf(3271,plain,
! [SV762: $i,SV361: $i,SV52: $i,SV923: $i] :
( ( ( ~ ( in @ SV923 @ ( powerset @ SV52 ) ) )
= $true )
| ( ( ! [SY4098: $i] :
( ~ ( in @ SY4098 @ SV52 )
| ~ ( in @ SY4098 @ ( binintersect @ SV361 @ SV762 ) )
| ( in @ SY4098 @ ( binunion @ SV762 @ SV923 ) ) ) )
= $true )
| ( ( in @ SV762 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3054]) ).
thf(3272,plain,
! [SV763: $i,SV55: $i,SV364: $i] :
( ( ( subset @ SV364 @ ( setminus @ SV55 @ SV763 ) )
= $false )
| ( ( subset @ SV763 @ ( setminus @ SV55 @ SV364 ) )
= $true )
| ( ( in @ SV763 @ ( powerset @ SV55 ) )
= $false )
| ( ( in @ SV364 @ ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3056]) ).
thf(3273,plain,
! [SV764: $i,SV365: $i,SV56: $i,SV924: $i] :
( ( ( ~ ( in @ SV924 @ ( powerset @ SV56 ) ) )
= $true )
| ( ( ! [SY4099: $i] :
( ~ ( in @ SY4099 @ ( powerset @ SV56 ) )
| ( ( setminus @ SV56 @ ( binintersect @ ( binunion @ SV365 @ SV764 ) @ ( binunion @ SV924 @ SY4099 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV56 @ SV365 ) @ ( setminus @ SV56 @ SV764 ) ) @ ( binintersect @ ( setminus @ SV56 @ SV924 ) @ ( setminus @ SV56 @ SY4099 ) ) ) ) ) )
= $true )
| ( ( in @ SV764 @ ( powerset @ SV56 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV56 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3057]) ).
thf(3274,plain,
! [SV57: $i,SV366: $i] :
( ( ( ~ ~ ( ~ ( in @ SV366 @ ( sK52_SY3265 @ SV57 @ SV366 ) )
| ~ ( in @ ( sK52_SY3265 @ SV57 @ SV366 ) @ SV57 ) ) )
= $false )
| ( ( in @ SV366 @ ( setunion @ SV57 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3058]) ).
thf(3275,plain,
! [SV57: $i,SV973: $i,SV366: $i] :
( ( ( ~ ~ ( ~ ( in @ SV366 @ SV973 )
| ~ ( in @ SV973 @ SV57 ) ) )
= $true )
| ( ( in @ SV366 @ ( setunion @ SV57 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3059]) ).
thf(3276,plain,
! [SV765: $i,SV58: $i > $o] :
( ( ( SV58 @ SV765 )
= $false )
| ( ( ~ ! [SY3949: $i] :
( ~ ( SV58 @ SY3949 )
| ( SV765 = SY3949 ) ) )
= $true )
| ( ( ! [SY2464: $i,SY2465: $i] :
( ~ ( SV58 @ SY2464 )
| ~ ( SV58 @ SY2465 )
| ( SY2464 = SY2465 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3060]) ).
thf(3277,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ( ~ ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
| ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 ) ) )
= $true )
| ( ( ~ ( ( ( sK37_SY3950 @ SV766 @ SV59 )
!= SV766 )
| ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) ) ) )
= $true )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3061]) ).
thf(3278,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( SV60 @ SV767 )
= $false )
| ( ( ~ ! [SY3951: $i] :
( ~ ( SV60 @ SY3951 )
| ( SV767 = SY3951 ) ) )
= $true )
| ( ( ~ ! [SY2472: $i] :
~ ~ ( ~ ( SV60 @ SY2472 )
| ~ ! [SY2473: $i] :
( ~ ( SV60 @ SY2473 )
| ( SY2472 = SY2473 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3062]) ).
thf(3279,plain,
! [SV858: $i,SV367: $i > $o,SV61: $i] :
( ( ( ! [SY3268: $i] :
~ ~ ( ~ ( in @ SY3268 @ SV61 )
| ~ ~ ( SV367 @ SY3268 ) ) )
= $false )
| ( ( SV367 @ SV858 )
= $true )
| ( ( in @ SV858 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3063]) ).
thf(3280,plain,
! [SV65: $i,SV371: $i] :
( ( ( ~ ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 )
| ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 ) ) )
= $true )
| ( ( SV65 = SV371 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3066]) ).
thf(3281,plain,
! [SV65: $i,SV371: $i] :
( ( ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 )
| ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 ) ) )
= $true )
| ( ( SV65 = SV371 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3066]) ).
thf(3282,plain,
! [SV768: $i,SV68: $i,SV372: $i] :
( ( ( subset @ SV372 @ ( setminus @ SV68 @ SV768 ) )
= $false )
| ( ( ! [SY3952: $i] :
( ~ ( in @ SY3952 @ SV68 )
| ~ ( in @ SY3952 @ SV768 )
| ( in @ SY3952 @ ( setminus @ SV68 @ SV372 ) ) ) )
= $true )
| ( ( in @ SV768 @ ( powerset @ SV68 ) )
= $false )
| ( ( in @ SV372 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3067]) ).
thf(3283,plain,
! [SV769: $i,SV373: $i,SV69: $i,SV925: $i] :
( ( ( ~ ( in @ SV925 @ SV69 ) )
= $true )
| ( ( ~ ( in @ SV925 @ ( setminus @ SV69 @ ( binintersect @ SV373 @ SV769 ) ) )
| ( in @ SV925 @ ( binunion @ ( setminus @ SV69 @ SV373 ) @ ( setminus @ SV69 @ SV769 ) ) ) )
= $true )
| ( ( in @ SV769 @ ( powerset @ SV69 ) )
= $false )
| ( ( in @ SV373 @ ( powerset @ SV69 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3068]) ).
thf(3284,plain,
! [SV860: $o,SV376: $i,SV72: $i,SV621: $i] :
( ( ( SV621 != SV72 )
= $false )
| ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| SV860 )
| SV860 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3069]) ).
thf(3285,plain,
! [SV72: $i,SV376: $i,SV621: $i,SV860: $o] :
( ( SV860 = $false )
| ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| SV860 )
| SV860 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3069]) ).
thf(3286,plain,
! [SV376: $i,SV72: $i,SV621: $i] :
( ( ( SV621 != SV72 )
= $false )
| ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| $true )
| $true )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3070]) ).
thf(3287,plain,
! [SV72: $i,SV376: $i,SV621: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| $true )
| $true )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3070]) ).
thf(3288,plain,
! [SV376: $i,SV72: $i,SV621: $i] :
( ( ( SV621 != SV72 )
= $false )
| ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| $false )
| $false )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3071]) ).
thf(3289,plain,
! [SV72: $i,SV376: $i,SV621: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| $false )
| $false )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3071]) ).
thf(3290,plain,
! [SV772: $i,SV379: $i,SV75: $i,SV926: $i] :
( ( ( ~ ( in @ SV926 @ SV75 ) )
= $true )
| ( ( ~ ( in @ SV926 @ ( setminus @ SV75 @ ( binunion @ SV379 @ SV772 ) ) )
| ( in @ SV926 @ ( setminus @ SV75 @ SV772 ) ) )
= $true )
| ( ( in @ SV772 @ ( powerset @ SV75 ) )
= $false )
| ( ( in @ SV379 @ ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3072]) ).
thf(3291,plain,
! [SV380: $i > $i,SV622: $i,SV76: $i] :
( ( ( ! [SY3750: $i] :
~ ~ ( ~ ( in @ SY3750 @ SV76 )
| ( SV622
!= ( SV380 @ SY3750 ) ) ) )
= $false )
| ( ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3287: $i] : ( SV380 @ SY3287 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3073]) ).
thf(3292,plain,
! [SV380: $i > $i,SV622: $i,SV76: $i] :
( ( ( ! [SY3751: $i] :
~ ~ ( ~ ( in @ SY3751 @ SV76 )
| ( SV622
!= ( SV380 @ SY3751 ) ) ) )
= $true )
| ( ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3290: $i] : ( SV380 @ SY3290 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3074]) ).
thf(3293,plain,
! [SV381: $i > $i,SV623: $i,SV77: $i,SV918: $i] :
( ( ( ~ ( in @ SV918 @ SV77 )
| ( SV623
!= ( SV381 @ SV918 ) ) )
= $true )
| ( ( in @ SV623
@ ( image1 @ SV77
@ ^ [SY3293: $i] : ( SV381 @ SY3293 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3075]) ).
thf(3294,plain,
! [SV773: $i,SV382: $i,SV78: $i,SV927: $i] :
( ( ( ~ ( in @ SV927 @ SV78 ) )
= $true )
| ( ( ! [SY4100: $i] :
( ~ ( in @ SY4100 @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ SY4100 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
| ~ ! [SY4101: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY4101 @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ SY4101 ) @ SV382 ) )
| ~ ( in @ ( kpair @ SY4101 @ SY4100 ) @ SV773 ) ) ) )
= $true )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3076]) ).
thf(3295,plain,
! [SV384: $i,SV80: $i,SV625: $i] :
( ( ( SV625 = SV80 )
= $true )
| ( ( in @ SV625 @ SV384 )
= $true )
| ( ( in @ SV625 @ ( setadjoin @ SV80 @ SV384 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3077]) ).
thf(3296,plain,
! [SV384: $i,SV80: $i,SV625: $i] :
( ( ( SV625 = SV80 )
= $false )
| ( ( in @ SV625 @ ( setadjoin @ SV80 @ SV384 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3078]) ).
thf(3297,plain,
! [SV80: $i,SV384: $i,SV625: $i] :
( ( ( in @ SV625 @ SV384 )
= $false )
| ( ( in @ SV625 @ ( setadjoin @ SV80 @ SV384 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3078]) ).
thf(3298,plain,
! [SV774: $i,SV386: $i,SV82: $i,SV928: $i] :
( ( ( ~ ( in @ SV928 @ SV82 ) )
= $true )
| ( ( ! [SY4102: $i] :
( ~ ( in @ SY4102 @ SV82 )
| ~ ( in @ ( kpair @ SV928 @ SY4102 ) @ ( binunion @ SV386 @ SV774 ) )
| ( in @ ( kpair @ SV928 @ SY4102 ) @ SV386 )
| ( in @ ( kpair @ SV928 @ SY4102 ) @ SV774 ) ) )
= $true )
| ( ( breln1 @ SV82 @ SV774 )
= $false )
| ( ( breln1 @ SV82 @ SV386 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3079]) ).
thf(3299,plain,
! [SV776: $i,SV389: $i,SV86: $i,SV929: $i] :
( ( ( ~ ( in @ SV929 @ SV86 ) )
= $true )
| ( ( ~ ( subset @ SV389 @ ( setminus @ SV86 @ SV776 ) )
| ~ ( in @ SV929 @ SV776 )
| ~ ( in @ SV929 @ SV389 ) )
= $true )
| ( ( in @ SV776 @ ( powerset @ SV86 ) )
= $false )
| ( ( in @ SV389 @ ( powerset @ SV86 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3080]) ).
thf(3300,plain,
! [SV777: $i,SV390: $i,SV87: $i,SV930: $i] :
( ( ( ~ ( in @ SV930 @ SV87 ) )
= $true )
| ( ( ~ ( subset @ SV390 @ SV777 )
| ~ ~ ( in @ SV930 @ SV777 )
| ~ ( in @ SV930 @ SV390 ) )
= $true )
| ( ( in @ SV777 @ ( powerset @ SV87 ) )
= $false )
| ( ( in @ SV390 @ ( powerset @ SV87 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3081]) ).
thf(3301,plain,
! [SV779: $i,SV393: $i,SV90: $i,SV931: $i] :
( ( ( ~ ( in @ SV931 @ ( powerset @ SV90 ) ) )
= $true )
| ( ( ! [SY4103: $i] :
( ~ ( in @ SY4103 @ SV90 )
| ~ ( in @ SY4103 @ ( binintersect @ SV393 @ SV779 ) )
| ( in @ SY4103 @ ( binintersect @ ( binunion @ SV393 @ SV931 ) @ ( binunion @ SV779 @ SV931 ) ) ) ) )
= $true )
| ( ( in @ SV779 @ ( powerset @ SV90 ) )
= $false )
| ( ( in @ SV393 @ ( powerset @ SV90 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3082]) ).
thf(3302,plain,
! [SV780: $i,SV400: $i,SV99: $i,SV932: $i] :
( ( ( ~ ( in @ SV932 @ SV99 ) )
= $true )
| ( ( ~ ( in @ SV932 @ ( setminus @ SV99 @ ( binunion @ SV400 @ SV780 ) ) )
| ( in @ SV932 @ ( setminus @ SV99 @ SV400 ) ) )
= $true )
| ( ( in @ SV780 @ ( powerset @ SV99 ) )
= $false )
| ( ( in @ SV400 @ ( powerset @ SV99 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3086]) ).
thf(3303,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ! [SY4131: $i] :
( ~ ( SV100 @ ( sK53_SY2563 @ SV781 @ SV100 ) )
| ~ ( SV100 @ SY4131 )
| ( ( sK53_SY2563 @ SV781 @ SV100 )
= SY4131 ) ) )
= $false )
| ( ( ~ ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3087]) ).
thf(3304,plain,
! [SV102: $i,SV402: $i,SV631: $i] :
( ( ( in @ SV631 @ SV402 )
= $true )
| ( ( ~ ( in @ SV631 @ SV102 ) )
= $true )
| ( ( in @ SV631 @ ( setminus @ SV102 @ SV402 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3088]) ).
thf(3305,plain,
! [SV404: $i > $o,SV104: $i,SV862: $i] :
( ( ( ~ ( in @ SV862 @ SV104 ) )
= $true )
| ( ( ~ ~ ( SV404 @ SV862 ) )
= $true )
| ( ( ~ ! [SY3324: $i] :
( ~ ( in @ SY3324 @ SV104 )
| ( SV404 @ SY3324 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3089]) ).
thf(3306,plain,
! [SV106: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK44_SY2577 @ SV106 ) @ omega )
| ~ ( in @ ( sK44_SY2577 @ SV106 ) @ SV106 ) ) )
= $false )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( ! [SY2578: $i] :
( ~ ( in @ SY2578 @ omega )
| ( in @ SY2578 @ SV106 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3090]) ).
thf(3307,plain,
! [SV106: $i] :
( ( ( in @ ( setadjoin @ ( sK44_SY2577 @ SV106 ) @ ( sK44_SY2577 @ SV106 ) ) @ SV106 )
= $false )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( ! [SY2578: $i] :
( ~ ( in @ SY2578 @ omega )
| ( in @ SY2578 @ SV106 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3090]) ).
thf(3308,plain,
! [SV782: $i,SV407: $i,SV109: $i] :
( ( ( ! [SY3965: $i] :
( ~ ( in @ SY3965 @ SV109 )
| ~ ( in @ SY3965 @ SV407 )
| ( in @ SY3965 @ SV782 ) ) )
= $false )
| ( ( subset @ SV407 @ SV782 )
= $true )
| ( ( in @ SV782 @ ( powerset @ SV109 ) )
= $false )
| ( ( in @ SV407 @ ( powerset @ SV109 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3092]) ).
thf(3309,plain,
! [SV783: $i,SV408: $i,SV110: $i,SV933: $i] :
( ( ( ~ ( in @ SV933 @ SV110 ) )
= $true )
| ( ( ~ ~ ( in @ SV933 @ SV408 )
| ~ ( in @ SV933 @ ( binintersect @ SV408 @ SV783 ) ) )
= $true )
| ( ( in @ SV783 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV408 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3093]) ).
thf(3310,plain,
! [SV784: $i,SV411: $i,SV113: $i,SV934: $i] :
( ( ( ~ ( in @ SV934 @ SV113 ) )
= $true )
| ( ( ~ ( in @ SV934 @ ( setminus @ SV113 @ SV411 ) )
| ( in @ SV934 @ ( setminus @ SV113 @ ( binintersect @ SV411 @ SV784 ) ) ) )
= $true )
| ( ( in @ SV784 @ ( powerset @ SV113 ) )
= $false )
| ( ( in @ SV411 @ ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3095]) ).
thf(3311,plain,
! [SV114: $i,SV412: $i,SV785: $i] :
( ( ( in @ SV785 @ SV412 )
= $false )
| ( ( ~ ( in @ SV785 @ ( setminus @ SV114 @ SV412 ) ) )
= $true )
| ( ( in @ SV785 @ SV114 )
= $false )
| ( ( in @ SV412 @ ( powerset @ SV114 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3096]) ).
thf(3312,plain,
! [SV639: $i,SV416: $i > $o,SV118: $i] :
( ( ( ! [SY3768: $i] :
( ~ ( in @ SY3768 @ SV118 )
| ~ ( SV416 @ SY3768 )
| ( SY3768 = SV639 ) ) )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY3351: $i] : ( SV416 @ SY3351 ) )
= $true )
| ( ( SV416 @ SV639 )
= $false )
| ( ( in @ SV639 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3097]) ).
thf(3313,plain,
! [SV120: $i,SV418: $i,SV640: $i] :
( ( ( in @ SV640 @ SV418 )
= $true )
| ( ( ~ ( in @ SV640 @ ( symdiff @ SV120 @ SV418 ) ) )
= $true )
| ( ( in @ SV640 @ SV120 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3098]) ).
thf(3314,plain,
! [SV641: $i > $i,SV419: $i,SV121: $i,SV974: $i] :
( ( ( ~ ( in @ SV974 @ SV121 )
| ( ( ap @ SV121 @ SV419
@ ( lam @ SV121 @ SV419
@ ^ [SY3772: $i] : ( SV641 @ SY3772 ) )
@ SV974 )
= ( SV641 @ SV974 ) ) )
= $true )
| ( ( in @ ( sK24_SY3770 @ SV419 @ SV641 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3099]) ).
thf(3315,plain,
! [SV641: $i > $i,SV419: $i,SV121: $i,SV935: $i] :
( ( ( ~ ( in @ SV935 @ SV121 ) )
= $true )
| ( ( ( ap @ SV121 @ SV419
@ ( lam @ SV121 @ SV419
@ ^ [SY3772: $i] : ( SV641 @ SY3772 ) )
@ SV935 )
= ( SV641 @ SV935 ) )
= $true )
| ( ( in @ ( SV641 @ ( sK24_SY3770 @ SV419 @ SV641 @ SV121 ) ) @ SV419 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3100]) ).
thf(3316,plain,
! [SV122: $i,SV420: $i,SV788: $i > $o,SV865: $i > $o] :
( ( ( ~ ( in @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) @ SV122 )
| ! [SY4133: $i] :
( ~ ( in @ SY4133 @ SV420 )
| ( ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 )
!= SY4133 )
| ~ ( ~ ( ~ ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) )
| ( SV865 @ SY4133 ) )
| ~ ( ~ ( SV865 @ SY4133 )
| ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3101]) ).
thf(3317,plain,
! [SV789: $i,SV421: $i > $o,SV123: $i,SV936: $i] :
( ( ( ~ ( in @ SV936 @ SV123 ) )
= $true )
| ( ( ~ ( SV421 @ SV789 )
| ~ ( SV421 @ SV936 )
| ( SV789 = SV936 ) )
= $true )
| ( ( in @ SV789 @ SV123 )
= $false )
| ( ( ex1 @ SV123
@ ^ [SY3363: $i] : ( SV421 @ SY3363 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3102]) ).
thf(3318,plain,
! [SV423: $i,SV790: $i,SV125: $i,SV937: $i] :
( ( ( ~ ( in @ SV937 @ SV125 ) )
= $true )
| ( ( ! [SY4105: $i] :
( ~ ( in @ SY4105 @ SV125 )
| ~ ( in @ ( kpair @ SV937 @ SY4105 ) @ SV790 )
| ( in @ ( kpair @ SV937 @ SY4105 ) @ ( binunion @ SV423 @ SV790 ) ) ) )
= $true )
| ( ( breln1 @ SV125 @ SV790 )
= $false )
| ( ( breln1 @ SV125 @ SV423 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3103]) ).
thf(3319,plain,
! [SV642: $i,SV126: $i,SV866: $i,SV424: $o] :
( ( ( ~ ~ SV424 )
= $true )
| ( ( in @ SV866
@ ( dsetconstr @ SV126
@ ^ [SY4056: $i] :
( ~ ( ~ SV424
| ( SY4056 != SV642 ) )
| ~ ( ~ ~ SV424
| ( SY4056 != SV866 ) ) ) ) )
= $true )
| ( ( in @ SV866 @ SV126 )
= $false )
| ( ( in @ SV642 @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3104]) ).
thf(3320,plain,
! [SV643: $i,SV126: $i,SV867: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( in @ SV867
@ ( dsetconstr @ SV126
@ ^ [SY4057: $i] :
( ~ ( ~ $true
| ( SY4057 != SV643 ) )
| ~ ( ~ ~ $true
| ( SY4057 != SV867 ) ) ) ) )
= $true )
| ( ( in @ SV867 @ SV126 )
= $false )
| ( ( in @ SV643 @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3105]) ).
thf(3321,plain,
! [SV644: $i,SV126: $i,SV868: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( in @ SV868
@ ( dsetconstr @ SV126
@ ^ [SY4058: $i] :
( ~ ( ~ $false
| ( SY4058 != SV644 ) )
| ~ ( ~ ~ $false
| ( SY4058 != SV868 ) ) ) ) )
= $true )
| ( ( in @ SV868 @ SV126 )
= $false )
| ( ( in @ SV644 @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3106]) ).
thf(3322,plain,
! [SV130: $i,SV427: $i,SV938: $i] :
( ( ( ~ ( in @ SV938 @ SV427 ) )
= $true )
| ( ( in @ SV938 @ SV130 )
= $true )
| ( ( in @ SV427 @ ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3108]) ).
thf(3323,plain,
! [SV427: $i,SV130: $i] :
( ( ( ~ ( in @ ( sK45_SY3375 @ SV130 @ SV427 ) @ SV427 ) )
= $false )
| ( ( in @ SV427 @ ( powerset @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3109]) ).
thf(3324,plain,
! [SV427: $i,SV130: $i] :
( ( ( in @ ( sK45_SY3375 @ SV130 @ SV427 ) @ SV130 )
= $false )
| ( ( in @ SV427 @ ( powerset @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3109]) ).
thf(3325,plain,
! [SV792: $i,SV428: $i,SV131: $i,SV939: $i] :
( ( ( ~ ( in @ SV939 @ SV131 ) )
= $true )
| ( ( ! [SY4106: $i] :
( ~ ( in @ SY4106 @ SV131 )
| ! [SY4107: $i] :
( ~ ( in @ SY4107 @ SV131 )
| ~ ( in @ ( kpair @ SV939 @ SY4107 ) @ SV428 )
| ~ ( in @ ( kpair @ SY4107 @ SY4106 ) @ SV792 )
| ( in @ ( kpair @ SV939 @ SY4106 ) @ ( breln1compset @ SV131 @ SV428 @ SV792 ) ) ) ) )
= $true )
| ( ( breln1 @ SV131 @ SV792 )
= $false )
| ( ( breln1 @ SV131 @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3110]) ).
thf(3326,plain,
! [SV794: $i,SV432: $i,SV135: $i] :
( ( ( ! [SY3983: $i] :
( ~ ( in @ SY3983 @ SV135 )
| ! [SY3984: $i] :
( ~ ( in @ SY3984 @ SV135 )
| ~ ( in @ ( kpair @ SY3983 @ SY3984 ) @ SV432 )
| ( in @ ( kpair @ SY3983 @ SY3984 ) @ SV794 ) ) ) )
= $false )
| ( ( subset @ SV432 @ SV794 )
= $true )
| ( ( breln1 @ SV135 @ SV794 )
= $false )
| ( ( breln1 @ SV135 @ SV432 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3111]) ).
thf(3327,plain,
! [SV136: $i] :
( ( ( ~ ( in @ ( sK25_SY2669 @ SV136 ) @ SV136 ) )
= $false )
| ( ( SV136 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3112]) ).
thf(3328,plain,
! [SV136: $i] :
( ( ( ( binintersect @ ( sK25_SY2669 @ SV136 ) @ SV136 )
!= emptyset )
= $false )
| ( ( SV136 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3112]) ).
thf(3329,plain,
! [SV434: $i,SV869: $i,SV138: $i,SV795: $i] :
( ( ( ~ ( ~ ( in @ SV795 @ SV138 )
| ( in @ SV869 @ SV434 ) )
| ~ ( ~ ( in @ SV869 @ SV434 )
| ( in @ SV795 @ SV138 ) ) )
= $false )
| ( ( SV795 = SV869 )
= $false )
| ( ( SV138 = SV434 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3113]) ).
thf(3330,plain,
! [SV796: $i,SV435: $i,SV139: $i,SV940: $i] :
( ( ( ~ ( in @ SV940 @ ( powerset @ SV139 ) ) )
= $true )
| ( ( ~ ( subset @ SV435 @ SV940 )
| ( subset @ ( binintersect @ SV435 @ SV796 ) @ SV940 ) )
= $true )
| ( ( in @ SV796 @ ( powerset @ SV139 ) )
= $false )
| ( ( in @ SV435 @ ( powerset @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3114]) ).
thf(3331,plain,
! [SV870: $i,SV650: $i,SV436: $i,SV140: $i] :
( ( ( ~ ! [SY4059: $i] :
( ~ ( in @ SY4059 @ SV140 )
| ! [SY4060: $i] :
( ~ ( in @ SY4060 @ SV436 )
| ~ ( in @ ( kpair @ SY4059 @ SY4060 ) @ SV650 )
| ( in @ ( kpair @ SY4059 @ SY4060 ) @ SV870 ) ) ) )
= $true )
| ( ( ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) )
| ( SV650 = SV870 ) )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3115]) ).
thf(3332,plain,
! [SV654: $i > $i,SV144: $i,SV440: $i,SV975: $i] :
( ( ( ~ ( in @ SV975 @ ( funcSet @ SV440 @ SV144 ) )
| ~ ! [SY4134: $i] :
( ~ ( in @ SY4134 @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SV975 @ ( SV654 @ SY4134 ) )
= SY4134 ) )
| ( surjective @ SV440 @ SV144 @ SV975 ) )
= $true )
| ( ( in @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) @ SV144 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3118]) ).
thf(3333,plain,
! [SV654: $i > $i,SV144: $i,SV440: $i,SV941: $i] :
( ( ( ~ ( in @ SV941 @ ( funcSet @ SV440 @ SV144 ) ) )
= $true )
| ( ( ~ ! [SY4108: $i] :
( ~ ( in @ SY4108 @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SV941 @ ( SV654 @ SY4108 ) )
= SY4108 ) )
| ( surjective @ SV440 @ SV144 @ SV941 ) )
= $true )
| ( ( in @ ( SV654 @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) ) @ SV440 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3119]) ).
thf(3334,plain,
! [SV145: $i,SV441: $i,SV797: $i] :
( ( ( in @ SV797 @ SV441 )
= $false )
| ( ( in @ SV797 @ ( setminus @ SV145 @ ( setminus @ SV145 @ SV441 ) ) )
= $true )
| ( ( in @ SV797 @ SV145 )
= $false )
| ( ( in @ SV441 @ ( powerset @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3120]) ).
thf(3335,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ( ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) ) )
= $false )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( in @ ( sK11_SY3407 @ SV442 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3121]) ).
thf(3336,plain,
! [SV146: $i,SV442: $i > $o] :
( ( ( in @ ( sK38_SY3987 @ SV442 @ SV146 ) @ SV146 )
= $true )
| ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) )
| ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3122]) ).
thf(3337,plain,
! [SV146: $i,SV442: $i > $o] :
( ( ( ~ ( SV442 @ ( sK11_SY3407 @ SV442 @ SV146 ) ) )
= $false )
| ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) )
| ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3123]) ).
thf(3338,plain,
! [SV146: $i,SV442: $i > $o] :
( ( ( ~ ( SV442 @ ( sK38_SY3987 @ SV442 @ SV146 ) )
| ( ( sK11_SY3407 @ SV442 @ SV146 )
= ( sK38_SY3987 @ SV442 @ SV146 ) ) )
= $false )
| ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) )
| ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3123]) ).
thf(3339,plain,
! [SV798: $i,SV443: $i,SV147: $i,SV942: $i] :
( ( ( ~ ( in @ SV942 @ SV147 ) )
= $true )
| ( ( ~ ( in @ SV942 @ ( setminus @ SV147 @ SV443 ) )
| ~ ( in @ SV942 @ ( binintersect @ SV443 @ SV798 ) ) )
= $true )
| ( ( in @ SV798 @ ( powerset @ SV147 ) )
= $false )
| ( ( in @ SV443 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3124]) ).
thf(3340,plain,
! [SV799: $i,SV444: $i,SV148: $i,SV943: $i] :
( ( ( ~ ( in @ SV943 @ ( powerset @ SV148 ) ) )
= $true )
| ( ( ! [SY4109: $i] :
( ~ ( in @ SY4109 @ SV148 )
| ~ ( in @ SY4109 @ ( binintersect @ SV444 @ SV799 ) )
| ( in @ SY4109 @ ( binunion @ SV444 @ SV943 ) ) ) )
= $true )
| ( ( in @ SV799 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV444 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3125]) ).
thf(3341,plain,
! [SV149: $i,SV445: $i > $o] :
( ( ( ~ ( in @ ( sK27_SY3417 @ SV445 @ SV149 ) @ SV149 ) )
= $false )
| ( ( ex1 @ SV149
@ ^ [SY3416: $i] : ( SV445 @ SY3416 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3126]) ).
thf(3342,plain,
! [SV149: $i,SV445: $i > $o] :
( ( ( ~ ( SV445 @ ( sK27_SY3417 @ SV445 @ SV149 ) ) )
= $false )
| ( ( ex1 @ SV149
@ ^ [SY3416: $i] : ( SV445 @ SY3416 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3126]) ).
thf(3343,plain,
! [SV800: $i,SV446: $i,SV944: $i,SV150: $i] :
( ( ( ~ ( breln1 @ SV150 @ SV944 ) )
= $true )
| ( ( ( breln1compset @ SV150 @ ( binunion @ SV446 @ SV800 ) @ SV944 )
= ( binunion @ ( breln1compset @ SV150 @ SV446 @ SV944 ) @ ( breln1compset @ SV150 @ SV800 @ SV944 ) ) )
= $true )
| ( ( breln1 @ SV150 @ SV800 )
= $false )
| ( ( breln1 @ SV150 @ SV446 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3127]) ).
thf(3344,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3128]) ).
thf(3345,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ( ~ ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
| ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
| ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3129]) ).
thf(3346,plain,
! [SV873: $i,SV657: $i,SV155: $i,SV451: $o] :
( ( ( ~ ~ SV451 )
= $true )
| ( ( ( dsetconstr @ SV155
@ ^ [SY4063: $i] :
( ~ ( ~ SV451
| ( SY4063 != SV657 ) )
| ~ ( ~ ~ SV451
| ( SY4063 != SV873 ) ) ) )
= ( setadjoin @ SV873 @ emptyset ) )
= $true )
| ( ( in @ SV873 @ SV155 )
= $false )
| ( ( in @ SV657 @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3130]) ).
thf(3347,plain,
! [SV874: $i,SV658: $i,SV155: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( ( dsetconstr @ SV155
@ ^ [SY4064: $i] :
( ~ ( ~ $true
| ( SY4064 != SV658 ) )
| ~ ( ~ ~ $true
| ( SY4064 != SV874 ) ) ) )
= ( setadjoin @ SV874 @ emptyset ) )
= $true )
| ( ( in @ SV874 @ SV155 )
= $false )
| ( ( in @ SV658 @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3131]) ).
thf(3348,plain,
! [SV875: $i,SV659: $i,SV155: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( ( dsetconstr @ SV155
@ ^ [SY4065: $i] :
( ~ ( ~ $false
| ( SY4065 != SV659 ) )
| ~ ( ~ ~ $false
| ( SY4065 != SV875 ) ) ) )
= ( setadjoin @ SV875 @ emptyset ) )
= $true )
| ( ( in @ SV875 @ SV155 )
= $false )
| ( ( in @ SV659 @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3132]) ).
thf(3349,plain,
! [SV453: $i,SV802: $i,SV157: $i,SV945: $i] :
( ( ( ~ ( in @ SV945 @ SV157 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV802 @ SV945 ) @ SV453 )
| ( in @ ( kpair @ SV945 @ SV802 ) @ ( breln1invset @ SV157 @ SV453 ) ) )
= $true )
| ( ( in @ SV802 @ SV157 )
= $false )
| ( ( breln1 @ SV157 @ SV453 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3133]) ).
thf(3350,plain,
! [SV459: $i,SV804: $i,SV163: $i,SV946: $i] :
( ( ( ~ ( in @ SV946 @ ( powerset @ SV163 ) ) )
= $true )
| ( ( ~ ( subset @ SV804 @ SV946 )
| ( subset @ ( binintersect @ SV459 @ SV804 ) @ SV946 ) )
= $true )
| ( ( in @ SV804 @ ( powerset @ SV163 ) )
= $false )
| ( ( in @ SV459 @ ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3135]) ).
thf(3351,plain,
! [SV463: $i,SV876: $i,SV167: $i,SV805: $i] :
( ( ( ~ ( in @ SV805 @ SV167 ) )
= $true )
| ( ( in @ SV876 @ SV463 )
= $true )
| ( ( SV805 = SV876 )
= $false )
| ( ( SV167 = SV463 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3136]) ).
thf(3352,plain,
! [SV877: $i,SV666: $i,SV464: $i,SV168: $i] :
( ( ( ~ ! [SY4066: $i] :
( ~ ( in @ SY4066 @ SV168 )
| ! [SY4067: $i] :
( ~ ( in @ SY4067 @ SV464 )
| ~ ( in @ ( kpair @ SY4066 @ SY4067 ) @ SV666 )
| ( in @ ( kpair @ SY4066 @ SY4067 ) @ SV877 ) ) ) )
= $true )
| ( ( subset @ SV666 @ SV877 )
= $true )
| ( ( breln @ SV168 @ SV464 @ SV877 )
= $false )
| ( ( breln @ SV168 @ SV464 @ SV666 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3137]) ).
thf(3353,plain,
! [SV806: $i,SV465: $i,SV947: $i,SV169: $i] :
( ( ( ~ ( breln1 @ SV169 @ SV947 ) )
= $true )
| ( ( ( breln1compset @ SV169 @ ( binunion @ SV465 @ SV806 ) @ SV947 )
= ( binunion @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SV947 ) @ ( breln1invset @ SV169 @ SV806 ) ) ) @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SV947 ) @ ( breln1invset @ SV169 @ SV465 ) ) ) ) )
= $true )
| ( ( breln1 @ SV169 @ SV806 )
= $false )
| ( ( breln1 @ SV169 @ SV465 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3138]) ).
thf(3354,plain,
! [SV171: $i,SV807: $i,SV466: $i,SV948: $i] :
( ( ( ~ ( in @ SV948 @ ( binintersect @ SV466 @ SV807 ) ) )
= $true )
| ( ( in @ SV948 @ SV171 )
= $true )
| ( ( in @ SV807 @ ( powerset @ SV171 ) )
= $false )
| ( ( in @ SV466 @ ( powerset @ SV171 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3139]) ).
thf(3355,plain,
! [SV808: $i,SV173: $i,SV468: $i] :
( ( ( subset @ SV468 @ ( setminus @ SV173 @ SV808 ) )
= $false )
| ( ( subset @ SV808 @ ( setminus @ SV173 @ SV468 ) )
= $true )
| ( ( in @ SV808 @ ( powerset @ SV173 ) )
= $false )
| ( ( in @ SV468 @ ( powerset @ SV173 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3140]) ).
thf(3356,plain,
! [SV175: $i,SV470: $i > $i,SV976: $i] :
( ( ~ ( ~ ( ~ ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
| ~ ! [SY4135: $i] :
~ ~ ( ~ ( in @ SY4135 @ SV175 )
| ( SV976
!= ( SV470 @ SY4135 ) ) ) )
| ~ ( ~ ~ ! [SY4136: $i] :
~ ~ ( ~ ( in @ SY4136 @ SV175 )
| ( SV976
!= ( SV470 @ SY4136 ) ) )
| ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3141]) ).
thf(3357,plain,
! [SV470: $i > $i,SV175: $i,SV977: $i] :
( ( ~ ! [SY4137: $i] :
~ ( ~ ( ~ ( in @ SY4137 @ SV977 )
| ~ ! [SY3468: $i] :
~ ~ ( ~ ( in @ SY3468 @ SV175 )
| ( SY4137
!= ( SV470 @ SY3468 ) ) ) )
| ~ ( ~ ~ ! [SY3469: $i] :
~ ~ ( ~ ( in @ SY3469 @ SV175 )
| ( SY4137
!= ( SV470 @ SY3469 ) ) )
| ( in @ SY4137 @ SV977 ) ) )
| ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3142]) ).
thf(3358,plain,
! [SV670: $i > $i > $o,SV180: $i,SV475: $i,SV978: $i] :
( ( ( ~ ( in @ SV978 @ ( breln1Set @ SV475 ) )
| ~ ( reflwellordering @ SV475 @ SV978 )
| ! [SY4140: $i] :
( ~ ( in @ SY4140 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY4141: $i] :
~ ( ~ ( SV670 @ SY4140 @ SY4141 )
| ~ ! [SY4142: $i] :
( ~ ( in @ SY4142 @ SV475 )
| ~ ( SV670 @ SY4140 @ SY4142 )
| ( in @ ( kpair @ SY4141 @ SY4142 ) @ SV978 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV180 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3143]) ).
thf(3359,plain,
! [SV180: $i,SV670: $i > $i > $o,SV475: $i,SV979: $i] :
( ( ( ~ ~ ( ~ ( in @ SV979 @ SV475 )
| ~ ( SV670 @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV979 ) ) )
= $true )
| ( ( ! [SY3807: $i] :
( ~ ( in @ SY3807 @ ( breln1Set @ SV475 ) )
| ~ ( reflwellordering @ SV475 @ SY3807 )
| ! [SY3808: $i] :
( ~ ( in @ SY3808 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY3809: $i] :
~ ( ~ ( SV670 @ SY3808 @ SY3809 )
| ~ ! [SY3810: $i] :
( ~ ( in @ SY3810 @ SV475 )
| ~ ( SV670 @ SY3808 @ SY3810 )
| ( in @ ( kpair @ SY3809 @ SY3810 ) @ SY3807 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3144]) ).
thf(3360,plain,
! [SV672: $i > $i,SV477: $i,SV182: $i,SV980: $i] :
( ( ( ~ ( in @ SV980 @ SV182 )
| ( ( ap @ SV182 @ SV477
@ ( lam @ SV182 @ SV477
@ ^ [SY3814: $i] : ( SV672 @ SY3814 ) )
@ SV980 )
= ( SV672 @ SV980 ) ) )
= $true )
| ( ( in @ ( sK30_SY3812 @ SV477 @ SV672 @ SV182 ) @ SV182 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3146]) ).
thf(3361,plain,
! [SV672: $i > $i,SV477: $i,SV182: $i,SV949: $i] :
( ( ( ~ ( in @ SV949 @ SV182 ) )
= $true )
| ( ( ( ap @ SV182 @ SV477
@ ( lam @ SV182 @ SV477
@ ^ [SY3814: $i] : ( SV672 @ SY3814 ) )
@ SV949 )
= ( SV672 @ SV949 ) )
= $true )
| ( ( in @ ( SV672 @ ( sK30_SY3812 @ SV477 @ SV672 @ SV182 ) ) @ SV477 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3147]) ).
thf(3362,plain,
! [SV673: $i,SV478: $i,SV183: $i] :
( ( ( subset @ SV183 @ SV478 )
= $false )
| ( ( in @ SV673 @ SV478 )
= $true )
| ( ( in @ SV673 @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3148]) ).
thf(3363,plain,
! [SV674: $i,SV479: $i,SV184: $i] :
( ( ( SV184 = SV479 )
= $false )
| ( ( in @ SV674 @ SV479 )
= $true )
| ( ( in @ SV674 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3149]) ).
thf(3364,plain,
! [SV812: $i,SV481: $i,SV186: $i,SV950: $i] :
( ( ( ~ ( in @ SV950 @ SV186 ) )
= $true )
| ( ( ~ ( in @ SV481 @ ( powerset @ SV812 ) )
| ~ ( in @ SV950 @ SV481 )
| ( in @ SV950 @ SV812 ) )
= $true )
| ( ( in @ SV812 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV481 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3150]) ).
thf(3365,plain,
! [SV483: $i > $o,SV188: $i,SV675: $i] :
( ( ( ~ ( in @ SV675
@ ( dsetconstr @ SV188
@ ^ [SY3494: $i] : ( SV483 @ SY3494 ) ) ) )
= $true )
| ( ( SV483 @ SV675 )
= $true )
| ( ( in @ SV675 @ SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3151]) ).
thf(3366,plain,
! [SV188: $i,SV675: $i,SV483: $i > $o] :
( ( ( ~ ( SV483 @ SV675 ) )
= $true )
| ( ( in @ SV675
@ ( dsetconstr @ SV188
@ ^ [SY3495: $i] : ( SV483 @ SY3495 ) ) )
= $true )
| ( ( in @ SV675 @ SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3152]) ).
thf(3367,plain,
! [SV879: $i,SV484: $i > $o,SV189: $i] :
( ( ( ! [SY3497: $i] :
~ ~ ( ~ ( in @ SY3497 @ SV189 )
| ~ ~ ( SV484 @ SY3497 ) ) )
= $false )
| ( ( SV484 @ SV879 )
= $true )
| ( ( in @ SV879 @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3153]) ).
thf(3368,plain,
! [SV190: $i,SV813: $o,SV485: $i] :
( ( ( ~ ( in @ SV485 @ ( sK46_SY4001 @ SV813 @ SV190 @ SV485 ) ) )
= $false )
| ( SV813 = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3154]) ).
thf(3369,plain,
! [SV485: $i,SV190: $i,SV813: $o] :
( ( ( ~ ( in @ ( sK46_SY4001 @ SV813 @ SV190 @ SV485 ) @ SV190 )
| SV813 )
= $false )
| ( SV813 = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3154]) ).
thf(3370,plain,
! [SV190: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ ( sK47_SX0 @ SV190 @ SV485 ) ) )
= $false )
| ( $true = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3155]) ).
thf(3371,plain,
! [SV485: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK47_SX0 @ SV190 @ SV485 ) @ SV190 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3155]) ).
thf(3372,plain,
! [SV190: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ ( sK48_SX0 @ SV190 @ SV485 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3156]) ).
thf(3373,plain,
! [SV485: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK48_SX0 @ SV190 @ SV485 ) @ SV190 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3156]) ).
thf(3374,plain,
! [SV191: $i,SV676: $i,SV880: $i,SV486: $i,SV981: $i] :
( ( ( ~ ( in @ SV981 @ SV486 )
| ~ ( in @ ( kpair @ SV880 @ SV981 ) @ SV676 )
| ( ( ap @ SV191 @ SV486 @ SV676 @ SV880 )
= SV981 ) )
= $true )
| ( ( in @ SV880 @ SV191 )
= $false )
| ( ( in @ SV676 @ ( funcSet @ SV191 @ SV486 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3157]) ).
thf(3375,plain,
! [SV193: $i,SV488: $i > $i,SV881: $i] :
( ( ~ ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
| ~ ! [SY4070: $i] :
~ ~ ( ~ ( in @ SY4070 @ SV193 )
| ( SV881
!= ( SV488 @ SY4070 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3158]) ).
thf(3376,plain,
! [SV488: $i > $i,SV881: $i,SV193: $i] :
( ( ~ ~ ! [SY4071: $i] :
~ ~ ( ~ ( in @ SY4071 @ SV193 )
| ( SV881
!= ( SV488 @ SY4071 ) ) )
| ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3159]) ).
thf(3377,plain,
! [SV489: $i,SV194: $i,SV814: $i] :
( ( ( ~ ( in @ SV814 @ ( setminus @ SV194 @ SV489 ) ) )
= $false )
| ( ( in @ SV814 @ SV489 )
= $true )
| ( ( in @ SV814 @ SV194 )
= $false )
| ( ( in @ SV489 @ ( powerset @ SV194 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3160]) ).
thf(3378,plain,
! [SV919: $i] :
( ( ( in @ SV919 @ sK5_SY3512 )
= $false )
| ( ( subset @ SV919 @ sK5_SY3512 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3161]) ).
thf(3379,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( SV196 @ SV816 )
= $false )
| ( ( ~ ! [SY4002: $i] :
( ~ ( SV196 @ SY4002 )
| ( SV816 = SY4002 ) ) )
= $true )
| ( ( ~ ! [SY2855: $i] :
~ ~ ( ~ ( SV196 @ SY2855 )
| ~ ! [SY2856: $i] :
( ~ ( SV196 @ SY2856 )
| ( SY2855 = SY2856 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3163]) ).
thf(3380,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3164]) ).
thf(3381,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
| ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
| ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3165]) ).
thf(3382,plain,
! [SV199: $i,SV492: $i,SV679: $i] :
( ( ( ~ ( in @ ( sK39_SY3820 @ SV679 @ SV492 @ SV199 ) @ SV199 )
| ~ ~ ! [SY4093: $i] :
~ ~ ( ~ ( in @ SY4093 @ SV492 )
| ( SV679
!= ( kpair @ ( sK39_SY3820 @ SV679 @ SV492 @ SV199 ) @ SY4093 ) ) ) )
= $false )
| ( ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3166]) ).
thf(3383,plain,
! [SV817: $i,SV493: $i,SV200: $i,SV951: $i] :
( ( ( ~ ( in @ SV951 @ SV200 ) )
= $true )
| ( ( ~ ~ ( in @ SV951 @ ( binunion @ SV493 @ SV817 ) )
| ~ ( in @ SV951 @ SV817 ) )
= $true )
| ( ( in @ SV817 @ ( powerset @ SV200 ) )
= $false )
| ( ( in @ SV493 @ ( powerset @ SV200 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3167]) ).
thf(3384,plain,
! [SV885: $o,SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV203 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SV885 )
| SV885 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3171]) ).
thf(3385,plain,
! [SV203: $i,SV885: $o,SV496: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV496 )
| SV885 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SV885 )
| SV885 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3171]) ).
thf(3386,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV203 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $true )
| $true )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3172]) ).
thf(3387,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV496 )
| $true )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $true )
| $true )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3172]) ).
thf(3388,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV203 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $false )
| $false )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3173]) ).
thf(3389,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV496 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $false )
| $false )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3173]) ).
thf(3390,plain,
! [SV207: $i,SV500: $i > $o] :
( ( ( ~ ( in @ ( sK40_SY3540 @ SV500 @ SV207 ) @ SV207 )
| ~ ( SV500 @ ( sK40_SY3540 @ SV500 @ SV207 ) ) )
= $false )
| ( ( ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SV207 )
| ~ ( SV500 @ SY3541 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3178]) ).
thf(3391,plain,
! [SV952: $o,SV818: $i,SV501: $i,SV208: $i,SV982: $i] :
( ( ( ~ ( in @ SV982 @ SV208 )
| ~ ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
| ~ ( ~ ( in @ SV982 @ SV501 )
| SV952 )
| ~ ( ~ ( in @ SV982 @ SV818 )
| SV952 )
| SV952 )
= $true )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3179]) ).
thf(3392,plain,
! [SV818: $i,SV501: $i,SV208: $i,SV983: $i] :
( ( ( ~ ( in @ SV983 @ SV208 )
| ~ ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
| ~ ( ~ ( in @ SV983 @ SV501 )
| $true )
| ~ ( ~ ( in @ SV983 @ SV818 )
| $true )
| $true )
= $true )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3180]) ).
thf(3393,plain,
! [SV818: $i,SV501: $i,SV208: $i,SV984: $i] :
( ( ( ~ ( in @ SV984 @ SV208 )
| ~ ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
| ~ ( ~ ( in @ SV984 @ SV501 )
| $false )
| ~ ( ~ ( in @ SV984 @ SV818 )
| $false )
| $false )
= $true )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3181]) ).
thf(3394,plain,
! [SV209: $i,SV502: $i,SV689: $i,SV889: $i > $o] :
( ( ( ~ ( in @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ SV209 )
| ! [SY4144: $i] :
( ~ ( in @ SY4144 @ SV502 )
| ~ ( in @ ( kpair @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ SY4144 ) @ SV689 )
| ( SV889 @ ( kpair @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ SY4144 ) ) ) )
= $false )
| ( ( ! [SY4074: $i] :
( ~ ( in @ SY4074 @ SV689 )
| ( SV889 @ SY4074 ) ) )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3182]) ).
thf(3395,plain,
! [SV890: $i,SV210: $i,SV690: $i,SV503: $o] :
( ( ( ~ SV503 ) = $true )
| ( ( in @ SV690
@ ( dsetconstr @ SV210
@ ^ [SY4075: $i] :
( ~ ( ~ SV503
| ( SY4075 != SV690 ) )
| ~ ( ~ ~ SV503
| ( SY4075 != SV890 ) ) ) ) )
= $true )
| ( ( in @ SV890 @ SV210 )
= $false )
| ( ( in @ SV690 @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3183]) ).
thf(3396,plain,
! [SV891: $i,SV210: $i,SV691: $i] :
( ( ( ~ $true ) = $true )
| ( ( in @ SV691
@ ( dsetconstr @ SV210
@ ^ [SY4076: $i] :
( ~ ( ~ $true
| ( SY4076 != SV691 ) )
| ~ ( ~ ~ $true
| ( SY4076 != SV891 ) ) ) ) )
= $true )
| ( ( in @ SV891 @ SV210 )
= $false )
| ( ( in @ SV691 @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3184]) ).
thf(3397,plain,
! [SV892: $i,SV210: $i,SV692: $i] :
( ( ( ~ $false ) = $true )
| ( ( in @ SV692
@ ( dsetconstr @ SV210
@ ^ [SY4077: $i] :
( ~ ( ~ $false
| ( SY4077 != SV692 ) )
| ~ ( ~ ~ $false
| ( SY4077 != SV892 ) ) ) ) )
= $true )
| ( ( in @ SV892 @ SV210 )
= $false )
| ( ( in @ SV692 @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3185]) ).
thf(3398,plain,
! [SV504: $i,SV212: $i,SV693: $i] :
( ( ( in @ SV693 @ SV212 )
= $false )
| ( ( in @ SV693 @ SV504 )
= $true )
| ( ( subset @ SV212 @ SV504 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3186]) ).
thf(3399,plain,
! [SV819: $i,SV508: $i,SV216: $i,SV953: $i] :
( ( ( ~ ( in @ SV953 @ SV216 ) )
= $true )
| ( ( ! [SY4112: $i] :
( ~ ( in @ SY4112 @ SV216 )
| ~ ( in @ ( kpair @ SV953 @ SY4112 ) @ ( binunion @ SV508 @ SV819 ) )
| ! [SY4113: $o] :
( ~ ( ~ ( in @ ( kpair @ SV953 @ SY4112 ) @ SV508 )
| SY4113 )
| ~ ( ~ ( in @ ( kpair @ SV953 @ SY4112 ) @ SV819 )
| SY4113 )
| SY4113 ) ) )
= $true )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3187]) ).
thf(3400,plain,
! [SV820: $i,SV509: $i,SV217: $i,SV954: $i] :
( ( ( ~ ( in @ SV954 @ SV217 ) )
= $true )
| ( ( ~ ( in @ SV954 @ ( setminus @ SV217 @ ( binunion @ SV509 @ SV820 ) ) )
| ( in @ SV954 @ ( binintersect @ ( setminus @ SV217 @ SV509 ) @ ( setminus @ SV217 @ SV820 ) ) ) )
= $true )
| ( ( in @ SV820 @ ( powerset @ SV217 ) )
= $false )
| ( ( in @ SV509 @ ( powerset @ SV217 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3188]) ).
thf(3401,plain,
! [SV218: $i,SV696: $i,SV510: $i > $i] :
( ( ( ~ ( in @ ( sK41_SY3843 @ SV510 @ SV696 @ SV218 ) @ SV218 )
| ( SV696
!= ( SV510 @ ( sK41_SY3843 @ SV510 @ SV696 @ SV218 ) ) ) )
= $false )
| ( ( in @ SV696
@ ( image1 @ SV218
@ ^ [SY3564: $i] : ( SV510 @ SY3564 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3189]) ).
thf(3402,plain,
! [SV224: $i,SV821: $i,SV515: $i] :
( ( ( subset @ SV515 @ SV821 )
= $false )
| ( ( subset @ ( setminus @ SV224 @ SV821 ) @ ( setminus @ SV224 @ SV515 ) )
= $true )
| ( ( in @ SV821 @ ( powerset @ SV224 ) )
= $false )
| ( ( in @ SV515 @ ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3193]) ).
thf(3403,plain,
! [SV226: $i] :
( ( ~ ~ ( ~ ! [SY3851: $i] :
( ~ ( in @ SY3851 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY2945: $i] :
( ~ ( in @ SY2945 @ SY3851 )
| ( in @ SY2945 @ SV226 ) ) )
| ~ ! [SY3853: $i,SY3854: $i] :
( ~ ~ ( ~ ( in @ SY3853 @ SV226 )
| ~ ( in @ SY3854 @ SV226 ) )
| ~ ! [SY3855: $i] :
( ~ ( in @ SY3855 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SY3853 @ SY3855 )
| ( in @ SY3854 @ SY3855 ) )
| ~ ( ~ ( in @ SY3854 @ SY3855 )
| ( in @ SY3853 @ SY3855 ) ) ) )
| ( SY3853 = SY3854 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3194]) ).
thf(3404,plain,
! [SV226: $i] :
( ( ~ ! [SY3856: $i,SY3857: $i] :
( ~ ~ ( ~ ( in @ SY3856 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY3857 @ ( sK2_SY2943 @ SV226 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3856 )
| ( in @ SX4 @ SY3857 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3857 )
| ( in @ SX4 @ SY3856 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3194]) ).
thf(3405,plain,
! [SV226: $i,SV955: $i] :
( ( ( ~ ~ ( ~ ! [SY4114: $i] :
( ~ ( in @ SY4114 @ SV955 )
| ( in @ SY4114 @ SV226 ) )
| ~ ~ ! [SY4115: $i] :
~ ( in @ SY4115 @ SV955 ) ) )
= $true )
| ( ( ~ ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3195]) ).
thf(3406,plain,
! [SV703: $i > $i > $o,SV227: $i,SV752: $i,SV517: $i,SV920: $i] :
( ( ( in @ SV920 @ SV517 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV752 @ SV920 )
@ ( dpsetconstr @ SV227 @ SV517
@ ^ [SY3870: $i,SY3871: $i] : ( SV703 @ SY3870 @ SY3871 ) ) )
| ( SV703 @ SV752 @ SV920 ) )
= $true )
| ( ( in @ SV752 @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3196]) ).
thf(3407,plain,
! [SV822: $i,SV519: $i,SV229: $i,SV956: $i] :
( ( ( ~ ( in @ SV956 @ SV229 ) )
= $true )
| ( ( ~ ~ ( in @ SV956 @ ( binunion @ SV519 @ SV822 ) )
| ~ ( in @ SV956 @ SV519 ) )
= $true )
| ( ( in @ SV822 @ ( powerset @ SV229 ) )
= $false )
| ( ( in @ SV519 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3197]) ).
thf(3408,plain,
! [SV520: $i,SV230: $i > $i > $o] :
( ( ( ~ ! [SY4145: $i] :
~ ( ~ ( ~ ( in @ SY4145 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY4145 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY4145 ) )
| ( in @ SY4145 @ ( sK56_SY3585 @ SV230 @ SV520 ) ) ) ) )
= $false )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3198]) ).
thf(3409,plain,
! [SV957: $i,SV520: $i,SV230: $i > $i > $o] :
( ( ( ~ ( ~ ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
| ~ ! [SY4121: $i] :
( ~ ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SY4121 )
| ( SV957 = SY4121 ) ) ) )
= $false )
| ( ( ~ ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3199]) ).
thf(3410,plain,
! [SV896: $i,SV705: $i,SV521: $i,SV231: $i] :
( ( ( ~ ! [SY4081: $i] :
( ~ ( in @ SY4081 @ SV231 )
| ( ( ap @ SV231 @ SV521 @ SV705 @ SY4081 )
= ( ap @ SV231 @ SV521 @ SV896 @ SY4081 ) ) ) )
= $true )
| ( ( SV705 = SV896 )
= $true )
| ( ( func @ SV231 @ SV521 @ SV896 )
= $false )
| ( ( func @ SV231 @ SV521 @ SV705 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3200]) ).
thf(3411,plain,
! [SV897: $i,SV706: $i,SV232: $i,SV522: $o] :
( ( ( ~ SV522 ) = $true )
| ( ( ( if @ SV232 @ SV522 @ SV706 @ SV897 )
= SV706 )
= $true )
| ( ( in @ SV897 @ SV232 )
= $false )
| ( ( in @ SV706 @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3201]) ).
thf(3412,plain,
! [SV898: $i,SV707: $i,SV232: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( if @ SV232 @ $true @ SV707 @ SV898 )
= SV707 )
= $true )
| ( ( in @ SV898 @ SV232 )
= $false )
| ( ( in @ SV707 @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3202]) ).
thf(3413,plain,
! [SV899: $i,SV708: $i,SV232: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( if @ SV232 @ $false @ SV708 @ SV899 )
= SV708 )
= $true )
| ( ( in @ SV899 @ SV232 )
= $false )
| ( ( in @ SV708 @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3203]) ).
thf(3414,plain,
! [SV233: $i,SV523: $i,SV823: $i > $o] :
( ( ( ~ ( in @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ SV233 ) )
= $false )
| ( ( ! [SY4016: $i] :
( ~ ( in @ SY4016 @ SV523 )
| ( SV823 @ SY4016 ) ) )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3204]) ).
thf(3415,plain,
! [SV523: $i,SV823: $i > $o,SV233: $i] :
( ( ( ! [SY4122: $i] :
( ~ ( in @ SY4122 @ SV233 )
| ~ ( in @ ( kpair @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ SY4122 ) @ SV523 )
| ( SV823 @ ( kpair @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ SY4122 ) ) ) )
= $false )
| ( ( ! [SY4016: $i] :
( ~ ( in @ SY4016 @ SV523 )
| ( SV823 @ SY4016 ) ) )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3204]) ).
thf(3416,plain,
! [SV235: $i,SV525: $i] :
( ( ( ~ ( in @ ( sK34_SY3599 @ SV525 @ SV235 ) @ SV235 ) )
= $false )
| ( ( in @ SV525 @ ( setunion @ SV235 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3205]) ).
thf(3417,plain,
! [SV235: $i,SV525: $i] :
( ( ( ~ ( in @ SV525 @ ( sK34_SY3599 @ SV525 @ SV235 ) ) )
= $false )
| ( ( in @ SV525 @ ( setunion @ SV235 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3205]) ).
thf(3418,plain,
! [SV825: $i,SV531: $i,SV243: $i,SV958: $i] :
( ( ( ~ ( in @ SV958 @ ( powerset @ SV243 ) ) )
= $true )
| ( ( in @ ( binintersect @ SV531 @ SV825 ) @ ( powerset @ ( binintersect @ ( binunion @ SV531 @ SV958 ) @ ( binunion @ SV825 @ SV958 ) ) ) )
= $true )
| ( ( in @ SV825 @ ( powerset @ SV243 ) )
= $false )
| ( ( in @ SV531 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3207]) ).
thf(3419,plain,
! [SV532: $i,SV244: $i,SV826: $i] :
( ( ( in @ SV826 @ ( setminus @ SV244 @ ( setminus @ SV244 @ SV532 ) ) )
= $false )
| ( ( in @ SV826 @ SV532 )
= $true )
| ( ( in @ SV826 @ SV244 )
= $false )
| ( ( in @ SV532 @ ( powerset @ SV244 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3208]) ).
thf(3420,plain,
! [SV533: $i > $o,SV245: $i,SV901: $i] :
( ( ( ~ ( in @ SV901 @ SV245 ) )
= $true )
| ( ( ~ ( SV533 @ SV901 ) )
= $true )
| ( ( ( ( dsetconstr @ SV245
@ ^ [SY3609: $i] : ( SV533 @ SY3609 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3209]) ).
thf(3421,plain,
! [SV535: $i,SV827: $i,SV247: $i,SV959: $i] :
( ( ( ~ ( in @ SV959 @ SV247 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV959 @ SV827 ) @ ( breln1invset @ SV247 @ SV535 ) )
| ( in @ ( kpair @ SV827 @ SV959 ) @ SV535 ) )
= $true )
| ( ( in @ SV827 @ SV247 )
= $false )
| ( ( breln1 @ SV247 @ SV535 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3211]) ).
thf(3422,plain,
! [SV249: $i,SV921: $i] :
( ( ( in @ SV921 @ SV249 )
= $false )
| ( ( subset @ SV921 @ SV249 )
= $true )
| ( ( in @ ( sK7_SY3023 @ SV249 ) @ SV249 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3212]) ).
thf(3423,plain,
! [SV828: $i,SV538: $i,SV251: $i,SV960: $i] :
( ( ( ~ ( in @ SV960 @ SV251 ) )
= $true )
| ( ( ~ ~ ( in @ SV960 @ SV538 )
| ~ ~ ( in @ SV960 @ SV828 )
| ~ ( in @ SV960 @ ( binunion @ SV538 @ SV828 ) ) )
= $true )
| ( ( in @ SV828 @ ( powerset @ SV251 ) )
= $false )
| ( ( in @ SV538 @ ( powerset @ SV251 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3214]) ).
thf(3424,plain,
! [SV904: $i,SV714: $i,SV252: $i,SV539: $o] :
( ( ( ~ SV539 ) = $true )
| ( ( ( dsetconstr @ SV252
@ ^ [SY4083: $i] :
( ~ ( ~ SV539
| ( SY4083 != SV714 ) )
| ~ ( ~ ~ SV539
| ( SY4083 != SV904 ) ) ) )
= ( setadjoin @ SV714 @ emptyset ) )
= $true )
| ( ( in @ SV904 @ SV252 )
= $false )
| ( ( in @ SV714 @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3215]) ).
thf(3425,plain,
! [SV905: $i,SV715: $i,SV252: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( dsetconstr @ SV252
@ ^ [SY4084: $i] :
( ~ ( ~ $true
| ( SY4084 != SV715 ) )
| ~ ( ~ ~ $true
| ( SY4084 != SV905 ) ) ) )
= ( setadjoin @ SV715 @ emptyset ) )
= $true )
| ( ( in @ SV905 @ SV252 )
= $false )
| ( ( in @ SV715 @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3216]) ).
thf(3426,plain,
! [SV906: $i,SV716: $i,SV252: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( dsetconstr @ SV252
@ ^ [SY4085: $i] :
( ~ ( ~ $false
| ( SY4085 != SV716 ) )
| ~ ( ~ ~ $false
| ( SY4085 != SV906 ) ) ) )
= ( setadjoin @ SV716 @ emptyset ) )
= $true )
| ( ( in @ SV906 @ SV252 )
= $false )
| ( ( in @ SV716 @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3217]) ).
thf(3427,plain,
! [SV259: $i,SV719: $i,SV908: $i,SV548: $i,SV985: $i] :
( ( ( ~ ( in @ SV985 @ SV548 )
| ~ ( in @ ( kpair @ SV908 @ SV985 ) @ SV719 )
| ( ( ap @ SV259 @ SV548 @ SV719 @ SV908 )
= SV985 ) )
= $true )
| ( ( in @ SV908 @ SV259 )
= $false )
| ( ( func @ SV259 @ SV548 @ SV719 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3220]) ).
thf(3428,plain,
! [SV829: $i,SV549: $i,SV260: $i] :
( ( ( ! [SY4020: $i] :
( ~ ( in @ SY4020 @ SV260 )
| ! [SY4021: $i] :
( ~ ( in @ SY4021 @ SV260 )
| ~ ( in @ ( kpair @ SY4020 @ SY4021 ) @ SV549 )
| ( in @ ( kpair @ SY4020 @ SY4021 ) @ SV829 ) ) ) )
= $false )
| ( ( ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) )
| ( SV549 = SV829 ) )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3221]) ).
thf(3429,plain,
! [SV830: $i,SV553: $i,SV264: $i,SV961: $i] :
( ( ( ~ ( in @ SV961 @ SV264 ) )
= $true )
| ( ( ! [SY4123: $i] :
( ~ ( in @ SY4123 @ SV264 )
| ~ ( ( in @ ( kpair @ SV961 @ SY4123 ) @ SV553 )
| ( in @ ( kpair @ SV961 @ SY4123 ) @ SV830 ) )
| ( in @ ( kpair @ SV961 @ SY4123 ) @ ( binunion @ SV553 @ SV830 ) ) ) )
= $true )
| ( ( breln1 @ SV264 @ SV830 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3222]) ).
thf(3430,plain,
! [SV271: $i,SV559: $i,SV833: $i > $o] :
( ( ( ~ ( in @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ SV271 ) )
= $false )
| ( ( ! [SY4028: $i] :
( ~ ( in @ SY4028 @ SV559 )
| ( SV833 @ SY4028 ) ) )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3224]) ).
thf(3431,plain,
! [SV559: $i,SV833: $i > $o,SV271: $i] :
( ( ( ! [SY4124: $i] :
( ~ ( in @ SY4124 @ SV271 )
| ~ ( in @ ( kpair @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ SY4124 ) @ SV559 )
| ( SV833 @ ( kpair @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ SY4124 ) ) ) )
= $false )
| ( ( ! [SY4028: $i] :
( ~ ( in @ SY4028 @ SV559 )
| ( SV833 @ SY4028 ) ) )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3224]) ).
thf(3432,plain,
! [SV562: $i,SV834: $i,SV274: $i] :
( ( ( subset @ ( setminus @ SV274 @ SV834 ) @ ( setminus @ SV274 @ SV562 ) )
= $false )
| ( ( subset @ SV562 @ SV834 )
= $true )
| ( ( in @ SV834 @ ( powerset @ SV274 ) )
= $false )
| ( ( in @ SV562 @ ( powerset @ SV274 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3227]) ).
thf(3433,plain,
! [SV563: $i > $o,SV275: $i] :
( ( ( ! [SY3654: $i] :
~ ~ ( ~ ( in @ SY3654 @ SV275 )
| ~ ( SV563 @ SY3654 ) ) )
= $true )
| ( ( in @ ( sK16_SY3653 @ SV563 @ SV275 ) @ SV275 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3228]) ).
thf(3434,plain,
! [SV563: $i > $o,SV275: $i] :
( ( ( ! [SY3654: $i] :
~ ~ ( ~ ( in @ SY3654 @ SV275 )
| ~ ( SV563 @ SY3654 ) ) )
= $true )
| ( ( SV563 @ ( sK16_SY3653 @ SV563 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3229]) ).
thf(3435,plain,
! [SV835: $i,SV565: $i,SV277: $i,SV962: $i] :
( ( ( ~ ( in @ SV962 @ SV277 ) )
= $true )
| ( ( ~ ( in @ SV962 @ ( setminus @ SV277 @ ( binunion @ SV565 @ SV835 ) ) )
| ( in @ SV962 @ ( setminus @ SV277 @ SV565 ) ) )
= $true )
| ( ( in @ SV835 @ ( powerset @ SV277 ) )
= $false )
| ( ( in @ SV565 @ ( powerset @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3230]) ).
thf(3436,plain,
! [SV278: $i,SV566: $i] :
( ( ( ! [SY3658: $i] :
( ~ ( in @ SY3658 @ SV566 )
| ( in @ SY3658 @ SV278 ) ) )
= $false )
| ( ( SV278 = SV566 )
= $true )
| ( ( in @ ( sK17_SY3657 @ SV566 @ SV278 ) @ SV278 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3231]) ).
thf(3437,plain,
! [SV566: $i,SV278: $i] :
( ( ( ~ ( in @ ( sK57_SY3658 @ SV278 @ SV566 ) @ SV566 )
| ( in @ ( sK57_SY3658 @ SV278 @ SV566 ) @ SV278 ) )
= $false )
| ( ( SV278 = SV566 )
= $true )
| ( ( in @ ( sK17_SY3657 @ SV566 @ SV278 ) @ SV566 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3232]) ).
thf(3438,plain,
! [SV836: $i,SV568: $i,SV280: $i,SV963: $i] :
( ( ( ~ ( in @ SV963 @ SV280 ) )
= $true )
| ( ( ! [SY4125: $i] :
( ~ ( in @ SY4125 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SY4125 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
| ! [SY4126: $o] :
( ~ ! [SY4127: $i] :
( ~ ( in @ SY4127 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SY4127 ) @ SV568 )
| ~ ( in @ ( kpair @ SY4127 @ SY4125 ) @ SV836 )
| SY4126 )
| SY4126 ) ) )
= $true )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3233]) ).
thf(3439,plain,
! [SV284: $i,SV572: $i] :
( ( ( ~ ( in @ ( sK42_SY3668 @ SV572 @ SV284 ) @ SV284 )
| ~ ( in @ ( sK42_SY3668 @ SV572 @ SV284 ) @ SV572 ) )
= $false )
| ( ( ( binintersect @ SV284 @ SV572 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3235]) ).
thf(3440,plain,
! [SV837: $i,SV288: $i > $o] :
( ( ( SV288 @ SV837 )
= $false )
| ( ( ~ ! [SY4034: $i] :
( ~ ( SV288 @ SY4034 )
| ( SV837 = SY4034 ) ) )
= $true )
| ( ( ! [SY3119: $i,SY3120: $i] :
( ~ ( SV288 @ SY3119 )
| ~ ( SV288 @ SY3120 )
| ( SY3119 = SY3120 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3236]) ).
thf(3441,plain,
! [SV289: $i,SV575: $i > $o] :
( ( ( ~ ( in @ ( sK43_SY3670 @ SV575 @ SV289 ) @ SV289 )
| ~ ( SV575 @ ( sK43_SY3670 @ SV575 @ SV289 ) ) )
= $false )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV289 )
| ~ ( SV575 @ SY3671 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3237]) ).
thf(3442,plain,
! [SV293: $i,SV755: $i,SV732: $i > $i > $o,SV579: $i,SV922: $i] :
( ( ( in @ SV922 @ SV579 )
= $false )
| ( ( ~ ( SV732 @ SV755 @ SV922 )
| ( in @ ( kpair @ SV755 @ SV922 )
@ ( dpsetconstr @ SV293 @ SV579
@ ^ [SY3897: $i,SY3898: $i] : ( SV732 @ SY3897 @ SY3898 ) ) ) )
= $true )
| ( ( in @ SV755 @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3238]) ).
thf(3443,plain,
! [SV757: $o,SV583: $i,SV298: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV298 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| SV757 )
| SV757 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3239]) ).
thf(3444,plain,
! [SV298: $i,SV583: $i,SV733: $i,SV757: $o] :
( ( SV757 = $false )
| ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| SV757 )
| SV757 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3239]) ).
thf(3445,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV298 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| $true )
| $true )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3240]) ).
thf(3446,plain,
! [SV298: $i,SV583: $i,SV733: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| $true )
| $true )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3240]) ).
thf(3447,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV298 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| $false )
| $false )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3241]) ).
thf(3448,plain,
! [SV298: $i,SV583: $i,SV733: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| $false )
| $false )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3241]) ).
thf(3449,plain,
! [SV840: $i,SV584: $i,SV299: $i] :
( ( ( ! [SY4035: $i] :
( ~ ( in @ SY4035 @ SV299 )
| ~ ( in @ SY4035 @ SV584 )
| ( in @ SY4035 @ SV840 ) ) )
= $false )
| ( ( ~ ! [SY4036: $i] :
( ~ ( in @ SY4036 @ SV299 )
| ~ ( in @ SY4036 @ SV840 )
| ( in @ SY4036 @ SV584 ) )
| ( SV584 = SV840 ) )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3242]) ).
thf(3450,plain,
! [SV841: $i,SV585: $i,SV300: $i,SV964: $i] :
( ( ( ~ ( in @ SV964 @ SV300 ) )
= $true )
| ( ( ! [SY4128: $i] :
( ~ ( in @ SY4128 @ SV300 )
| ~ ( in @ ( kpair @ SV964 @ SY4128 ) @ SV585 )
| ( in @ ( kpair @ SV964 @ SY4128 ) @ ( binunion @ SV585 @ SV841 ) ) ) )
= $true )
| ( ( breln1 @ SV300 @ SV841 )
= $false )
| ( ( breln1 @ SV300 @ SV585 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3243]) ).
thf(3451,plain,
! [SV911: $i,SV734: $i,SV586: $i,SV301: $i] :
( ( ( ~ ! [SY4087: $i] :
( ~ ( in @ SY4087 @ SV301 )
| ( ( ap @ SV301 @ SV586 @ SV734 @ SY4087 )
= ( ap @ SV301 @ SV586 @ SV911 @ SY4087 ) ) ) )
= $true )
| ( ( ! [SY4088: $i] :
( ~ ( in @ SY4088 @ SV301 )
| ! [SY4089: $i] :
( ~ ( in @ SY4089 @ SV586 )
| ~ ( in @ ( kpair @ SY4088 @ SY4089 ) @ SV911 )
| ( in @ ( kpair @ SY4088 @ SY4089 ) @ SV734 ) ) ) )
= $true )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3244]) ).
thf(3452,plain,
! [SV842: $i,SV587: $i,SV302: $i,SV965: $i] :
( ( ( ~ ( in @ SV965 @ SV302 ) )
= $true )
| ( ( ~ ( in @ SV965 @ ( binunion @ ( setminus @ SV302 @ SV587 ) @ ( setminus @ SV302 @ SV842 ) ) )
| ( in @ SV965 @ ( setminus @ SV302 @ ( binintersect @ SV587 @ SV842 ) ) ) )
= $true )
| ( ( in @ SV842 @ ( powerset @ SV302 ) )
= $false )
| ( ( in @ SV587 @ ( powerset @ SV302 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3245]) ).
thf(3453,plain,
! [SV843: $i,SV589: $i,SV305: $i,SV966: $i] :
( ( ( ~ ( in @ SV966 @ ( powerset @ SV305 ) ) )
= $true )
| ( ( in @ ( binintersect @ SV589 @ SV843 ) @ ( powerset @ ( binintersect @ ( binunion @ SV589 @ SV966 ) @ ( binunion @ SV843 @ SV966 ) ) ) )
= $true )
| ( ( in @ SV843 @ ( powerset @ SV305 ) )
= $false )
| ( ( in @ SV589 @ ( powerset @ SV305 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3246]) ).
thf(3454,plain,
! [SV844: $i,SV590: $i,SV307: $i,SV967: $i] :
( ( ( ~ ( in @ SV967 @ SV307 ) )
= $true )
| ( ( ~ ( in @ SV967 @ ( binintersect @ ( setminus @ SV307 @ SV590 ) @ ( setminus @ SV307 @ SV844 ) ) )
| ( in @ SV967 @ ( setminus @ SV307 @ ( binunion @ SV590 @ SV844 ) ) ) )
= $true )
| ( ( in @ SV844 @ ( powerset @ SV307 ) )
= $false )
| ( ( in @ SV590 @ ( powerset @ SV307 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3247]) ).
thf(3455,plain,
! [SV845: $i,SV591: $i,SV308: $i] :
( ( ( ! [SY4042: $i] :
( ~ ( in @ SY4042 @ SV308 )
| ~ ( in @ SY4042 @ SV591 )
| ( in @ SY4042 @ SV845 ) ) )
= $false )
| ( ( in @ SV591 @ ( powerset @ SV845 ) )
= $true )
| ( ( in @ SV845 @ ( powerset @ SV308 ) )
= $false )
| ( ( in @ SV591 @ ( powerset @ SV308 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3248]) ).
thf(3456,plain,
! [SV846: $i,SV592: $i,SV309: $i,SV968: $i] :
( ( ( ~ ( in @ SV968 @ SV309 ) )
= $true )
| ( ( ~ ( in @ SV968 @ ( setminus @ SV309 @ SV592 ) )
| ~ ( in @ SV968 @ ( setminus @ SV309 @ SV846 ) )
| ( in @ SV968 @ ( setminus @ SV309 @ ( binunion @ SV592 @ SV846 ) ) ) )
= $true )
| ( ( in @ SV846 @ ( powerset @ SV309 ) )
= $false )
| ( ( in @ SV592 @ ( powerset @ SV309 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3249]) ).
thf(3457,plain,
! [SV847: $i,SV598: $i,SV315: $i,SV969: $i] :
( ( ( ~ ( in @ SV969 @ SV315 ) )
= $true )
| ( ( ~ ( in @ SV969 @ ( setminus @ SV315 @ ( binunion @ SV598 @ SV847 ) ) )
| ~ ( in @ SV969 @ SV598 ) )
= $true )
| ( ( in @ SV847 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV598 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3252]) ).
thf(3458,plain,
! [SV848: $i,SV316: $i > $o] :
( ( ( SV316 @ SV848 )
= $false )
| ( ( ~ ! [SY4045: $i] :
( ~ ( SV316 @ SY4045 )
| ( SV848 = SY4045 ) ) )
= $true )
| ( ( ~ ! [SY3190: $i] :
~ ! [SY3191: $i] :
~ ( ~ ( ~ ( SV316 @ SY3191 )
| ( SY3191 = SY3190 ) )
| ~ ( ( SY3191 != SY3190 )
| ( SV316 @ SY3191 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3253]) ).
thf(3459,plain,
! [SV849: $i,SV599: $i,SV317: $i,SV970: $i] :
( ( ( ~ ( in @ SV970 @ ( powerset @ SV317 ) ) )
= $true )
| ( ( ! [SY4129: $i] :
( ~ ( in @ SY4129 @ ( powerset @ SV317 ) )
| ~ ( subset @ SV599 @ SV970 )
| ~ ( subset @ SV849 @ SY4129 )
| ( subset @ ( binintersect @ SV599 @ SV849 ) @ ( binintersect @ SV970 @ SY4129 ) ) ) )
= $true )
| ( ( in @ SV849 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3254]) ).
thf(3460,plain,
! [SV600: $i,SV850: $i,SV318: $i,SV971: $i] :
( ( ( ~ ( in @ SV971 @ SV318 ) )
= $true )
| ( ( ~ ~ ( in @ SV971 @ SV850 )
| ~ ( in @ SV971 @ ( binintersect @ SV600 @ SV850 ) ) )
= $true )
| ( ( in @ SV850 @ ( powerset @ SV318 ) )
= $false )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3255]) ).
thf(3461,plain,
! [SV319: $i,SV601: $i,SV738: $i,SV914: $i > $o] :
( ( ( ~ ( in @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ SV319 )
| ! [SY4148: $i] :
( ~ ( in @ SY4148 @ SV601 )
| ~ ( in @ ( kpair @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ SY4148 ) @ SV738 )
| ( SV914 @ ( kpair @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ SY4148 ) ) ) )
= $false )
| ( ( ! [SY4092: $i] :
( ~ ( in @ SY4092 @ SV738 )
| ( SV914 @ SY4092 ) ) )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3256]) ).
thf(3462,plain,
! [SV915: $i,SV739: $i,SV321: $i,SV603: $o] :
( ( ( ~ ~ SV603 )
= $true )
| ( ( ( if @ SV321 @ SV603 @ SV739 @ SV915 )
= SV915 )
= $true )
| ( ( in @ SV915 @ SV321 )
= $false )
| ( ( in @ SV739 @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3257]) ).
thf(3463,plain,
! [SV916: $i,SV740: $i,SV321: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( ( if @ SV321 @ $true @ SV740 @ SV916 )
= SV916 )
= $true )
| ( ( in @ SV916 @ SV321 )
= $false )
| ( ( in @ SV740 @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3258]) ).
thf(3464,plain,
! [SV917: $i,SV741: $i,SV321: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( ( if @ SV321 @ $false @ SV741 @ SV917 )
= SV917 )
= $true )
| ( ( in @ SV917 @ SV321 )
= $false )
| ( ( in @ SV741 @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3259]) ).
thf(3465,plain,
! [SV322: $i,SV851: $i] :
( ( ( ~ ( ~ ( in @ ( sK51_SY3211 @ SV851 @ SV322 ) @ SV322 )
| ~ ~ ~ ! [SY4130: $i] :
~ ~ ( ~ ( in @ SY4130 @ ( sK51_SY3211 @ SV851 @ SV322 ) )
| ~ ( in @ SY4130 @ SV322 ) ) ) )
= $true )
| ( ( in @ SV851 @ SV322 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3260]) ).
thf(3466,plain,
! [SV852: $i,SV606: $i,SV325: $i,SV972: $i] :
( ( ( ~ ( in @ SV972 @ ( powerset @ SV325 ) ) )
= $true )
| ( ( ~ ( subset @ SV606 @ SV852 )
| ~ ( subset @ SV606 @ SV972 )
| ( subset @ SV606 @ ( binintersect @ SV852 @ SV972 ) ) )
= $true )
| ( ( in @ SV852 @ ( powerset @ SV325 ) )
= $false )
| ( ( in @ SV606 @ ( powerset @ SV325 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3261]) ).
thf(3467,plain,
! [SV37: $i] :
( ( ( in @ ( sK20_SY2402 @ SV37 ) @ SV37 )
= $true )
| ( ( SV37 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3262]) ).
thf(3468,plain,
! [SV37: $i] :
( ( $true = $true )
| ( ( SV37 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3263]) ).
thf(3469,plain,
! [SV759: $i,SV40: $i > $o] :
( ( ( ! [SY3941: $i] :
( ~ ( SV40 @ SY3941 )
| ( SV759 = SY3941 ) ) )
= $false )
| ( ( SV40 @ SV759 )
= $false )
| ( ( ~ ! [SY2411: $i] :
~ ( SV40 @ SY2411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3264]) ).
thf(3470,plain,
! [SV760: $i,SV42: $i > $o] :
( ( ( ! [SY3942: $i] :
( ~ ( SV42 @ SY3942 )
| ( SV760 = SY3942 ) ) )
= $false )
| ( ( SV42 @ SV760 )
= $false )
| ( ( SV42
@ ( descr
@ ^ [SY2417: $i] : ( SV42 @ SY2417 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3265]) ).
thf(3471,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ( ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( in @ ( sK9_SY3238 @ SV353 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3266]) ).
thf(3472,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( in @ ( sK36_SY3943 @ SV353 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3267]) ).
thf(3473,plain,
! [SV44: $i,SV353: $i > $o] :
( ( ( SV353 @ ( sK9_SY3238 @ SV353 @ SV44 ) )
= $true )
| ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) )
| ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3268]) ).
thf(3474,plain,
! [SV44: $i,SV353: $i > $o] :
( ( ( ~ ( SV353 @ ( sK36_SY3943 @ SV353 @ SV44 ) ) )
= $false )
| ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) )
| ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3269]) ).
thf(3475,plain,
! [SV44: $i,SV353: $i > $o] :
( ( ( ( sK9_SY3238 @ SV353 @ SV44 )
= ( sK36_SY3943 @ SV353 @ SV44 ) )
= $false )
| ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) )
| ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3269]) ).
thf(3476,plain,
! [SV854: $i,SV612: $i,SV354: $i,SV45: $i] :
( ( ( ! [SY4050: $i] :
( ~ ( in @ SY4050 @ SV45 )
| ( ( ap @ SV45 @ SV354 @ SV612 @ SY4050 )
= ( ap @ SV45 @ SV354 @ SV854 @ SY4050 ) ) ) )
= $false )
| ( ( SV612 = SV854 )
= $true )
| ( ( in @ SV854 @ ( funcSet @ SV45 @ SV354 ) )
= $false )
| ( ( in @ SV612 @ ( funcSet @ SV45 @ SV354 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3270]) ).
thf(3477,plain,
! [SV762: $i,SV361: $i,SV52: $i,SV923: $i] :
( ( ( in @ SV923 @ ( powerset @ SV52 ) )
= $false )
| ( ( ! [SY4098: $i] :
( ~ ( in @ SY4098 @ SV52 )
| ~ ( in @ SY4098 @ ( binintersect @ SV361 @ SV762 ) )
| ( in @ SY4098 @ ( binunion @ SV762 @ SV923 ) ) ) )
= $true )
| ( ( in @ SV762 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3271]) ).
thf(3478,plain,
! [SV764: $i,SV365: $i,SV56: $i,SV924: $i] :
( ( ( in @ SV924 @ ( powerset @ SV56 ) )
= $false )
| ( ( ! [SY4099: $i] :
( ~ ( in @ SY4099 @ ( powerset @ SV56 ) )
| ( ( setminus @ SV56 @ ( binintersect @ ( binunion @ SV365 @ SV764 ) @ ( binunion @ SV924 @ SY4099 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV56 @ SV365 ) @ ( setminus @ SV56 @ SV764 ) ) @ ( binintersect @ ( setminus @ SV56 @ SV924 ) @ ( setminus @ SV56 @ SY4099 ) ) ) ) ) )
= $true )
| ( ( in @ SV764 @ ( powerset @ SV56 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3273]) ).
thf(3479,plain,
! [SV57: $i,SV366: $i] :
( ( ( ~ ( ~ ( in @ SV366 @ ( sK52_SY3265 @ SV57 @ SV366 ) )
| ~ ( in @ ( sK52_SY3265 @ SV57 @ SV366 ) @ SV57 ) ) )
= $true )
| ( ( in @ SV366 @ ( setunion @ SV57 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3274]) ).
thf(3480,plain,
! [SV57: $i,SV973: $i,SV366: $i] :
( ( ( ~ ( ~ ( in @ SV366 @ SV973 )
| ~ ( in @ SV973 @ SV57 ) ) )
= $false )
| ( ( in @ SV366 @ ( setunion @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3275]) ).
thf(3481,plain,
! [SV765: $i,SV58: $i > $o] :
( ( ( ! [SY3949: $i] :
( ~ ( SV58 @ SY3949 )
| ( SV765 = SY3949 ) ) )
= $false )
| ( ( SV58 @ SV765 )
= $false )
| ( ( ! [SY2464: $i,SY2465: $i] :
( ~ ( SV58 @ SY2464 )
| ~ ( SV58 @ SY2465 )
| ( SY2464 = SY2465 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3276]) ).
thf(3482,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
| ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 ) )
= $false )
| ( ( ~ ( ( ( sK37_SY3950 @ SV766 @ SV59 )
!= SV766 )
| ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) ) ) )
= $true )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3277]) ).
thf(3483,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ! [SY3951: $i] :
( ~ ( SV60 @ SY3951 )
| ( SV767 = SY3951 ) ) )
= $false )
| ( ( SV60 @ SV767 )
= $false )
| ( ( ~ ! [SY2472: $i] :
~ ~ ( ~ ( SV60 @ SY2472 )
| ~ ! [SY2473: $i] :
( ~ ( SV60 @ SY2473 )
| ( SY2472 = SY2473 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3278]) ).
thf(3484,plain,
! [SV61: $i,SV367: $i > $o,SV858: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK59_SY3268 @ SV858 @ SV367 @ SV61 ) @ SV61 )
| ~ ~ ( SV367 @ ( sK59_SY3268 @ SV858 @ SV367 @ SV61 ) ) ) )
= $false )
| ( ( SV367 @ SV858 )
= $true )
| ( ( in @ SV858 @ SV61 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3279]) ).
thf(3485,plain,
! [SV65: $i,SV371: $i] :
( ( ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 )
| ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 ) ) )
= $true )
| ( ( SV65 = SV371 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3280]) ).
thf(3486,plain,
! [SV65: $i,SV371: $i] :
( ( ( ~ ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 )
| ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 ) )
= $false )
| ( ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 )
= $false )
| ( ( SV65 = SV371 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3281]) ).
thf(3487,plain,
! [SV372: $i,SV768: $i,SV68: $i,SV986: $i] :
( ( ( ~ ( in @ SV986 @ SV68 )
| ~ ( in @ SV986 @ SV768 )
| ( in @ SV986 @ ( setminus @ SV68 @ SV372 ) ) )
= $true )
| ( ( subset @ SV372 @ ( setminus @ SV68 @ SV768 ) )
= $false )
| ( ( in @ SV768 @ ( powerset @ SV68 ) )
= $false )
| ( ( in @ SV372 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3282]) ).
thf(3488,plain,
! [SV769: $i,SV373: $i,SV69: $i,SV925: $i] :
( ( ( in @ SV925 @ SV69 )
= $false )
| ( ( ~ ( in @ SV925 @ ( setminus @ SV69 @ ( binintersect @ SV373 @ SV769 ) ) )
| ( in @ SV925 @ ( binunion @ ( setminus @ SV69 @ SV373 ) @ ( setminus @ SV69 @ SV769 ) ) ) )
= $true )
| ( ( in @ SV769 @ ( powerset @ SV69 ) )
= $false )
| ( ( in @ SV373 @ ( powerset @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3283]) ).
thf(3489,plain,
! [SV860: $o,SV376: $i,SV72: $i,SV621: $i] :
( ( ( SV621 = SV72 )
= $true )
| ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| SV860 )
| SV860 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3284]) ).
thf(3490,plain,
! [SV72: $i,SV860: $o,SV376: $i,SV621: $i] :
( ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| SV860 ) )
= $true )
| ( SV860 = $true )
| ( SV860 = $false )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3285]) ).
thf(3491,plain,
! [SV376: $i,SV72: $i,SV621: $i] :
( ( ( SV621 = SV72 )
= $true )
| ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| $true )
| $true )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3286]) ).
thf(3492,plain,
! [SV72: $i,SV376: $i,SV621: $i] :
( ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3287]) ).
thf(3493,plain,
! [SV376: $i,SV72: $i,SV621: $i] :
( ( ( SV621 = SV72 )
= $true )
| ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| $false )
| $false )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3288]) ).
thf(3494,plain,
! [SV72: $i,SV376: $i,SV621: $i] :
( ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3289]) ).
thf(3495,plain,
! [SV772: $i,SV379: $i,SV75: $i,SV926: $i] :
( ( ( in @ SV926 @ SV75 )
= $false )
| ( ( ~ ( in @ SV926 @ ( setminus @ SV75 @ ( binunion @ SV379 @ SV772 ) ) )
| ( in @ SV926 @ ( setminus @ SV75 @ SV772 ) ) )
= $true )
| ( ( in @ SV772 @ ( powerset @ SV75 ) )
= $false )
| ( ( in @ SV379 @ ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3290]) ).
thf(3496,plain,
! [SV76: $i,SV622: $i,SV380: $i > $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK60_SY3750 @ SV380 @ SV622 @ SV76 ) @ SV76 )
| ( SV622
!= ( SV380 @ ( sK60_SY3750 @ SV380 @ SV622 @ SV76 ) ) ) ) )
= $false )
| ( ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3287: $i] : ( SV380 @ SY3287 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3291]) ).
thf(3497,plain,
! [SV380: $i > $i,SV622: $i,SV76: $i,SV987: $i] :
( ( ( ~ ~ ( ~ ( in @ SV987 @ SV76 )
| ( SV622
!= ( SV380 @ SV987 ) ) ) )
= $true )
| ( ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3290: $i] : ( SV380 @ SY3290 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3292]) ).
thf(3498,plain,
! [SV381: $i > $i,SV623: $i,SV77: $i,SV918: $i] :
( ( ( ~ ( in @ SV918 @ SV77 ) )
= $true )
| ( ( SV623
!= ( SV381 @ SV918 ) )
= $true )
| ( ( in @ SV623
@ ( image1 @ SV77
@ ^ [SY3293: $i] : ( SV381 @ SY3293 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3293]) ).
thf(3499,plain,
! [SV773: $i,SV382: $i,SV78: $i,SV927: $i] :
( ( ( in @ SV927 @ SV78 )
= $false )
| ( ( ! [SY4100: $i] :
( ~ ( in @ SY4100 @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ SY4100 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
| ~ ! [SY4101: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY4101 @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ SY4101 ) @ SV382 ) )
| ~ ( in @ ( kpair @ SY4101 @ SY4100 ) @ SV773 ) ) ) )
= $true )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3294]) ).
thf(3500,plain,
! [SV774: $i,SV386: $i,SV82: $i,SV928: $i] :
( ( ( in @ SV928 @ SV82 )
= $false )
| ( ( ! [SY4102: $i] :
( ~ ( in @ SY4102 @ SV82 )
| ~ ( in @ ( kpair @ SV928 @ SY4102 ) @ ( binunion @ SV386 @ SV774 ) )
| ( in @ ( kpair @ SV928 @ SY4102 ) @ SV386 )
| ( in @ ( kpair @ SV928 @ SY4102 ) @ SV774 ) ) )
= $true )
| ( ( breln1 @ SV82 @ SV774 )
= $false )
| ( ( breln1 @ SV82 @ SV386 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3298]) ).
thf(3501,plain,
! [SV776: $i,SV389: $i,SV86: $i,SV929: $i] :
( ( ( in @ SV929 @ SV86 )
= $false )
| ( ( ~ ( subset @ SV389 @ ( setminus @ SV86 @ SV776 ) )
| ~ ( in @ SV929 @ SV776 )
| ~ ( in @ SV929 @ SV389 ) )
= $true )
| ( ( in @ SV776 @ ( powerset @ SV86 ) )
= $false )
| ( ( in @ SV389 @ ( powerset @ SV86 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3299]) ).
thf(3502,plain,
! [SV777: $i,SV390: $i,SV87: $i,SV930: $i] :
( ( ( in @ SV930 @ SV87 )
= $false )
| ( ( ~ ( subset @ SV390 @ SV777 )
| ~ ~ ( in @ SV930 @ SV777 )
| ~ ( in @ SV930 @ SV390 ) )
= $true )
| ( ( in @ SV777 @ ( powerset @ SV87 ) )
= $false )
| ( ( in @ SV390 @ ( powerset @ SV87 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3300]) ).
thf(3503,plain,
! [SV779: $i,SV393: $i,SV90: $i,SV931: $i] :
( ( ( in @ SV931 @ ( powerset @ SV90 ) )
= $false )
| ( ( ! [SY4103: $i] :
( ~ ( in @ SY4103 @ SV90 )
| ~ ( in @ SY4103 @ ( binintersect @ SV393 @ SV779 ) )
| ( in @ SY4103 @ ( binintersect @ ( binunion @ SV393 @ SV931 ) @ ( binunion @ SV779 @ SV931 ) ) ) ) )
= $true )
| ( ( in @ SV779 @ ( powerset @ SV90 ) )
= $false )
| ( ( in @ SV393 @ ( powerset @ SV90 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3301]) ).
thf(3504,plain,
! [SV780: $i,SV400: $i,SV99: $i,SV932: $i] :
( ( ( in @ SV932 @ SV99 )
= $false )
| ( ( ~ ( in @ SV932 @ ( setminus @ SV99 @ ( binunion @ SV400 @ SV780 ) ) )
| ( in @ SV932 @ ( setminus @ SV99 @ SV400 ) ) )
= $true )
| ( ( in @ SV780 @ ( powerset @ SV99 ) )
= $false )
| ( ( in @ SV400 @ ( powerset @ SV99 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3302]) ).
thf(3505,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK53_SY2563 @ SV781 @ SV100 ) )
| ~ ( SV100 @ ( sK61_SY4131 @ SV781 @ SV100 ) )
| ( ( sK53_SY2563 @ SV781 @ SV100 )
= ( sK61_SY4131 @ SV781 @ SV100 ) ) )
= $false )
| ( ( ~ ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3303]) ).
thf(3506,plain,
! [SV402: $i,SV102: $i,SV631: $i] :
( ( ( in @ SV631 @ SV102 )
= $false )
| ( ( in @ SV631 @ SV402 )
= $true )
| ( ( in @ SV631 @ ( setminus @ SV102 @ SV402 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3304]) ).
thf(3507,plain,
! [SV404: $i > $o,SV104: $i,SV862: $i] :
( ( ( in @ SV862 @ SV104 )
= $false )
| ( ( ~ ~ ( SV404 @ SV862 ) )
= $true )
| ( ( ~ ! [SY3324: $i] :
( ~ ( in @ SY3324 @ SV104 )
| ( SV404 @ SY3324 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3305]) ).
thf(3508,plain,
! [SV106: $i] :
( ( ( ~ ( ~ ( in @ ( sK44_SY2577 @ SV106 ) @ omega )
| ~ ( in @ ( sK44_SY2577 @ SV106 ) @ SV106 ) ) )
= $true )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( ! [SY2578: $i] :
( ~ ( in @ SY2578 @ omega )
| ( in @ SY2578 @ SV106 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3306]) ).
thf(3509,plain,
! [SV106: $i,SV988: $i] :
( ( ( ~ ( in @ SV988 @ omega )
| ( in @ SV988 @ SV106 ) )
= $true )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( in @ ( setadjoin @ ( sK44_SY2577 @ SV106 ) @ ( sK44_SY2577 @ SV106 ) ) @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3307]) ).
thf(3510,plain,
! [SV109: $i,SV407: $i,SV782: $i] :
( ( ( ~ ( in @ ( sK62_SY3965 @ SV782 @ SV407 @ SV109 ) @ SV109 )
| ~ ( in @ ( sK62_SY3965 @ SV782 @ SV407 @ SV109 ) @ SV407 )
| ( in @ ( sK62_SY3965 @ SV782 @ SV407 @ SV109 ) @ SV782 ) )
= $false )
| ( ( subset @ SV407 @ SV782 )
= $true )
| ( ( in @ SV782 @ ( powerset @ SV109 ) )
= $false )
| ( ( in @ SV407 @ ( powerset @ SV109 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3308]) ).
thf(3511,plain,
! [SV783: $i,SV408: $i,SV110: $i,SV933: $i] :
( ( ( in @ SV933 @ SV110 )
= $false )
| ( ( ~ ~ ( in @ SV933 @ SV408 )
| ~ ( in @ SV933 @ ( binintersect @ SV408 @ SV783 ) ) )
= $true )
| ( ( in @ SV783 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV408 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3309]) ).
thf(3512,plain,
! [SV784: $i,SV411: $i,SV113: $i,SV934: $i] :
( ( ( in @ SV934 @ SV113 )
= $false )
| ( ( ~ ( in @ SV934 @ ( setminus @ SV113 @ SV411 ) )
| ( in @ SV934 @ ( setminus @ SV113 @ ( binintersect @ SV411 @ SV784 ) ) ) )
= $true )
| ( ( in @ SV784 @ ( powerset @ SV113 ) )
= $false )
| ( ( in @ SV411 @ ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3310]) ).
thf(3513,plain,
! [SV412: $i,SV114: $i,SV785: $i] :
( ( ( in @ SV785 @ ( setminus @ SV114 @ SV412 ) )
= $false )
| ( ( in @ SV785 @ SV412 )
= $false )
| ( ( in @ SV785 @ SV114 )
= $false )
| ( ( in @ SV412 @ ( powerset @ SV114 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3311]) ).
thf(3514,plain,
! [SV118: $i,SV416: $i > $o,SV639: $i] :
( ( ( ~ ( in @ ( sK63_SY3768 @ SV639 @ SV416 @ SV118 ) @ SV118 )
| ~ ( SV416 @ ( sK63_SY3768 @ SV639 @ SV416 @ SV118 ) )
| ( ( sK63_SY3768 @ SV639 @ SV416 @ SV118 )
= SV639 ) )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY3351: $i] : ( SV416 @ SY3351 ) )
= $true )
| ( ( SV416 @ SV639 )
= $false )
| ( ( in @ SV639 @ SV118 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3312]) ).
thf(3515,plain,
! [SV418: $i,SV120: $i,SV640: $i] :
( ( ( in @ SV640 @ ( symdiff @ SV120 @ SV418 ) )
= $false )
| ( ( in @ SV640 @ SV418 )
= $true )
| ( ( in @ SV640 @ SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3313]) ).
thf(3516,plain,
! [SV641: $i > $i,SV419: $i,SV121: $i,SV974: $i] :
( ( ( ~ ( in @ SV974 @ SV121 ) )
= $true )
| ( ( ( ap @ SV121 @ SV419
@ ( lam @ SV121 @ SV419
@ ^ [SY3772: $i] : ( SV641 @ SY3772 ) )
@ SV974 )
= ( SV641 @ SV974 ) )
= $true )
| ( ( in @ ( sK24_SY3770 @ SV419 @ SV641 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3314]) ).
thf(3517,plain,
! [SV641: $i > $i,SV419: $i,SV121: $i,SV935: $i] :
( ( ( in @ SV935 @ SV121 )
= $false )
| ( ( ( ap @ SV121 @ SV419
@ ( lam @ SV121 @ SV419
@ ^ [SY3772: $i] : ( SV641 @ SY3772 ) )
@ SV935 )
= ( SV641 @ SV935 ) )
= $true )
| ( ( in @ ( SV641 @ ( sK24_SY3770 @ SV419 @ SV641 @ SV121 ) ) @ SV419 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3315]) ).
thf(3518,plain,
! [SV122: $i,SV420: $i,SV788: $i > $o,SV865: $i > $o] :
( ( ( ~ ( in @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) @ SV122 ) )
= $false )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3316]) ).
thf(3519,plain,
! [SV122: $i,SV788: $i > $o,SV865: $i > $o,SV420: $i] :
( ( ( ! [SY4133: $i] :
( ~ ( in @ SY4133 @ SV420 )
| ( ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 )
!= SY4133 )
| ~ ( ~ ( ~ ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) )
| ( SV865 @ SY4133 ) )
| ~ ( ~ ( SV865 @ SY4133 )
| ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3316]) ).
thf(3520,plain,
! [SV789: $i,SV421: $i > $o,SV123: $i,SV936: $i] :
( ( ( in @ SV936 @ SV123 )
= $false )
| ( ( ~ ( SV421 @ SV789 )
| ~ ( SV421 @ SV936 )
| ( SV789 = SV936 ) )
= $true )
| ( ( in @ SV789 @ SV123 )
= $false )
| ( ( ex1 @ SV123
@ ^ [SY3363: $i] : ( SV421 @ SY3363 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3317]) ).
thf(3521,plain,
! [SV423: $i,SV790: $i,SV125: $i,SV937: $i] :
( ( ( in @ SV937 @ SV125 )
= $false )
| ( ( ! [SY4105: $i] :
( ~ ( in @ SY4105 @ SV125 )
| ~ ( in @ ( kpair @ SV937 @ SY4105 ) @ SV790 )
| ( in @ ( kpair @ SV937 @ SY4105 ) @ ( binunion @ SV423 @ SV790 ) ) ) )
= $true )
| ( ( breln1 @ SV125 @ SV790 )
= $false )
| ( ( breln1 @ SV125 @ SV423 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3318]) ).
thf(3522,plain,
! [SV642: $i,SV126: $i,SV866: $i,SV424: $o] :
( ( ( ~ SV424 ) = $false )
| ( ( in @ SV866
@ ( dsetconstr @ SV126
@ ^ [SY4056: $i] :
( ~ ( ~ SV424
| ( SY4056 != SV642 ) )
| ~ ( ~ ~ SV424
| ( SY4056 != SV866 ) ) ) ) )
= $true )
| ( ( in @ SV866 @ SV126 )
= $false )
| ( ( in @ SV642 @ SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3319]) ).
thf(3523,plain,
! [SV643: $i,SV126: $i,SV867: $i] :
( ( ( ~ $true ) = $false )
| ( ( in @ SV867
@ ( dsetconstr @ SV126
@ ^ [SY4057: $i] :
( ~ ( ~ $true
| ( SY4057 != SV643 ) )
| ~ ( ~ ~ $true
| ( SY4057 != SV867 ) ) ) ) )
= $true )
| ( ( in @ SV867 @ SV126 )
= $false )
| ( ( in @ SV643 @ SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3320]) ).
thf(3524,plain,
! [SV644: $i,SV126: $i,SV868: $i] :
( ( ( ~ $false ) = $false )
| ( ( in @ SV868
@ ( dsetconstr @ SV126
@ ^ [SY4058: $i] :
( ~ ( ~ $false
| ( SY4058 != SV644 ) )
| ~ ( ~ ~ $false
| ( SY4058 != SV868 ) ) ) ) )
= $true )
| ( ( in @ SV868 @ SV126 )
= $false )
| ( ( in @ SV644 @ SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3321]) ).
thf(3525,plain,
! [SV130: $i,SV427: $i,SV938: $i] :
( ( ( in @ SV938 @ SV427 )
= $false )
| ( ( in @ SV938 @ SV130 )
= $true )
| ( ( in @ SV427 @ ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3322]) ).
thf(3526,plain,
! [SV427: $i,SV130: $i] :
( ( ( in @ ( sK45_SY3375 @ SV130 @ SV427 ) @ SV427 )
= $true )
| ( ( in @ SV427 @ ( powerset @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3323]) ).
thf(3527,plain,
! [SV792: $i,SV428: $i,SV131: $i,SV939: $i] :
( ( ( in @ SV939 @ SV131 )
= $false )
| ( ( ! [SY4106: $i] :
( ~ ( in @ SY4106 @ SV131 )
| ! [SY4107: $i] :
( ~ ( in @ SY4107 @ SV131 )
| ~ ( in @ ( kpair @ SV939 @ SY4107 ) @ SV428 )
| ~ ( in @ ( kpair @ SY4107 @ SY4106 ) @ SV792 )
| ( in @ ( kpair @ SV939 @ SY4106 ) @ ( breln1compset @ SV131 @ SV428 @ SV792 ) ) ) ) )
= $true )
| ( ( breln1 @ SV131 @ SV792 )
= $false )
| ( ( breln1 @ SV131 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3325]) ).
thf(3528,plain,
! [SV135: $i,SV432: $i,SV794: $i] :
( ( ( ~ ( in @ ( sK64_SY3983 @ SV794 @ SV432 @ SV135 ) @ SV135 )
| ! [SY4149: $i] :
( ~ ( in @ SY4149 @ SV135 )
| ~ ( in @ ( kpair @ ( sK64_SY3983 @ SV794 @ SV432 @ SV135 ) @ SY4149 ) @ SV432 )
| ( in @ ( kpair @ ( sK64_SY3983 @ SV794 @ SV432 @ SV135 ) @ SY4149 ) @ SV794 ) ) )
= $false )
| ( ( subset @ SV432 @ SV794 )
= $true )
| ( ( breln1 @ SV135 @ SV794 )
= $false )
| ( ( breln1 @ SV135 @ SV432 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3326]) ).
thf(3529,plain,
! [SV136: $i] :
( ( ( in @ ( sK25_SY2669 @ SV136 ) @ SV136 )
= $true )
| ( ( SV136 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3327]) ).
thf(3530,plain,
! [SV136: $i] :
( ( ( ( binintersect @ ( sK25_SY2669 @ SV136 ) @ SV136 )
= emptyset )
= $true )
| ( ( SV136 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3328]) ).
thf(3531,plain,
! [SV434: $i,SV869: $i,SV138: $i,SV795: $i] :
( ( ( ~ ( ~ ( in @ SV795 @ SV138 )
| ( in @ SV869 @ SV434 ) ) )
= $false )
| ( ( SV795 = SV869 )
= $false )
| ( ( SV138 = SV434 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3329]) ).
thf(3532,plain,
! [SV138: $i,SV795: $i,SV434: $i,SV869: $i] :
( ( ( ~ ( ~ ( in @ SV869 @ SV434 )
| ( in @ SV795 @ SV138 ) ) )
= $false )
| ( ( SV795 = SV869 )
= $false )
| ( ( SV138 = SV434 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3329]) ).
thf(3533,plain,
! [SV796: $i,SV435: $i,SV139: $i,SV940: $i] :
( ( ( in @ SV940 @ ( powerset @ SV139 ) )
= $false )
| ( ( ~ ( subset @ SV435 @ SV940 )
| ( subset @ ( binintersect @ SV435 @ SV796 ) @ SV940 ) )
= $true )
| ( ( in @ SV796 @ ( powerset @ SV139 ) )
= $false )
| ( ( in @ SV435 @ ( powerset @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3330]) ).
thf(3534,plain,
! [SV870: $i,SV650: $i,SV436: $i,SV140: $i] :
( ( ( ! [SY4059: $i] :
( ~ ( in @ SY4059 @ SV140 )
| ! [SY4060: $i] :
( ~ ( in @ SY4060 @ SV436 )
| ~ ( in @ ( kpair @ SY4059 @ SY4060 ) @ SV650 )
| ( in @ ( kpair @ SY4059 @ SY4060 ) @ SV870 ) ) ) )
= $false )
| ( ( ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) )
| ( SV650 = SV870 ) )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3331]) ).
thf(3535,plain,
! [SV654: $i > $i,SV144: $i,SV440: $i,SV975: $i] :
( ( ( ~ ( in @ SV975 @ ( funcSet @ SV440 @ SV144 ) ) )
= $true )
| ( ( ~ ! [SY4134: $i] :
( ~ ( in @ SY4134 @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SV975 @ ( SV654 @ SY4134 ) )
= SY4134 ) )
| ( surjective @ SV440 @ SV144 @ SV975 ) )
= $true )
| ( ( in @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) @ SV144 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3332]) ).
thf(3536,plain,
! [SV654: $i > $i,SV144: $i,SV440: $i,SV941: $i] :
( ( ( in @ SV941 @ ( funcSet @ SV440 @ SV144 ) )
= $false )
| ( ( ~ ! [SY4108: $i] :
( ~ ( in @ SY4108 @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SV941 @ ( SV654 @ SY4108 ) )
= SY4108 ) )
| ( surjective @ SV440 @ SV144 @ SV941 ) )
= $true )
| ( ( in @ ( SV654 @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) ) @ SV440 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3333]) ).
thf(3537,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ( ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( in @ ( sK11_SY3407 @ SV442 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3335]) ).
thf(3538,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( in @ ( sK38_SY3987 @ SV442 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3336]) ).
thf(3539,plain,
! [SV146: $i,SV442: $i > $o] :
( ( ( SV442 @ ( sK11_SY3407 @ SV442 @ SV146 ) )
= $true )
| ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) )
| ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3337]) ).
thf(3540,plain,
! [SV146: $i,SV442: $i > $o] :
( ( ( ~ ( SV442 @ ( sK38_SY3987 @ SV442 @ SV146 ) ) )
= $false )
| ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) )
| ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3338]) ).
thf(3541,plain,
! [SV146: $i,SV442: $i > $o] :
( ( ( ( sK11_SY3407 @ SV442 @ SV146 )
= ( sK38_SY3987 @ SV442 @ SV146 ) )
= $false )
| ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) )
| ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3338]) ).
thf(3542,plain,
! [SV798: $i,SV443: $i,SV147: $i,SV942: $i] :
( ( ( in @ SV942 @ SV147 )
= $false )
| ( ( ~ ( in @ SV942 @ ( setminus @ SV147 @ SV443 ) )
| ~ ( in @ SV942 @ ( binintersect @ SV443 @ SV798 ) ) )
= $true )
| ( ( in @ SV798 @ ( powerset @ SV147 ) )
= $false )
| ( ( in @ SV443 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3339]) ).
thf(3543,plain,
! [SV799: $i,SV444: $i,SV148: $i,SV943: $i] :
( ( ( in @ SV943 @ ( powerset @ SV148 ) )
= $false )
| ( ( ! [SY4109: $i] :
( ~ ( in @ SY4109 @ SV148 )
| ~ ( in @ SY4109 @ ( binintersect @ SV444 @ SV799 ) )
| ( in @ SY4109 @ ( binunion @ SV444 @ SV943 ) ) ) )
= $true )
| ( ( in @ SV799 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV444 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3340]) ).
thf(3544,plain,
! [SV149: $i,SV445: $i > $o] :
( ( ( in @ ( sK27_SY3417 @ SV445 @ SV149 ) @ SV149 )
= $true )
| ( ( ex1 @ SV149
@ ^ [SY3416: $i] : ( SV445 @ SY3416 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3341]) ).
thf(3545,plain,
! [SV149: $i,SV445: $i > $o] :
( ( ( SV445 @ ( sK27_SY3417 @ SV445 @ SV149 ) )
= $true )
| ( ( ex1 @ SV149
@ ^ [SY3416: $i] : ( SV445 @ SY3416 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3342]) ).
thf(3546,plain,
! [SV800: $i,SV446: $i,SV944: $i,SV150: $i] :
( ( ( breln1 @ SV150 @ SV944 )
= $false )
| ( ( ( breln1compset @ SV150 @ ( binunion @ SV446 @ SV800 ) @ SV944 )
= ( binunion @ ( breln1compset @ SV150 @ SV446 @ SV944 ) @ ( breln1compset @ SV150 @ SV800 @ SV944 ) ) )
= $true )
| ( ( breln1 @ SV150 @ SV800 )
= $false )
| ( ( breln1 @ SV150 @ SV446 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3343]) ).
thf(3547,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3344]) ).
thf(3548,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
| ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) ) )
= $false )
| ( ( ~ ( ~ ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
| ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3345]) ).
thf(3549,plain,
! [SV873: $i,SV657: $i,SV155: $i,SV451: $o] :
( ( ( ~ SV451 ) = $false )
| ( ( ( dsetconstr @ SV155
@ ^ [SY4063: $i] :
( ~ ( ~ SV451
| ( SY4063 != SV657 ) )
| ~ ( ~ ~ SV451
| ( SY4063 != SV873 ) ) ) )
= ( setadjoin @ SV873 @ emptyset ) )
= $true )
| ( ( in @ SV873 @ SV155 )
= $false )
| ( ( in @ SV657 @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3346]) ).
thf(3550,plain,
! [SV874: $i,SV658: $i,SV155: $i] :
( ( ( ~ $true ) = $false )
| ( ( ( dsetconstr @ SV155
@ ^ [SY4064: $i] :
( ~ ( ~ $true
| ( SY4064 != SV658 ) )
| ~ ( ~ ~ $true
| ( SY4064 != SV874 ) ) ) )
= ( setadjoin @ SV874 @ emptyset ) )
= $true )
| ( ( in @ SV874 @ SV155 )
= $false )
| ( ( in @ SV658 @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3347]) ).
thf(3551,plain,
! [SV875: $i,SV659: $i,SV155: $i] :
( ( ( ~ $false ) = $false )
| ( ( ( dsetconstr @ SV155
@ ^ [SY4065: $i] :
( ~ ( ~ $false
| ( SY4065 != SV659 ) )
| ~ ( ~ ~ $false
| ( SY4065 != SV875 ) ) ) )
= ( setadjoin @ SV875 @ emptyset ) )
= $true )
| ( ( in @ SV875 @ SV155 )
= $false )
| ( ( in @ SV659 @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3348]) ).
thf(3552,plain,
! [SV453: $i,SV802: $i,SV157: $i,SV945: $i] :
( ( ( in @ SV945 @ SV157 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV802 @ SV945 ) @ SV453 )
| ( in @ ( kpair @ SV945 @ SV802 ) @ ( breln1invset @ SV157 @ SV453 ) ) )
= $true )
| ( ( in @ SV802 @ SV157 )
= $false )
| ( ( breln1 @ SV157 @ SV453 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3349]) ).
thf(3553,plain,
! [SV459: $i,SV804: $i,SV163: $i,SV946: $i] :
( ( ( in @ SV946 @ ( powerset @ SV163 ) )
= $false )
| ( ( ~ ( subset @ SV804 @ SV946 )
| ( subset @ ( binintersect @ SV459 @ SV804 ) @ SV946 ) )
= $true )
| ( ( in @ SV804 @ ( powerset @ SV163 ) )
= $false )
| ( ( in @ SV459 @ ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3350]) ).
thf(3554,plain,
! [SV463: $i,SV876: $i,SV167: $i,SV805: $i] :
( ( ( in @ SV805 @ SV167 )
= $false )
| ( ( in @ SV876 @ SV463 )
= $true )
| ( ( SV805 = SV876 )
= $false )
| ( ( SV167 = SV463 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3351]) ).
thf(3555,plain,
! [SV877: $i,SV666: $i,SV464: $i,SV168: $i] :
( ( ( ! [SY4066: $i] :
( ~ ( in @ SY4066 @ SV168 )
| ! [SY4067: $i] :
( ~ ( in @ SY4067 @ SV464 )
| ~ ( in @ ( kpair @ SY4066 @ SY4067 ) @ SV666 )
| ( in @ ( kpair @ SY4066 @ SY4067 ) @ SV877 ) ) ) )
= $false )
| ( ( subset @ SV666 @ SV877 )
= $true )
| ( ( breln @ SV168 @ SV464 @ SV877 )
= $false )
| ( ( breln @ SV168 @ SV464 @ SV666 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3352]) ).
thf(3556,plain,
! [SV806: $i,SV465: $i,SV947: $i,SV169: $i] :
( ( ( breln1 @ SV169 @ SV947 )
= $false )
| ( ( ( breln1compset @ SV169 @ ( binunion @ SV465 @ SV806 ) @ SV947 )
= ( binunion @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SV947 ) @ ( breln1invset @ SV169 @ SV806 ) ) ) @ ( breln1invset @ SV169 @ ( breln1compset @ SV169 @ ( breln1invset @ SV169 @ SV947 ) @ ( breln1invset @ SV169 @ SV465 ) ) ) ) )
= $true )
| ( ( breln1 @ SV169 @ SV806 )
= $false )
| ( ( breln1 @ SV169 @ SV465 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3353]) ).
thf(3557,plain,
! [SV171: $i,SV807: $i,SV466: $i,SV948: $i] :
( ( ( in @ SV948 @ ( binintersect @ SV466 @ SV807 ) )
= $false )
| ( ( in @ SV948 @ SV171 )
= $true )
| ( ( in @ SV807 @ ( powerset @ SV171 ) )
= $false )
| ( ( in @ SV466 @ ( powerset @ SV171 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3354]) ).
thf(3558,plain,
! [SV175: $i,SV470: $i > $i,SV976: $i] :
( ( ~ ( ~ ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
| ~ ! [SY4135: $i] :
~ ~ ( ~ ( in @ SY4135 @ SV175 )
| ( SV976
!= ( SV470 @ SY4135 ) ) ) )
| ~ ( ~ ~ ! [SY4136: $i] :
~ ~ ( ~ ( in @ SY4136 @ SV175 )
| ( SV976
!= ( SV470 @ SY4136 ) ) )
| ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3356]) ).
thf(3559,plain,
! [SV470: $i > $i,SV175: $i,SV977: $i] :
( ( ( ~ ! [SY4137: $i] :
~ ( ~ ( ~ ( in @ SY4137 @ SV977 )
| ~ ! [SY3468: $i] :
~ ~ ( ~ ( in @ SY3468 @ SV175 )
| ( SY4137
!= ( SV470 @ SY3468 ) ) ) )
| ~ ( ~ ~ ! [SY3469: $i] :
~ ~ ( ~ ( in @ SY3469 @ SV175 )
| ( SY4137
!= ( SV470 @ SY3469 ) ) )
| ( in @ SY4137 @ SV977 ) ) ) )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3357]) ).
thf(3560,plain,
! [SV670: $i > $i > $o,SV180: $i,SV475: $i,SV978: $i] :
( ( ( ~ ( in @ SV978 @ ( breln1Set @ SV475 ) ) )
= $true )
| ( ( ~ ( reflwellordering @ SV475 @ SV978 )
| ! [SY4140: $i] :
( ~ ( in @ SY4140 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY4141: $i] :
~ ( ~ ( SV670 @ SY4140 @ SY4141 )
| ~ ! [SY4142: $i] :
( ~ ( in @ SY4142 @ SV475 )
| ~ ( SV670 @ SY4140 @ SY4142 )
| ( in @ ( kpair @ SY4141 @ SY4142 ) @ SV978 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV180 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3358]) ).
thf(3561,plain,
! [SV180: $i,SV670: $i > $i > $o,SV475: $i,SV979: $i] :
( ( ( ~ ( ~ ( in @ SV979 @ SV475 )
| ~ ( SV670 @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV979 ) ) )
= $false )
| ( ( ! [SY3807: $i] :
( ~ ( in @ SY3807 @ ( breln1Set @ SV475 ) )
| ~ ( reflwellordering @ SV475 @ SY3807 )
| ! [SY3808: $i] :
( ~ ( in @ SY3808 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY3809: $i] :
~ ( ~ ( SV670 @ SY3808 @ SY3809 )
| ~ ! [SY3810: $i] :
( ~ ( in @ SY3810 @ SV475 )
| ~ ( SV670 @ SY3808 @ SY3810 )
| ( in @ ( kpair @ SY3809 @ SY3810 ) @ SY3807 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3359]) ).
thf(3562,plain,
! [SV672: $i > $i,SV477: $i,SV182: $i,SV980: $i] :
( ( ( ~ ( in @ SV980 @ SV182 ) )
= $true )
| ( ( ( ap @ SV182 @ SV477
@ ( lam @ SV182 @ SV477
@ ^ [SY3814: $i] : ( SV672 @ SY3814 ) )
@ SV980 )
= ( SV672 @ SV980 ) )
= $true )
| ( ( in @ ( sK30_SY3812 @ SV477 @ SV672 @ SV182 ) @ SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3360]) ).
thf(3563,plain,
! [SV672: $i > $i,SV477: $i,SV182: $i,SV949: $i] :
( ( ( in @ SV949 @ SV182 )
= $false )
| ( ( ( ap @ SV182 @ SV477
@ ( lam @ SV182 @ SV477
@ ^ [SY3814: $i] : ( SV672 @ SY3814 ) )
@ SV949 )
= ( SV672 @ SV949 ) )
= $true )
| ( ( in @ ( SV672 @ ( sK30_SY3812 @ SV477 @ SV672 @ SV182 ) ) @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3361]) ).
thf(3564,plain,
! [SV812: $i,SV481: $i,SV186: $i,SV950: $i] :
( ( ( in @ SV950 @ SV186 )
= $false )
| ( ( ~ ( in @ SV481 @ ( powerset @ SV812 ) )
| ~ ( in @ SV950 @ SV481 )
| ( in @ SV950 @ SV812 ) )
= $true )
| ( ( in @ SV812 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV481 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3364]) ).
thf(3565,plain,
! [SV483: $i > $o,SV188: $i,SV675: $i] :
( ( ( in @ SV675
@ ( dsetconstr @ SV188
@ ^ [SY3494: $i] : ( SV483 @ SY3494 ) ) )
= $false )
| ( ( SV483 @ SV675 )
= $true )
| ( ( in @ SV675 @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3365]) ).
thf(3566,plain,
! [SV188: $i,SV675: $i,SV483: $i > $o] :
( ( ( SV483 @ SV675 )
= $false )
| ( ( in @ SV675
@ ( dsetconstr @ SV188
@ ^ [SY3495: $i] : ( SV483 @ SY3495 ) ) )
= $true )
| ( ( in @ SV675 @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3366]) ).
thf(3567,plain,
! [SV189: $i,SV484: $i > $o,SV879: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK65_SY3497 @ SV879 @ SV484 @ SV189 ) @ SV189 )
| ~ ~ ( SV484 @ ( sK65_SY3497 @ SV879 @ SV484 @ SV189 ) ) ) )
= $false )
| ( ( SV484 @ SV879 )
= $true )
| ( ( in @ SV879 @ SV189 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3367]) ).
thf(3568,plain,
! [SV190: $i,SV813: $o,SV485: $i] :
( ( ( in @ SV485 @ ( sK46_SY4001 @ SV813 @ SV190 @ SV485 ) )
= $true )
| ( SV813 = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3368]) ).
thf(3569,plain,
! [SV485: $i,SV190: $i,SV813: $o] :
( ( ( ~ ( in @ ( sK46_SY4001 @ SV813 @ SV190 @ SV485 ) @ SV190 ) )
= $false )
| ( SV813 = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3369]) ).
thf(3570,plain,
! [SV190: $i,SV485: $i,SV813: $o] :
( ( SV813 = $false )
| ( SV813 = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3369]) ).
thf(3571,plain,
! [SV190: $i,SV485: $i] :
( ( ( in @ SV485 @ ( sK47_SX0 @ SV190 @ SV485 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3370]) ).
thf(3572,plain,
! [SV485: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK47_SX0 @ SV190 @ SV485 ) @ SV190 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3371]) ).
thf(3573,plain,
! [SV190: $i,SV485: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3371]) ).
thf(3574,plain,
! [SV190: $i,SV485: $i] :
( ( ( in @ SV485 @ ( sK48_SX0 @ SV190 @ SV485 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3372]) ).
thf(3575,plain,
! [SV485: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK48_SX0 @ SV190 @ SV485 ) @ SV190 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3373]) ).
thf(3576,plain,
! [SV190: $i,SV485: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3373]) ).
thf(3577,plain,
! [SV191: $i,SV676: $i,SV880: $i,SV486: $i,SV981: $i] :
( ( ( ~ ( in @ SV981 @ SV486 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV880 @ SV981 ) @ SV676 )
| ( ( ap @ SV191 @ SV486 @ SV676 @ SV880 )
= SV981 ) )
= $true )
| ( ( in @ SV880 @ SV191 )
= $false )
| ( ( in @ SV676 @ ( funcSet @ SV191 @ SV486 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3374]) ).
thf(3578,plain,
! [SV193: $i,SV488: $i > $i,SV881: $i] :
( ( ( ~ ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) ) )
= $true )
| ( ( ~ ! [SY4070: $i] :
~ ~ ( ~ ( in @ SY4070 @ SV193 )
| ( SV881
!= ( SV488 @ SY4070 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3375]) ).
thf(3579,plain,
! [SV488: $i > $i,SV881: $i,SV193: $i] :
( ( ( ~ ~ ! [SY4071: $i] :
~ ~ ( ~ ( in @ SY4071 @ SV193 )
| ( SV881
!= ( SV488 @ SY4071 ) ) ) )
= $true )
| ( ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3376]) ).
thf(3580,plain,
! [SV489: $i,SV194: $i,SV814: $i] :
( ( ( in @ SV814 @ ( setminus @ SV194 @ SV489 ) )
= $true )
| ( ( in @ SV814 @ SV489 )
= $true )
| ( ( in @ SV814 @ SV194 )
= $false )
| ( ( in @ SV489 @ ( powerset @ SV194 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3377]) ).
thf(3581,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ! [SY4002: $i] :
( ~ ( SV196 @ SY4002 )
| ( SV816 = SY4002 ) ) )
= $false )
| ( ( SV196 @ SV816 )
= $false )
| ( ( ~ ! [SY2855: $i] :
~ ~ ( ~ ( SV196 @ SY2855 )
| ~ ! [SY2856: $i] :
( ~ ( SV196 @ SY2856 )
| ( SY2855 = SY2856 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3379]) ).
thf(3582,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3380]) ).
thf(3583,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3380]) ).
thf(3584,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
| ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) ) )
= $false )
| ( ( ~ ( ~ ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
| ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3381]) ).
thf(3585,plain,
! [SV199: $i,SV492: $i,SV679: $i] :
( ( ( ~ ( in @ ( sK39_SY3820 @ SV679 @ SV492 @ SV199 ) @ SV199 ) )
= $false )
| ( ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3382]) ).
thf(3586,plain,
! [SV199: $i,SV679: $i,SV492: $i] :
( ( ( ~ ~ ! [SY4093: $i] :
~ ~ ( ~ ( in @ SY4093 @ SV492 )
| ( SV679
!= ( kpair @ ( sK39_SY3820 @ SV679 @ SV492 @ SV199 ) @ SY4093 ) ) ) )
= $false )
| ( ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3382]) ).
thf(3587,plain,
! [SV817: $i,SV493: $i,SV200: $i,SV951: $i] :
( ( ( in @ SV951 @ SV200 )
= $false )
| ( ( ~ ~ ( in @ SV951 @ ( binunion @ SV493 @ SV817 ) )
| ~ ( in @ SV951 @ SV817 ) )
= $true )
| ( ( in @ SV817 @ ( powerset @ SV200 ) )
= $false )
| ( ( in @ SV493 @ ( powerset @ SV200 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3383]) ).
thf(3588,plain,
! [SV885: $o,SV496: $i,SV203: $i,SV683: $i] :
( ( ( in @ SV683 @ SV203 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SV885 )
| SV885 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3384]) ).
thf(3589,plain,
! [SV885: $o,SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV496 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SV885 )
| SV885 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3385]) ).
thf(3590,plain,
! [SV496: $i,SV203: $i,SV683: $i,SV885: $o] :
( ( SV885 = $false )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SV885 )
| SV885 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3385]) ).
thf(3591,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( in @ SV683 @ SV203 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $true )
| $true )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3386]) ).
thf(3592,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV496 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $true )
| $true )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3387]) ).
thf(3593,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $true )
| $true )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3387]) ).
thf(3594,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( in @ SV683 @ SV203 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $false )
| $false )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3388]) ).
thf(3595,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV496 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $false )
| $false )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3389]) ).
thf(3596,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $false )
| $false )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3389]) ).
thf(3597,plain,
! [SV207: $i,SV500: $i > $o] :
( ( ( ~ ( in @ ( sK40_SY3540 @ SV500 @ SV207 ) @ SV207 ) )
= $false )
| ( ( ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SV207 )
| ~ ( SV500 @ SY3541 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3390]) ).
thf(3598,plain,
! [SV207: $i,SV500: $i > $o] :
( ( ( ~ ( SV500 @ ( sK40_SY3540 @ SV500 @ SV207 ) ) )
= $false )
| ( ( ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SV207 )
| ~ ( SV500 @ SY3541 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3390]) ).
thf(3599,plain,
! [SV952: $o,SV818: $i,SV501: $i,SV208: $i,SV982: $i] :
( ( ( ~ ( in @ SV982 @ SV208 ) )
= $true )
| ( ( ~ ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
| ~ ( ~ ( in @ SV982 @ SV501 )
| SV952 )
| ~ ( ~ ( in @ SV982 @ SV818 )
| SV952 )
| SV952 )
= $true )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3391]) ).
thf(3600,plain,
! [SV818: $i,SV501: $i,SV208: $i,SV983: $i] :
( ( ( ~ ( in @ SV983 @ SV208 ) )
= $true )
| ( ( ~ ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
| ~ ( ~ ( in @ SV983 @ SV501 )
| $true )
| ~ ( ~ ( in @ SV983 @ SV818 )
| $true )
| $true )
= $true )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3392]) ).
thf(3601,plain,
! [SV818: $i,SV501: $i,SV208: $i,SV984: $i] :
( ( ( ~ ( in @ SV984 @ SV208 ) )
= $true )
| ( ( ~ ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
| ~ ( ~ ( in @ SV984 @ SV501 )
| $false )
| ~ ( ~ ( in @ SV984 @ SV818 )
| $false )
| $false )
= $true )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3393]) ).
thf(3602,plain,
! [SV209: $i,SV502: $i,SV689: $i,SV889: $i > $o] :
( ( ( ~ ( in @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ SV209 ) )
= $false )
| ( ( ! [SY4074: $i] :
( ~ ( in @ SY4074 @ SV689 )
| ( SV889 @ SY4074 ) ) )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3394]) ).
thf(3603,plain,
! [SV209: $i,SV689: $i,SV889: $i > $o,SV502: $i] :
( ( ( ! [SY4144: $i] :
( ~ ( in @ SY4144 @ SV502 )
| ~ ( in @ ( kpair @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ SY4144 ) @ SV689 )
| ( SV889 @ ( kpair @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ SY4144 ) ) ) )
= $false )
| ( ( ! [SY4074: $i] :
( ~ ( in @ SY4074 @ SV689 )
| ( SV889 @ SY4074 ) ) )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3394]) ).
thf(3604,plain,
! [SV890: $i,SV210: $i,SV690: $i,SV503: $o] :
( ( SV503 = $false )
| ( ( in @ SV690
@ ( dsetconstr @ SV210
@ ^ [SY4075: $i] :
( ~ ( ~ SV503
| ( SY4075 != SV690 ) )
| ~ ( ~ ~ SV503
| ( SY4075 != SV890 ) ) ) ) )
= $true )
| ( ( in @ SV890 @ SV210 )
= $false )
| ( ( in @ SV690 @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3395]) ).
thf(3605,plain,
! [SV891: $i,SV210: $i,SV691: $i] :
( ( $true = $false )
| ( ( in @ SV691
@ ( dsetconstr @ SV210
@ ^ [SY4076: $i] :
( ~ ( ~ $true
| ( SY4076 != SV691 ) )
| ~ ( ~ ~ $true
| ( SY4076 != SV891 ) ) ) ) )
= $true )
| ( ( in @ SV891 @ SV210 )
= $false )
| ( ( in @ SV691 @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3396]) ).
thf(3606,plain,
! [SV892: $i,SV210: $i,SV692: $i] :
( ( $false = $false )
| ( ( in @ SV692
@ ( dsetconstr @ SV210
@ ^ [SY4077: $i] :
( ~ ( ~ $false
| ( SY4077 != SV692 ) )
| ~ ( ~ ~ $false
| ( SY4077 != SV892 ) ) ) ) )
= $true )
| ( ( in @ SV892 @ SV210 )
= $false )
| ( ( in @ SV692 @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3397]) ).
thf(3607,plain,
! [SV819: $i,SV508: $i,SV216: $i,SV953: $i] :
( ( ( in @ SV953 @ SV216 )
= $false )
| ( ( ! [SY4112: $i] :
( ~ ( in @ SY4112 @ SV216 )
| ~ ( in @ ( kpair @ SV953 @ SY4112 ) @ ( binunion @ SV508 @ SV819 ) )
| ! [SY4113: $o] :
( ~ ( ~ ( in @ ( kpair @ SV953 @ SY4112 ) @ SV508 )
| SY4113 )
| ~ ( ~ ( in @ ( kpair @ SV953 @ SY4112 ) @ SV819 )
| SY4113 )
| SY4113 ) ) )
= $true )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3399]) ).
thf(3608,plain,
! [SV820: $i,SV509: $i,SV217: $i,SV954: $i] :
( ( ( in @ SV954 @ SV217 )
= $false )
| ( ( ~ ( in @ SV954 @ ( setminus @ SV217 @ ( binunion @ SV509 @ SV820 ) ) )
| ( in @ SV954 @ ( binintersect @ ( setminus @ SV217 @ SV509 ) @ ( setminus @ SV217 @ SV820 ) ) ) )
= $true )
| ( ( in @ SV820 @ ( powerset @ SV217 ) )
= $false )
| ( ( in @ SV509 @ ( powerset @ SV217 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3400]) ).
thf(3609,plain,
! [SV218: $i,SV696: $i,SV510: $i > $i] :
( ( ( ~ ( in @ ( sK41_SY3843 @ SV510 @ SV696 @ SV218 ) @ SV218 ) )
= $false )
| ( ( in @ SV696
@ ( image1 @ SV218
@ ^ [SY3564: $i] : ( SV510 @ SY3564 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3401]) ).
thf(3610,plain,
! [SV218: $i,SV510: $i > $i,SV696: $i] :
( ( ( SV696
!= ( SV510 @ ( sK41_SY3843 @ SV510 @ SV696 @ SV218 ) ) )
= $false )
| ( ( in @ SV696
@ ( image1 @ SV218
@ ^ [SY3564: $i] : ( SV510 @ SY3564 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3401]) ).
thf(3611,plain,
! [SV226: $i] :
( ( ~ ( ~ ! [SY3851: $i] :
( ~ ( in @ SY3851 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY2945: $i] :
( ~ ( in @ SY2945 @ SY3851 )
| ( in @ SY2945 @ SV226 ) ) )
| ~ ! [SY3853: $i,SY3854: $i] :
( ~ ~ ( ~ ( in @ SY3853 @ SV226 )
| ~ ( in @ SY3854 @ SV226 ) )
| ~ ! [SY3855: $i] :
( ~ ( in @ SY3855 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SY3853 @ SY3855 )
| ( in @ SY3854 @ SY3855 ) )
| ~ ( ~ ( in @ SY3854 @ SY3855 )
| ( in @ SY3853 @ SY3855 ) ) ) )
| ( SY3853 = SY3854 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3403]) ).
thf(3612,plain,
! [SV226: $i] :
( ( ! [SY3856: $i,SY3857: $i] :
( ~ ~ ( ~ ( in @ SY3856 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY3857 @ ( sK2_SY2943 @ SV226 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3856 )
| ( in @ SX4 @ SY3857 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3857 )
| ( in @ SX4 @ SY3856 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3404]) ).
thf(3613,plain,
! [SV226: $i,SV955: $i] :
( ( ( ~ ( ~ ! [SY4114: $i] :
( ~ ( in @ SY4114 @ SV955 )
| ( in @ SY4114 @ SV226 ) )
| ~ ~ ! [SY4115: $i] :
~ ( in @ SY4115 @ SV955 ) ) )
= $false )
| ( ( ~ ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3405]) ).
thf(3614,plain,
! [SV703: $i > $i > $o,SV517: $i,SV227: $i,SV920: $i,SV752: $i] :
( ( ( ~ ( in @ ( kpair @ SV752 @ SV920 )
@ ( dpsetconstr @ SV227 @ SV517
@ ^ [SY3870: $i,SY3871: $i] : ( SV703 @ SY3870 @ SY3871 ) ) ) )
= $true )
| ( ( SV703 @ SV752 @ SV920 )
= $true )
| ( ( in @ SV920 @ SV517 )
= $false )
| ( ( in @ SV752 @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3406]) ).
thf(3615,plain,
! [SV822: $i,SV519: $i,SV229: $i,SV956: $i] :
( ( ( in @ SV956 @ SV229 )
= $false )
| ( ( ~ ~ ( in @ SV956 @ ( binunion @ SV519 @ SV822 ) )
| ~ ( in @ SV956 @ SV519 ) )
= $true )
| ( ( in @ SV822 @ ( powerset @ SV229 ) )
= $false )
| ( ( in @ SV519 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3407]) ).
thf(3616,plain,
! [SV520: $i,SV230: $i > $i > $o] :
( ( ( ! [SY4145: $i] :
~ ( ~ ( ~ ( in @ SY4145 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY4145 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY4145 ) )
| ( in @ SY4145 @ ( sK56_SY3585 @ SV230 @ SV520 ) ) ) ) )
= $true )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3408]) ).
thf(3617,plain,
! [SV957: $i,SV520: $i,SV230: $i > $i > $o] :
( ( ( ~ ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
| ~ ! [SY4121: $i] :
( ~ ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SY4121 )
| ( SV957 = SY4121 ) ) )
= $true )
| ( ( ~ ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3409]) ).
thf(3618,plain,
! [SV896: $i,SV705: $i,SV521: $i,SV231: $i] :
( ( ( ! [SY4081: $i] :
( ~ ( in @ SY4081 @ SV231 )
| ( ( ap @ SV231 @ SV521 @ SV705 @ SY4081 )
= ( ap @ SV231 @ SV521 @ SV896 @ SY4081 ) ) ) )
= $false )
| ( ( SV705 = SV896 )
= $true )
| ( ( func @ SV231 @ SV521 @ SV896 )
= $false )
| ( ( func @ SV231 @ SV521 @ SV705 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3410]) ).
thf(3619,plain,
! [SV897: $i,SV706: $i,SV232: $i,SV522: $o] :
( ( SV522 = $false )
| ( ( ( if @ SV232 @ SV522 @ SV706 @ SV897 )
= SV706 )
= $true )
| ( ( in @ SV897 @ SV232 )
= $false )
| ( ( in @ SV706 @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3411]) ).
thf(3620,plain,
! [SV898: $i,SV707: $i,SV232: $i] :
( ( $true = $false )
| ( ( ( if @ SV232 @ $true @ SV707 @ SV898 )
= SV707 )
= $true )
| ( ( in @ SV898 @ SV232 )
= $false )
| ( ( in @ SV707 @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3412]) ).
thf(3621,plain,
! [SV899: $i,SV708: $i,SV232: $i] :
( ( $false = $false )
| ( ( ( if @ SV232 @ $false @ SV708 @ SV899 )
= SV708 )
= $true )
| ( ( in @ SV899 @ SV232 )
= $false )
| ( ( in @ SV708 @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3413]) ).
thf(3622,plain,
! [SV233: $i,SV523: $i,SV823: $i > $o] :
( ( ( in @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ SV233 )
= $true )
| ( ( ! [SY4016: $i] :
( ~ ( in @ SY4016 @ SV523 )
| ( SV823 @ SY4016 ) ) )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3414]) ).
thf(3623,plain,
! [SV233: $i,SV823: $i > $o,SV523: $i] :
( ( ( ~ ( in @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) @ SV233 )
| ~ ( in @ ( kpair @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) ) @ SV523 )
| ( SV823 @ ( kpair @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) ) ) )
= $false )
| ( ( ! [SY4016: $i] :
( ~ ( in @ SY4016 @ SV523 )
| ( SV823 @ SY4016 ) ) )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3415]) ).
thf(3624,plain,
! [SV235: $i,SV525: $i] :
( ( ( in @ ( sK34_SY3599 @ SV525 @ SV235 ) @ SV235 )
= $true )
| ( ( in @ SV525 @ ( setunion @ SV235 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3416]) ).
thf(3625,plain,
! [SV235: $i,SV525: $i] :
( ( ( in @ SV525 @ ( sK34_SY3599 @ SV525 @ SV235 ) )
= $true )
| ( ( in @ SV525 @ ( setunion @ SV235 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3417]) ).
thf(3626,plain,
! [SV825: $i,SV531: $i,SV243: $i,SV958: $i] :
( ( ( in @ SV958 @ ( powerset @ SV243 ) )
= $false )
| ( ( in @ ( binintersect @ SV531 @ SV825 ) @ ( powerset @ ( binintersect @ ( binunion @ SV531 @ SV958 ) @ ( binunion @ SV825 @ SV958 ) ) ) )
= $true )
| ( ( in @ SV825 @ ( powerset @ SV243 ) )
= $false )
| ( ( in @ SV531 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3418]) ).
thf(3627,plain,
! [SV533: $i > $o,SV245: $i,SV901: $i] :
( ( ( in @ SV901 @ SV245 )
= $false )
| ( ( ~ ( SV533 @ SV901 ) )
= $true )
| ( ( ( ( dsetconstr @ SV245
@ ^ [SY3609: $i] : ( SV533 @ SY3609 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3420]) ).
thf(3628,plain,
! [SV535: $i,SV827: $i,SV247: $i,SV959: $i] :
( ( ( in @ SV959 @ SV247 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV959 @ SV827 ) @ ( breln1invset @ SV247 @ SV535 ) )
| ( in @ ( kpair @ SV827 @ SV959 ) @ SV535 ) )
= $true )
| ( ( in @ SV827 @ SV247 )
= $false )
| ( ( breln1 @ SV247 @ SV535 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3421]) ).
thf(3629,plain,
! [SV828: $i,SV538: $i,SV251: $i,SV960: $i] :
( ( ( in @ SV960 @ SV251 )
= $false )
| ( ( ~ ~ ( in @ SV960 @ SV538 )
| ~ ~ ( in @ SV960 @ SV828 )
| ~ ( in @ SV960 @ ( binunion @ SV538 @ SV828 ) ) )
= $true )
| ( ( in @ SV828 @ ( powerset @ SV251 ) )
= $false )
| ( ( in @ SV538 @ ( powerset @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3423]) ).
thf(3630,plain,
! [SV904: $i,SV714: $i,SV252: $i,SV539: $o] :
( ( SV539 = $false )
| ( ( ( dsetconstr @ SV252
@ ^ [SY4083: $i] :
( ~ ( ~ SV539
| ( SY4083 != SV714 ) )
| ~ ( ~ ~ SV539
| ( SY4083 != SV904 ) ) ) )
= ( setadjoin @ SV714 @ emptyset ) )
= $true )
| ( ( in @ SV904 @ SV252 )
= $false )
| ( ( in @ SV714 @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3424]) ).
thf(3631,plain,
! [SV905: $i,SV715: $i,SV252: $i] :
( ( $true = $false )
| ( ( ( dsetconstr @ SV252
@ ^ [SY4084: $i] :
( ~ ( ~ $true
| ( SY4084 != SV715 ) )
| ~ ( ~ ~ $true
| ( SY4084 != SV905 ) ) ) )
= ( setadjoin @ SV715 @ emptyset ) )
= $true )
| ( ( in @ SV905 @ SV252 )
= $false )
| ( ( in @ SV715 @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3425]) ).
thf(3632,plain,
! [SV906: $i,SV716: $i,SV252: $i] :
( ( $false = $false )
| ( ( ( dsetconstr @ SV252
@ ^ [SY4085: $i] :
( ~ ( ~ $false
| ( SY4085 != SV716 ) )
| ~ ( ~ ~ $false
| ( SY4085 != SV906 ) ) ) )
= ( setadjoin @ SV716 @ emptyset ) )
= $true )
| ( ( in @ SV906 @ SV252 )
= $false )
| ( ( in @ SV716 @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3426]) ).
thf(3633,plain,
! [SV259: $i,SV719: $i,SV908: $i,SV548: $i,SV985: $i] :
( ( ( ~ ( in @ SV985 @ SV548 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV908 @ SV985 ) @ SV719 )
| ( ( ap @ SV259 @ SV548 @ SV719 @ SV908 )
= SV985 ) )
= $true )
| ( ( in @ SV908 @ SV259 )
= $false )
| ( ( func @ SV259 @ SV548 @ SV719 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3427]) ).
thf(3634,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SV260 )
| ! [SY4150: $i] :
( ~ ( in @ SY4150 @ SV260 )
| ~ ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SY4150 ) @ SV549 )
| ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SY4150 ) @ SV829 ) ) )
= $false )
| ( ( ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) )
| ( SV549 = SV829 ) )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3428]) ).
thf(3635,plain,
! [SV830: $i,SV553: $i,SV264: $i,SV961: $i] :
( ( ( in @ SV961 @ SV264 )
= $false )
| ( ( ! [SY4123: $i] :
( ~ ( in @ SY4123 @ SV264 )
| ~ ( ( in @ ( kpair @ SV961 @ SY4123 ) @ SV553 )
| ( in @ ( kpair @ SV961 @ SY4123 ) @ SV830 ) )
| ( in @ ( kpair @ SV961 @ SY4123 ) @ ( binunion @ SV553 @ SV830 ) ) ) )
= $true )
| ( ( breln1 @ SV264 @ SV830 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3429]) ).
thf(3636,plain,
! [SV271: $i,SV559: $i,SV833: $i > $o] :
( ( ( in @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ SV271 )
= $true )
| ( ( ! [SY4028: $i] :
( ~ ( in @ SY4028 @ SV559 )
| ( SV833 @ SY4028 ) ) )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3430]) ).
thf(3637,plain,
! [SV271: $i,SV833: $i > $o,SV559: $i] :
( ( ( ~ ( in @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) @ SV271 )
| ~ ( in @ ( kpair @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) ) @ SV559 )
| ( SV833 @ ( kpair @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) ) ) )
= $false )
| ( ( ! [SY4028: $i] :
( ~ ( in @ SY4028 @ SV559 )
| ( SV833 @ SY4028 ) ) )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3431]) ).
thf(3638,plain,
! [SV563: $i > $o,SV275: $i,SV989: $i] :
( ( ( ~ ~ ( ~ ( in @ SV989 @ SV275 )
| ~ ( SV563 @ SV989 ) ) )
= $true )
| ( ( in @ ( sK16_SY3653 @ SV563 @ SV275 ) @ SV275 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3433]) ).
thf(3639,plain,
! [SV563: $i > $o,SV275: $i,SV990: $i] :
( ( ( ~ ~ ( ~ ( in @ SV990 @ SV275 )
| ~ ( SV563 @ SV990 ) ) )
= $true )
| ( ( SV563 @ ( sK16_SY3653 @ SV563 @ SV275 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3434]) ).
thf(3640,plain,
! [SV835: $i,SV565: $i,SV277: $i,SV962: $i] :
( ( ( in @ SV962 @ SV277 )
= $false )
| ( ( ~ ( in @ SV962 @ ( setminus @ SV277 @ ( binunion @ SV565 @ SV835 ) ) )
| ( in @ SV962 @ ( setminus @ SV277 @ SV565 ) ) )
= $true )
| ( ( in @ SV835 @ ( powerset @ SV277 ) )
= $false )
| ( ( in @ SV565 @ ( powerset @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3435]) ).
thf(3641,plain,
! [SV566: $i,SV278: $i] :
( ( ( ~ ( in @ ( sK69_SY3658 @ SV278 @ SV566 ) @ SV566 )
| ( in @ ( sK69_SY3658 @ SV278 @ SV566 ) @ SV278 ) )
= $false )
| ( ( SV278 = SV566 )
= $true )
| ( ( in @ ( sK17_SY3657 @ SV566 @ SV278 ) @ SV278 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3436]) ).
thf(3642,plain,
! [SV566: $i,SV278: $i] :
( ( ( ~ ( in @ ( sK57_SY3658 @ SV278 @ SV566 ) @ SV566 ) )
= $false )
| ( ( SV278 = SV566 )
= $true )
| ( ( in @ ( sK17_SY3657 @ SV566 @ SV278 ) @ SV566 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3437]) ).
thf(3643,plain,
! [SV566: $i,SV278: $i] :
( ( ( in @ ( sK57_SY3658 @ SV278 @ SV566 ) @ SV278 )
= $false )
| ( ( SV278 = SV566 )
= $true )
| ( ( in @ ( sK17_SY3657 @ SV566 @ SV278 ) @ SV566 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3437]) ).
thf(3644,plain,
! [SV836: $i,SV568: $i,SV280: $i,SV963: $i] :
( ( ( in @ SV963 @ SV280 )
= $false )
| ( ( ! [SY4125: $i] :
( ~ ( in @ SY4125 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SY4125 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
| ! [SY4126: $o] :
( ~ ! [SY4127: $i] :
( ~ ( in @ SY4127 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SY4127 ) @ SV568 )
| ~ ( in @ ( kpair @ SY4127 @ SY4125 ) @ SV836 )
| SY4126 )
| SY4126 ) ) )
= $true )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3438]) ).
thf(3645,plain,
! [SV284: $i,SV572: $i] :
( ( ( ~ ( in @ ( sK42_SY3668 @ SV572 @ SV284 ) @ SV284 ) )
= $false )
| ( ( ( binintersect @ SV284 @ SV572 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3439]) ).
thf(3646,plain,
! [SV284: $i,SV572: $i] :
( ( ( ~ ( in @ ( sK42_SY3668 @ SV572 @ SV284 ) @ SV572 ) )
= $false )
| ( ( ( binintersect @ SV284 @ SV572 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3439]) ).
thf(3647,plain,
! [SV837: $i,SV288: $i > $o] :
( ( ( ! [SY4034: $i] :
( ~ ( SV288 @ SY4034 )
| ( SV837 = SY4034 ) ) )
= $false )
| ( ( SV288 @ SV837 )
= $false )
| ( ( ! [SY3119: $i,SY3120: $i] :
( ~ ( SV288 @ SY3119 )
| ~ ( SV288 @ SY3120 )
| ( SY3119 = SY3120 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3440]) ).
thf(3648,plain,
! [SV289: $i,SV575: $i > $o] :
( ( ( ~ ( in @ ( sK43_SY3670 @ SV575 @ SV289 ) @ SV289 ) )
= $false )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV289 )
| ~ ( SV575 @ SY3671 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3441]) ).
thf(3649,plain,
! [SV289: $i,SV575: $i > $o] :
( ( ( ~ ( SV575 @ ( sK43_SY3670 @ SV575 @ SV289 ) ) )
= $false )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV289 )
| ~ ( SV575 @ SY3671 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3441]) ).
thf(3650,plain,
! [SV579: $i,SV293: $i,SV922: $i,SV755: $i,SV732: $i > $i > $o] :
( ( ( ~ ( SV732 @ SV755 @ SV922 ) )
= $true )
| ( ( in @ ( kpair @ SV755 @ SV922 )
@ ( dpsetconstr @ SV293 @ SV579
@ ^ [SY3897: $i,SY3898: $i] : ( SV732 @ SY3897 @ SY3898 ) ) )
= $true )
| ( ( in @ SV922 @ SV579 )
= $false )
| ( ( in @ SV755 @ SV293 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3442]) ).
thf(3651,plain,
! [SV757: $o,SV583: $i,SV298: $i,SV733: $i] :
( ( ( in @ SV733 @ SV298 )
= $true )
| ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| SV757 )
| SV757 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3443]) ).
thf(3652,plain,
! [SV298: $i,SV757: $o,SV583: $i,SV733: $i] :
( ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| SV757 ) )
= $true )
| ( SV757 = $true )
| ( SV757 = $false )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3444]) ).
thf(3653,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( ( in @ SV733 @ SV298 )
= $true )
| ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| $true )
| $true )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3445]) ).
thf(3654,plain,
! [SV298: $i,SV583: $i,SV733: $i] :
( ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3446]) ).
thf(3655,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( ( in @ SV733 @ SV298 )
= $true )
| ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| $false )
| $false )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3447]) ).
thf(3656,plain,
! [SV298: $i,SV583: $i,SV733: $i] :
( ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3448]) ).
thf(3657,plain,
! [SV299: $i,SV584: $i,SV840: $i] :
( ( ( ~ ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV299 )
| ~ ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV584 )
| ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV840 ) )
= $false )
| ( ( ~ ! [SY4036: $i] :
( ~ ( in @ SY4036 @ SV299 )
| ~ ( in @ SY4036 @ SV840 )
| ( in @ SY4036 @ SV584 ) )
| ( SV584 = SV840 ) )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3449]) ).
thf(3658,plain,
! [SV841: $i,SV585: $i,SV300: $i,SV964: $i] :
( ( ( in @ SV964 @ SV300 )
= $false )
| ( ( ! [SY4128: $i] :
( ~ ( in @ SY4128 @ SV300 )
| ~ ( in @ ( kpair @ SV964 @ SY4128 ) @ SV585 )
| ( in @ ( kpair @ SV964 @ SY4128 ) @ ( binunion @ SV585 @ SV841 ) ) ) )
= $true )
| ( ( breln1 @ SV300 @ SV841 )
= $false )
| ( ( breln1 @ SV300 @ SV585 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3450]) ).
thf(3659,plain,
! [SV911: $i,SV734: $i,SV586: $i,SV301: $i] :
( ( ( ! [SY4087: $i] :
( ~ ( in @ SY4087 @ SV301 )
| ( ( ap @ SV301 @ SV586 @ SV734 @ SY4087 )
= ( ap @ SV301 @ SV586 @ SV911 @ SY4087 ) ) ) )
= $false )
| ( ( ! [SY4088: $i] :
( ~ ( in @ SY4088 @ SV301 )
| ! [SY4089: $i] :
( ~ ( in @ SY4089 @ SV586 )
| ~ ( in @ ( kpair @ SY4088 @ SY4089 ) @ SV911 )
| ( in @ ( kpair @ SY4088 @ SY4089 ) @ SV734 ) ) ) )
= $true )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3451]) ).
thf(3660,plain,
! [SV842: $i,SV587: $i,SV302: $i,SV965: $i] :
( ( ( in @ SV965 @ SV302 )
= $false )
| ( ( ~ ( in @ SV965 @ ( binunion @ ( setminus @ SV302 @ SV587 ) @ ( setminus @ SV302 @ SV842 ) ) )
| ( in @ SV965 @ ( setminus @ SV302 @ ( binintersect @ SV587 @ SV842 ) ) ) )
= $true )
| ( ( in @ SV842 @ ( powerset @ SV302 ) )
= $false )
| ( ( in @ SV587 @ ( powerset @ SV302 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3452]) ).
thf(3661,plain,
! [SV843: $i,SV589: $i,SV305: $i,SV966: $i] :
( ( ( in @ SV966 @ ( powerset @ SV305 ) )
= $false )
| ( ( in @ ( binintersect @ SV589 @ SV843 ) @ ( powerset @ ( binintersect @ ( binunion @ SV589 @ SV966 ) @ ( binunion @ SV843 @ SV966 ) ) ) )
= $true )
| ( ( in @ SV843 @ ( powerset @ SV305 ) )
= $false )
| ( ( in @ SV589 @ ( powerset @ SV305 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3453]) ).
thf(3662,plain,
! [SV844: $i,SV590: $i,SV307: $i,SV967: $i] :
( ( ( in @ SV967 @ SV307 )
= $false )
| ( ( ~ ( in @ SV967 @ ( binintersect @ ( setminus @ SV307 @ SV590 ) @ ( setminus @ SV307 @ SV844 ) ) )
| ( in @ SV967 @ ( setminus @ SV307 @ ( binunion @ SV590 @ SV844 ) ) ) )
= $true )
| ( ( in @ SV844 @ ( powerset @ SV307 ) )
= $false )
| ( ( in @ SV590 @ ( powerset @ SV307 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3454]) ).
thf(3663,plain,
! [SV308: $i,SV591: $i,SV845: $i] :
( ( ( ~ ( in @ ( sK71_SY4042 @ SV845 @ SV591 @ SV308 ) @ SV308 )
| ~ ( in @ ( sK71_SY4042 @ SV845 @ SV591 @ SV308 ) @ SV591 )
| ( in @ ( sK71_SY4042 @ SV845 @ SV591 @ SV308 ) @ SV845 ) )
= $false )
| ( ( in @ SV591 @ ( powerset @ SV845 ) )
= $true )
| ( ( in @ SV845 @ ( powerset @ SV308 ) )
= $false )
| ( ( in @ SV591 @ ( powerset @ SV308 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3455]) ).
thf(3664,plain,
! [SV846: $i,SV592: $i,SV309: $i,SV968: $i] :
( ( ( in @ SV968 @ SV309 )
= $false )
| ( ( ~ ( in @ SV968 @ ( setminus @ SV309 @ SV592 ) )
| ~ ( in @ SV968 @ ( setminus @ SV309 @ SV846 ) )
| ( in @ SV968 @ ( setminus @ SV309 @ ( binunion @ SV592 @ SV846 ) ) ) )
= $true )
| ( ( in @ SV846 @ ( powerset @ SV309 ) )
= $false )
| ( ( in @ SV592 @ ( powerset @ SV309 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3456]) ).
thf(3665,plain,
! [SV847: $i,SV598: $i,SV315: $i,SV969: $i] :
( ( ( in @ SV969 @ SV315 )
= $false )
| ( ( ~ ( in @ SV969 @ ( setminus @ SV315 @ ( binunion @ SV598 @ SV847 ) ) )
| ~ ( in @ SV969 @ SV598 ) )
= $true )
| ( ( in @ SV847 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV598 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3457]) ).
thf(3666,plain,
! [SV848: $i,SV316: $i > $o] :
( ( ( ! [SY4045: $i] :
( ~ ( SV316 @ SY4045 )
| ( SV848 = SY4045 ) ) )
= $false )
| ( ( SV316 @ SV848 )
= $false )
| ( ( ~ ! [SY3190: $i] :
~ ! [SY3191: $i] :
~ ( ~ ( ~ ( SV316 @ SY3191 )
| ( SY3191 = SY3190 ) )
| ~ ( ( SY3191 != SY3190 )
| ( SV316 @ SY3191 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3458]) ).
thf(3667,plain,
! [SV849: $i,SV599: $i,SV317: $i,SV970: $i] :
( ( ( in @ SV970 @ ( powerset @ SV317 ) )
= $false )
| ( ( ! [SY4129: $i] :
( ~ ( in @ SY4129 @ ( powerset @ SV317 ) )
| ~ ( subset @ SV599 @ SV970 )
| ~ ( subset @ SV849 @ SY4129 )
| ( subset @ ( binintersect @ SV599 @ SV849 ) @ ( binintersect @ SV970 @ SY4129 ) ) ) )
= $true )
| ( ( in @ SV849 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3459]) ).
thf(3668,plain,
! [SV600: $i,SV850: $i,SV318: $i,SV971: $i] :
( ( ( in @ SV971 @ SV318 )
= $false )
| ( ( ~ ~ ( in @ SV971 @ SV850 )
| ~ ( in @ SV971 @ ( binintersect @ SV600 @ SV850 ) ) )
= $true )
| ( ( in @ SV850 @ ( powerset @ SV318 ) )
= $false )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3460]) ).
thf(3669,plain,
! [SV319: $i,SV601: $i,SV738: $i,SV914: $i > $o] :
( ( ( ~ ( in @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ SV319 ) )
= $false )
| ( ( ! [SY4092: $i] :
( ~ ( in @ SY4092 @ SV738 )
| ( SV914 @ SY4092 ) ) )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3461]) ).
thf(3670,plain,
! [SV319: $i,SV738: $i,SV914: $i > $o,SV601: $i] :
( ( ( ! [SY4148: $i] :
( ~ ( in @ SY4148 @ SV601 )
| ~ ( in @ ( kpair @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ SY4148 ) @ SV738 )
| ( SV914 @ ( kpair @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ SY4148 ) ) ) )
= $false )
| ( ( ! [SY4092: $i] :
( ~ ( in @ SY4092 @ SV738 )
| ( SV914 @ SY4092 ) ) )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3461]) ).
thf(3671,plain,
! [SV915: $i,SV739: $i,SV321: $i,SV603: $o] :
( ( ( ~ SV603 ) = $false )
| ( ( ( if @ SV321 @ SV603 @ SV739 @ SV915 )
= SV915 )
= $true )
| ( ( in @ SV915 @ SV321 )
= $false )
| ( ( in @ SV739 @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3462]) ).
thf(3672,plain,
! [SV916: $i,SV740: $i,SV321: $i] :
( ( ( ~ $true ) = $false )
| ( ( ( if @ SV321 @ $true @ SV740 @ SV916 )
= SV916 )
= $true )
| ( ( in @ SV916 @ SV321 )
= $false )
| ( ( in @ SV740 @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3463]) ).
thf(3673,plain,
! [SV917: $i,SV741: $i,SV321: $i] :
( ( ( ~ $false ) = $false )
| ( ( ( if @ SV321 @ $false @ SV741 @ SV917 )
= SV917 )
= $true )
| ( ( in @ SV917 @ SV321 )
= $false )
| ( ( in @ SV741 @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3464]) ).
thf(3674,plain,
! [SV322: $i,SV851: $i] :
( ( ( ~ ( in @ ( sK51_SY3211 @ SV851 @ SV322 ) @ SV322 )
| ~ ~ ~ ! [SY4130: $i] :
~ ~ ( ~ ( in @ SY4130 @ ( sK51_SY3211 @ SV851 @ SV322 ) )
| ~ ( in @ SY4130 @ SV322 ) ) )
= $false )
| ( ( in @ SV851 @ SV322 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3465]) ).
thf(3675,plain,
! [SV852: $i,SV606: $i,SV325: $i,SV972: $i] :
( ( ( in @ SV972 @ ( powerset @ SV325 ) )
= $false )
| ( ( ~ ( subset @ SV606 @ SV852 )
| ~ ( subset @ SV606 @ SV972 )
| ( subset @ SV606 @ ( binintersect @ SV852 @ SV972 ) ) )
= $true )
| ( ( in @ SV852 @ ( powerset @ SV325 ) )
= $false )
| ( ( in @ SV606 @ ( powerset @ SV325 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3466]) ).
thf(3676,plain,
! [SV759: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ ( sK72_SY3941 @ SV759 @ SV40 ) )
| ( SV759
= ( sK72_SY3941 @ SV759 @ SV40 ) ) )
= $false )
| ( ( SV40 @ SV759 )
= $false )
| ( ( ~ ! [SY2411: $i] :
~ ( SV40 @ SY2411 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3469]) ).
thf(3677,plain,
! [SV760: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK73_SY3942 @ SV760 @ SV42 ) )
| ( SV760
= ( sK73_SY3942 @ SV760 @ SV42 ) ) )
= $false )
| ( ( SV42 @ SV760 )
= $false )
| ( ( SV42
@ ( descr
@ ^ [SY2417: $i] : ( SV42 @ SY2417 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3470]) ).
thf(3678,plain,
! [SV353: $i > $o,SV44: $i,SV991: $i] :
( ( ( ~ ~ ( ~ ( in @ SV991 @ SV44 )
| ~ ( SV353 @ SV991 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( in @ ( sK9_SY3238 @ SV353 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3471]) ).
thf(3679,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ( ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( in @ ( sK36_SY3943 @ SV353 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3472]) ).
thf(3680,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( SV353 @ ( sK9_SY3238 @ SV353 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3473]) ).
thf(3681,plain,
! [SV44: $i,SV353: $i > $o] :
( ( ( SV353 @ ( sK36_SY3943 @ SV353 @ SV44 ) )
= $true )
| ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) )
| ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3474]) ).
thf(3682,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( ( sK9_SY3238 @ SV353 @ SV44 )
= ( sK36_SY3943 @ SV353 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3475]) ).
thf(3683,plain,
! [SV45: $i,SV354: $i,SV612: $i,SV854: $i] :
( ( ( ~ ( in @ ( sK74_SY4050 @ SV854 @ SV612 @ SV354 @ SV45 ) @ SV45 )
| ( ( ap @ SV45 @ SV354 @ SV612 @ ( sK74_SY4050 @ SV854 @ SV612 @ SV354 @ SV45 ) )
= ( ap @ SV45 @ SV354 @ SV854 @ ( sK74_SY4050 @ SV854 @ SV612 @ SV354 @ SV45 ) ) ) )
= $false )
| ( ( SV612 = SV854 )
= $true )
| ( ( in @ SV854 @ ( funcSet @ SV45 @ SV354 ) )
= $false )
| ( ( in @ SV612 @ ( funcSet @ SV45 @ SV354 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3476]) ).
thf(3684,plain,
! [SV923: $i,SV762: $i,SV361: $i,SV52: $i,SV992: $i] :
( ( ( ~ ( in @ SV992 @ SV52 )
| ~ ( in @ SV992 @ ( binintersect @ SV361 @ SV762 ) )
| ( in @ SV992 @ ( binunion @ SV762 @ SV923 ) ) )
= $true )
| ( ( in @ SV923 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV762 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3477]) ).
thf(3685,plain,
! [SV924: $i,SV764: $i,SV365: $i,SV56: $i,SV993: $i] :
( ( ( ~ ( in @ SV993 @ ( powerset @ SV56 ) )
| ( ( setminus @ SV56 @ ( binintersect @ ( binunion @ SV365 @ SV764 ) @ ( binunion @ SV924 @ SV993 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV56 @ SV365 ) @ ( setminus @ SV56 @ SV764 ) ) @ ( binintersect @ ( setminus @ SV56 @ SV924 ) @ ( setminus @ SV56 @ SV993 ) ) ) ) )
= $true )
| ( ( in @ SV924 @ ( powerset @ SV56 ) )
= $false )
| ( ( in @ SV764 @ ( powerset @ SV56 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV56 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3478]) ).
thf(3686,plain,
! [SV57: $i,SV366: $i] :
( ( ( ~ ( in @ SV366 @ ( sK52_SY3265 @ SV57 @ SV366 ) )
| ~ ( in @ ( sK52_SY3265 @ SV57 @ SV366 ) @ SV57 ) )
= $false )
| ( ( in @ SV366 @ ( setunion @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3479]) ).
thf(3687,plain,
! [SV57: $i,SV973: $i,SV366: $i] :
( ( ( ~ ( in @ SV366 @ SV973 )
| ~ ( in @ SV973 @ SV57 ) )
= $true )
| ( ( in @ SV366 @ ( setunion @ SV57 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3480]) ).
thf(3688,plain,
! [SV765: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK75_SY3949 @ SV765 @ SV58 ) )
| ( SV765
= ( sK75_SY3949 @ SV765 @ SV58 ) ) )
= $false )
| ( ( SV58 @ SV765 )
= $false )
| ( ( ! [SY2464: $i,SY2465: $i] :
( ~ ( SV58 @ SY2464 )
| ~ ( SV58 @ SY2465 )
| ( SY2464 = SY2465 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3481]) ).
thf(3689,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) ) )
= $false )
| ( ( ~ ( ( ( sK37_SY3950 @ SV766 @ SV59 )
!= SV766 )
| ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) ) ) )
= $true )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3482]) ).
thf(3690,plain,
! [SV59: $i > $o,SV766: $i] :
( ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( ~ ( ( ( sK37_SY3950 @ SV766 @ SV59 )
!= SV766 )
| ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) ) ) )
= $true )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3482]) ).
thf(3691,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ~ ( SV60 @ ( sK76_SY3951 @ SV767 @ SV60 ) )
| ( SV767
= ( sK76_SY3951 @ SV767 @ SV60 ) ) )
= $false )
| ( ( SV60 @ SV767 )
= $false )
| ( ( ~ ! [SY2472: $i] :
~ ~ ( ~ ( SV60 @ SY2472 )
| ~ ! [SY2473: $i] :
( ~ ( SV60 @ SY2473 )
| ( SY2472 = SY2473 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3483]) ).
thf(3692,plain,
! [SV61: $i,SV367: $i > $o,SV858: $i] :
( ( ( ~ ( ~ ( in @ ( sK59_SY3268 @ SV858 @ SV367 @ SV61 ) @ SV61 )
| ~ ~ ( SV367 @ ( sK59_SY3268 @ SV858 @ SV367 @ SV61 ) ) ) )
= $true )
| ( ( SV367 @ SV858 )
= $true )
| ( ( in @ SV858 @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3484]) ).
thf(3693,plain,
! [SV65: $i,SV371: $i] :
( ( ( ~ ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 )
| ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 ) )
= $false )
| ( ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 )
= $true )
| ( ( SV65 = SV371 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3485]) ).
thf(3694,plain,
! [SV65: $i,SV371: $i] :
( ( ( ~ ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 ) )
= $false )
| ( ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 )
= $false )
| ( ( SV65 = SV371 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3486]) ).
thf(3695,plain,
! [SV65: $i,SV371: $i] :
( ( ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 )
= $false )
| ( ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 )
= $false )
| ( ( SV65 = SV371 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3486]) ).
thf(3696,plain,
! [SV372: $i,SV768: $i,SV68: $i,SV986: $i] :
( ( ( ~ ( in @ SV986 @ SV68 ) )
= $true )
| ( ( ~ ( in @ SV986 @ SV768 )
| ( in @ SV986 @ ( setminus @ SV68 @ SV372 ) ) )
= $true )
| ( ( subset @ SV372 @ ( setminus @ SV68 @ SV768 ) )
= $false )
| ( ( in @ SV768 @ ( powerset @ SV68 ) )
= $false )
| ( ( in @ SV372 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3487]) ).
thf(3697,plain,
! [SV769: $i,SV373: $i,SV69: $i,SV925: $i] :
( ( ( ~ ( in @ SV925 @ ( setminus @ SV69 @ ( binintersect @ SV373 @ SV769 ) ) ) )
= $true )
| ( ( in @ SV925 @ ( binunion @ ( setminus @ SV69 @ SV373 ) @ ( setminus @ SV69 @ SV769 ) ) )
= $true )
| ( ( in @ SV925 @ SV69 )
= $false )
| ( ( in @ SV769 @ ( powerset @ SV69 ) )
= $false )
| ( ( in @ SV373 @ ( powerset @ SV69 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3488]) ).
thf(3698,plain,
! [SV72: $i,SV860: $o,SV376: $i,SV621: $i] :
( ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| SV860 ) )
= $true )
| ( SV860 = $true )
| ( ( SV621 = SV72 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3489]) ).
thf(3699,plain,
! [SV72: $i,SV860: $o,SV376: $i,SV621: $i] :
( ( ( ~ ( in @ SV621 @ SV376 )
| SV860 )
= $false )
| ( SV860 = $true )
| ( SV860 = $false )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3490]) ).
thf(3700,plain,
! [SV72: $i,SV376: $i,SV621: $i] :
( ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( SV621 = SV72 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3491]) ).
thf(3701,plain,
! [SV72: $i,SV376: $i,SV621: $i] :
( ( ( ~ ( in @ SV621 @ SV376 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3492]) ).
thf(3702,plain,
! [SV72: $i,SV376: $i,SV621: $i] :
( ( ( ~ ( ~ ( in @ SV621 @ SV376 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( SV621 = SV72 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3493]) ).
thf(3703,plain,
! [SV72: $i,SV376: $i,SV621: $i] :
( ( ( ~ ( in @ SV621 @ SV376 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3494]) ).
thf(3704,plain,
! [SV772: $i,SV379: $i,SV75: $i,SV926: $i] :
( ( ( ~ ( in @ SV926 @ ( setminus @ SV75 @ ( binunion @ SV379 @ SV772 ) ) ) )
= $true )
| ( ( in @ SV926 @ ( setminus @ SV75 @ SV772 ) )
= $true )
| ( ( in @ SV926 @ SV75 )
= $false )
| ( ( in @ SV772 @ ( powerset @ SV75 ) )
= $false )
| ( ( in @ SV379 @ ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3495]) ).
thf(3705,plain,
! [SV76: $i,SV622: $i,SV380: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK60_SY3750 @ SV380 @ SV622 @ SV76 ) @ SV76 )
| ( SV622
!= ( SV380 @ ( sK60_SY3750 @ SV380 @ SV622 @ SV76 ) ) ) ) )
= $true )
| ( ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3287: $i] : ( SV380 @ SY3287 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3496]) ).
thf(3706,plain,
! [SV380: $i > $i,SV622: $i,SV76: $i,SV987: $i] :
( ( ( ~ ( ~ ( in @ SV987 @ SV76 )
| ( SV622
!= ( SV380 @ SV987 ) ) ) )
= $false )
| ( ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3290: $i] : ( SV380 @ SY3290 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3497]) ).
thf(3707,plain,
! [SV381: $i > $i,SV623: $i,SV77: $i,SV918: $i] :
( ( ( in @ SV918 @ SV77 )
= $false )
| ( ( SV623
!= ( SV381 @ SV918 ) )
= $true )
| ( ( in @ SV623
@ ( image1 @ SV77
@ ^ [SY3293: $i] : ( SV381 @ SY3293 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3498]) ).
thf(3708,plain,
! [SV773: $i,SV382: $i,SV927: $i,SV78: $i,SV994: $i] :
( ( ( ~ ( in @ SV994 @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ SV994 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
| ~ ! [SY4151: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY4151 @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ SY4151 ) @ SV382 ) )
| ~ ( in @ ( kpair @ SY4151 @ SV994 ) @ SV773 ) ) )
= $true )
| ( ( in @ SV927 @ SV78 )
= $false )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3499]) ).
thf(3709,plain,
! [SV774: $i,SV386: $i,SV928: $i,SV82: $i,SV995: $i] :
( ( ( ~ ( in @ SV995 @ SV82 )
| ~ ( in @ ( kpair @ SV928 @ SV995 ) @ ( binunion @ SV386 @ SV774 ) )
| ( in @ ( kpair @ SV928 @ SV995 ) @ SV386 )
| ( in @ ( kpair @ SV928 @ SV995 ) @ SV774 ) )
= $true )
| ( ( in @ SV928 @ SV82 )
= $false )
| ( ( breln1 @ SV82 @ SV774 )
= $false )
| ( ( breln1 @ SV82 @ SV386 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3500]) ).
thf(3710,plain,
! [SV929: $i,SV776: $i,SV86: $i,SV389: $i] :
( ( ( ~ ( subset @ SV389 @ ( setminus @ SV86 @ SV776 ) ) )
= $true )
| ( ( ~ ( in @ SV929 @ SV776 )
| ~ ( in @ SV929 @ SV389 ) )
= $true )
| ( ( in @ SV929 @ SV86 )
= $false )
| ( ( in @ SV776 @ ( powerset @ SV86 ) )
= $false )
| ( ( in @ SV389 @ ( powerset @ SV86 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3501]) ).
thf(3711,plain,
! [SV87: $i,SV930: $i,SV777: $i,SV390: $i] :
( ( ( ~ ( subset @ SV390 @ SV777 ) )
= $true )
| ( ( ~ ~ ( in @ SV930 @ SV777 )
| ~ ( in @ SV930 @ SV390 ) )
= $true )
| ( ( in @ SV930 @ SV87 )
= $false )
| ( ( in @ SV777 @ ( powerset @ SV87 ) )
= $false )
| ( ( in @ SV390 @ ( powerset @ SV87 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3502]) ).
thf(3712,plain,
! [SV931: $i,SV779: $i,SV393: $i,SV90: $i,SV996: $i] :
( ( ( ~ ( in @ SV996 @ SV90 )
| ~ ( in @ SV996 @ ( binintersect @ SV393 @ SV779 ) )
| ( in @ SV996 @ ( binintersect @ ( binunion @ SV393 @ SV931 ) @ ( binunion @ SV779 @ SV931 ) ) ) )
= $true )
| ( ( in @ SV931 @ ( powerset @ SV90 ) )
= $false )
| ( ( in @ SV779 @ ( powerset @ SV90 ) )
= $false )
| ( ( in @ SV393 @ ( powerset @ SV90 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3503]) ).
thf(3713,plain,
! [SV780: $i,SV400: $i,SV99: $i,SV932: $i] :
( ( ( ~ ( in @ SV932 @ ( setminus @ SV99 @ ( binunion @ SV400 @ SV780 ) ) ) )
= $true )
| ( ( in @ SV932 @ ( setminus @ SV99 @ SV400 ) )
= $true )
| ( ( in @ SV932 @ SV99 )
= $false )
| ( ( in @ SV780 @ ( powerset @ SV99 ) )
= $false )
| ( ( in @ SV400 @ ( powerset @ SV99 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3504]) ).
thf(3714,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK53_SY2563 @ SV781 @ SV100 ) ) )
= $false )
| ( ( ~ ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3505]) ).
thf(3715,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK61_SY4131 @ SV781 @ SV100 ) )
| ( ( sK53_SY2563 @ SV781 @ SV100 )
= ( sK61_SY4131 @ SV781 @ SV100 ) ) )
= $false )
| ( ( ~ ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3505]) ).
thf(3716,plain,
! [SV104: $i,SV862: $i,SV404: $i > $o] :
( ( ( ~ ( SV404 @ SV862 ) )
= $false )
| ( ( in @ SV862 @ SV104 )
= $false )
| ( ( ~ ! [SY3324: $i] :
( ~ ( in @ SY3324 @ SV104 )
| ( SV404 @ SY3324 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3507]) ).
thf(3717,plain,
! [SV106: $i] :
( ( ( ~ ( in @ ( sK44_SY2577 @ SV106 ) @ omega )
| ~ ( in @ ( sK44_SY2577 @ SV106 ) @ SV106 ) )
= $false )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( ! [SY2578: $i] :
( ~ ( in @ SY2578 @ omega )
| ( in @ SY2578 @ SV106 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3508]) ).
thf(3718,plain,
! [SV106: $i,SV988: $i] :
( ( ( ~ ( in @ SV988 @ omega ) )
= $true )
| ( ( in @ SV988 @ SV106 )
= $true )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( in @ ( setadjoin @ ( sK44_SY2577 @ SV106 ) @ ( sK44_SY2577 @ SV106 ) ) @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3509]) ).
thf(3719,plain,
! [SV109: $i,SV407: $i,SV782: $i] :
( ( ( ~ ( in @ ( sK62_SY3965 @ SV782 @ SV407 @ SV109 ) @ SV109 ) )
= $false )
| ( ( subset @ SV407 @ SV782 )
= $true )
| ( ( in @ SV782 @ ( powerset @ SV109 ) )
= $false )
| ( ( in @ SV407 @ ( powerset @ SV109 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3510]) ).
thf(3720,plain,
! [SV109: $i,SV407: $i,SV782: $i] :
( ( ( ~ ( in @ ( sK62_SY3965 @ SV782 @ SV407 @ SV109 ) @ SV407 )
| ( in @ ( sK62_SY3965 @ SV782 @ SV407 @ SV109 ) @ SV782 ) )
= $false )
| ( ( subset @ SV407 @ SV782 )
= $true )
| ( ( in @ SV782 @ ( powerset @ SV109 ) )
= $false )
| ( ( in @ SV407 @ ( powerset @ SV109 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3510]) ).
thf(3721,plain,
! [SV110: $i,SV783: $i,SV408: $i,SV933: $i] :
( ( ( ~ ~ ( in @ SV933 @ SV408 ) )
= $true )
| ( ( ~ ( in @ SV933 @ ( binintersect @ SV408 @ SV783 ) ) )
= $true )
| ( ( in @ SV933 @ SV110 )
= $false )
| ( ( in @ SV783 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV408 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3511]) ).
thf(3722,plain,
! [SV784: $i,SV411: $i,SV113: $i,SV934: $i] :
( ( ( ~ ( in @ SV934 @ ( setminus @ SV113 @ SV411 ) ) )
= $true )
| ( ( in @ SV934 @ ( setminus @ SV113 @ ( binintersect @ SV411 @ SV784 ) ) )
= $true )
| ( ( in @ SV934 @ SV113 )
= $false )
| ( ( in @ SV784 @ ( powerset @ SV113 ) )
= $false )
| ( ( in @ SV411 @ ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3512]) ).
thf(3723,plain,
! [SV118: $i,SV416: $i > $o,SV639: $i] :
( ( ( ~ ( in @ ( sK63_SY3768 @ SV639 @ SV416 @ SV118 ) @ SV118 ) )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY3351: $i] : ( SV416 @ SY3351 ) )
= $true )
| ( ( SV416 @ SV639 )
= $false )
| ( ( in @ SV639 @ SV118 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3514]) ).
thf(3724,plain,
! [SV118: $i,SV639: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK63_SY3768 @ SV639 @ SV416 @ SV118 ) )
| ( ( sK63_SY3768 @ SV639 @ SV416 @ SV118 )
= SV639 ) )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY3351: $i] : ( SV416 @ SY3351 ) )
= $true )
| ( ( SV416 @ SV639 )
= $false )
| ( ( in @ SV639 @ SV118 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3514]) ).
thf(3725,plain,
! [SV641: $i > $i,SV419: $i,SV121: $i,SV974: $i] :
( ( ( in @ SV974 @ SV121 )
= $false )
| ( ( ( ap @ SV121 @ SV419
@ ( lam @ SV121 @ SV419
@ ^ [SY3772: $i] : ( SV641 @ SY3772 ) )
@ SV974 )
= ( SV641 @ SV974 ) )
= $true )
| ( ( in @ ( sK24_SY3770 @ SV419 @ SV641 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3516]) ).
thf(3726,plain,
! [SV122: $i,SV420: $i,SV788: $i > $o,SV865: $i > $o] :
( ( ( in @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) @ SV122 )
= $true )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3518]) ).
thf(3727,plain,
! [SV420: $i,SV865: $i > $o,SV788: $i > $o,SV122: $i] :
( ( ( ~ ( in @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) @ SV420 )
| ( ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 )
!= ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
| ~ ( ~ ( ~ ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) )
| ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) ) )
| ~ ( ~ ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
| ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3519]) ).
thf(3728,plain,
! [SV123: $i,SV936: $i,SV789: $i,SV421: $i > $o] :
( ( ( ~ ( SV421 @ SV789 ) )
= $true )
| ( ( ~ ( SV421 @ SV936 )
| ( SV789 = SV936 ) )
= $true )
| ( ( in @ SV936 @ SV123 )
= $false )
| ( ( in @ SV789 @ SV123 )
= $false )
| ( ( ex1 @ SV123
@ ^ [SY3363: $i] : ( SV421 @ SY3363 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3520]) ).
thf(3729,plain,
! [SV423: $i,SV790: $i,SV937: $i,SV125: $i,SV997: $i] :
( ( ( ~ ( in @ SV997 @ SV125 )
| ~ ( in @ ( kpair @ SV937 @ SV997 ) @ SV790 )
| ( in @ ( kpair @ SV937 @ SV997 ) @ ( binunion @ SV423 @ SV790 ) ) )
= $true )
| ( ( in @ SV937 @ SV125 )
= $false )
| ( ( breln1 @ SV125 @ SV790 )
= $false )
| ( ( breln1 @ SV125 @ SV423 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3521]) ).
thf(3730,plain,
! [SV642: $i,SV126: $i,SV866: $i,SV424: $o] :
( ( SV424 = $true )
| ( ( in @ SV866
@ ( dsetconstr @ SV126
@ ^ [SY4056: $i] :
( ~ ( ~ SV424
| ( SY4056 != SV642 ) )
| ~ ( ~ ~ SV424
| ( SY4056 != SV866 ) ) ) ) )
= $true )
| ( ( in @ SV866 @ SV126 )
= $false )
| ( ( in @ SV642 @ SV126 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3522]) ).
thf(3731,plain,
! [SV643: $i,SV126: $i,SV867: $i] :
( ( $true = $true )
| ( ( in @ SV867
@ ( dsetconstr @ SV126
@ ^ [SY4057: $i] :
( ~ ( ~ $true
| ( SY4057 != SV643 ) )
| ~ ( ~ ~ $true
| ( SY4057 != SV867 ) ) ) ) )
= $true )
| ( ( in @ SV867 @ SV126 )
= $false )
| ( ( in @ SV643 @ SV126 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3523]) ).
thf(3732,plain,
! [SV644: $i,SV126: $i,SV868: $i] :
( ( $false = $true )
| ( ( in @ SV868
@ ( dsetconstr @ SV126
@ ^ [SY4058: $i] :
( ~ ( ~ $false
| ( SY4058 != SV644 ) )
| ~ ( ~ ~ $false
| ( SY4058 != SV868 ) ) ) ) )
= $true )
| ( ( in @ SV868 @ SV126 )
= $false )
| ( ( in @ SV644 @ SV126 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3524]) ).
thf(3733,plain,
! [SV792: $i,SV428: $i,SV939: $i,SV131: $i,SV998: $i] :
( ( ( ~ ( in @ SV998 @ SV131 )
| ! [SY4152: $i] :
( ~ ( in @ SY4152 @ SV131 )
| ~ ( in @ ( kpair @ SV939 @ SY4152 ) @ SV428 )
| ~ ( in @ ( kpair @ SY4152 @ SV998 ) @ SV792 )
| ( in @ ( kpair @ SV939 @ SV998 ) @ ( breln1compset @ SV131 @ SV428 @ SV792 ) ) ) )
= $true )
| ( ( in @ SV939 @ SV131 )
= $false )
| ( ( breln1 @ SV131 @ SV792 )
= $false )
| ( ( breln1 @ SV131 @ SV428 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3527]) ).
thf(3734,plain,
! [SV135: $i,SV432: $i,SV794: $i] :
( ( ( ~ ( in @ ( sK64_SY3983 @ SV794 @ SV432 @ SV135 ) @ SV135 ) )
= $false )
| ( ( subset @ SV432 @ SV794 )
= $true )
| ( ( breln1 @ SV135 @ SV794 )
= $false )
| ( ( breln1 @ SV135 @ SV432 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3528]) ).
thf(3735,plain,
! [SV432: $i,SV794: $i,SV135: $i] :
( ( ( ! [SY4149: $i] :
( ~ ( in @ SY4149 @ SV135 )
| ~ ( in @ ( kpair @ ( sK64_SY3983 @ SV794 @ SV432 @ SV135 ) @ SY4149 ) @ SV432 )
| ( in @ ( kpair @ ( sK64_SY3983 @ SV794 @ SV432 @ SV135 ) @ SY4149 ) @ SV794 ) ) )
= $false )
| ( ( subset @ SV432 @ SV794 )
= $true )
| ( ( breln1 @ SV135 @ SV794 )
= $false )
| ( ( breln1 @ SV135 @ SV432 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3528]) ).
thf(3736,plain,
! [SV434: $i,SV869: $i,SV138: $i,SV795: $i] :
( ( ( ~ ( in @ SV795 @ SV138 )
| ( in @ SV869 @ SV434 ) )
= $true )
| ( ( SV795 = SV869 )
= $false )
| ( ( SV138 = SV434 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3531]) ).
thf(3737,plain,
! [SV138: $i,SV795: $i,SV434: $i,SV869: $i] :
( ( ( ~ ( in @ SV869 @ SV434 )
| ( in @ SV795 @ SV138 ) )
= $true )
| ( ( SV795 = SV869 )
= $false )
| ( ( SV138 = SV434 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3532]) ).
thf(3738,plain,
! [SV139: $i,SV796: $i,SV940: $i,SV435: $i] :
( ( ( ~ ( subset @ SV435 @ SV940 ) )
= $true )
| ( ( subset @ ( binintersect @ SV435 @ SV796 ) @ SV940 )
= $true )
| ( ( in @ SV940 @ ( powerset @ SV139 ) )
= $false )
| ( ( in @ SV796 @ ( powerset @ SV139 ) )
= $false )
| ( ( in @ SV435 @ ( powerset @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3533]) ).
thf(3739,plain,
! [SV140: $i,SV436: $i,SV650: $i,SV870: $i] :
( ( ( ~ ( in @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SV140 )
| ! [SY4153: $i] :
( ~ ( in @ SY4153 @ SV436 )
| ~ ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SY4153 ) @ SV650 )
| ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SY4153 ) @ SV870 ) ) )
= $false )
| ( ( ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) )
| ( SV650 = SV870 ) )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3534]) ).
thf(3740,plain,
! [SV654: $i > $i,SV144: $i,SV440: $i,SV975: $i] :
( ( ( in @ SV975 @ ( funcSet @ SV440 @ SV144 ) )
= $false )
| ( ( ~ ! [SY4134: $i] :
( ~ ( in @ SY4134 @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SV975 @ ( SV654 @ SY4134 ) )
= SY4134 ) )
| ( surjective @ SV440 @ SV144 @ SV975 ) )
= $true )
| ( ( in @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) @ SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3535]) ).
thf(3741,plain,
! [SV654: $i > $i,SV941: $i,SV440: $i,SV144: $i] :
( ( ( ~ ! [SY4108: $i] :
( ~ ( in @ SY4108 @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SV941 @ ( SV654 @ SY4108 ) )
= SY4108 ) ) )
= $true )
| ( ( surjective @ SV440 @ SV144 @ SV941 )
= $true )
| ( ( in @ SV941 @ ( funcSet @ SV440 @ SV144 ) )
= $false )
| ( ( in @ ( SV654 @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) ) @ SV440 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3536]) ).
thf(3742,plain,
! [SV442: $i > $o,SV146: $i,SV999: $i] :
( ( ( ~ ~ ( ~ ( in @ SV999 @ SV146 )
| ~ ( SV442 @ SV999 ) ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( in @ ( sK11_SY3407 @ SV442 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3537]) ).
thf(3743,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ( ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) ) )
= $false )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( in @ ( sK38_SY3987 @ SV442 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3538]) ).
thf(3744,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( SV442 @ ( sK11_SY3407 @ SV442 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3539]) ).
thf(3745,plain,
! [SV146: $i,SV442: $i > $o] :
( ( ( SV442 @ ( sK38_SY3987 @ SV442 @ SV146 ) )
= $true )
| ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) )
| ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3540]) ).
thf(3746,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( ( sK11_SY3407 @ SV442 @ SV146 )
= ( sK38_SY3987 @ SV442 @ SV146 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3541]) ).
thf(3747,plain,
! [SV798: $i,SV443: $i,SV147: $i,SV942: $i] :
( ( ( ~ ( in @ SV942 @ ( setminus @ SV147 @ SV443 ) ) )
= $true )
| ( ( ~ ( in @ SV942 @ ( binintersect @ SV443 @ SV798 ) ) )
= $true )
| ( ( in @ SV942 @ SV147 )
= $false )
| ( ( in @ SV798 @ ( powerset @ SV147 ) )
= $false )
| ( ( in @ SV443 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3542]) ).
thf(3748,plain,
! [SV943: $i,SV799: $i,SV444: $i,SV148: $i,SV1000: $i] :
( ( ( ~ ( in @ SV1000 @ SV148 )
| ~ ( in @ SV1000 @ ( binintersect @ SV444 @ SV799 ) )
| ( in @ SV1000 @ ( binunion @ SV444 @ SV943 ) ) )
= $true )
| ( ( in @ SV943 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV799 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV444 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3543]) ).
thf(3749,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3547]) ).
thf(3750,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) ) )
= $false )
| ( ( ~ ( ~ ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
| ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3548]) ).
thf(3751,plain,
! [SV152: $i > $o,SV448: $i > $o] :
( ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( ~ ( ~ ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
| ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3548]) ).
thf(3752,plain,
! [SV873: $i,SV657: $i,SV155: $i,SV451: $o] :
( ( SV451 = $true )
| ( ( ( dsetconstr @ SV155
@ ^ [SY4063: $i] :
( ~ ( ~ SV451
| ( SY4063 != SV657 ) )
| ~ ( ~ ~ SV451
| ( SY4063 != SV873 ) ) ) )
= ( setadjoin @ SV873 @ emptyset ) )
= $true )
| ( ( in @ SV873 @ SV155 )
= $false )
| ( ( in @ SV657 @ SV155 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3549]) ).
thf(3753,plain,
! [SV874: $i,SV658: $i,SV155: $i] :
( ( $true = $true )
| ( ( ( dsetconstr @ SV155
@ ^ [SY4064: $i] :
( ~ ( ~ $true
| ( SY4064 != SV658 ) )
| ~ ( ~ ~ $true
| ( SY4064 != SV874 ) ) ) )
= ( setadjoin @ SV874 @ emptyset ) )
= $true )
| ( ( in @ SV874 @ SV155 )
= $false )
| ( ( in @ SV658 @ SV155 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3550]) ).
thf(3754,plain,
! [SV875: $i,SV659: $i,SV155: $i] :
( ( $false = $true )
| ( ( ( dsetconstr @ SV155
@ ^ [SY4065: $i] :
( ~ ( ~ $false
| ( SY4065 != SV659 ) )
| ~ ( ~ ~ $false
| ( SY4065 != SV875 ) ) ) )
= ( setadjoin @ SV875 @ emptyset ) )
= $true )
| ( ( in @ SV875 @ SV155 )
= $false )
| ( ( in @ SV659 @ SV155 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3551]) ).
thf(3755,plain,
! [SV157: $i,SV453: $i,SV945: $i,SV802: $i] :
( ( ( ~ ( in @ ( kpair @ SV802 @ SV945 ) @ SV453 ) )
= $true )
| ( ( in @ ( kpair @ SV945 @ SV802 ) @ ( breln1invset @ SV157 @ SV453 ) )
= $true )
| ( ( in @ SV945 @ SV157 )
= $false )
| ( ( in @ SV802 @ SV157 )
= $false )
| ( ( breln1 @ SV157 @ SV453 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3552]) ).
thf(3756,plain,
! [SV163: $i,SV459: $i,SV946: $i,SV804: $i] :
( ( ( ~ ( subset @ SV804 @ SV946 ) )
= $true )
| ( ( subset @ ( binintersect @ SV459 @ SV804 ) @ SV946 )
= $true )
| ( ( in @ SV946 @ ( powerset @ SV163 ) )
= $false )
| ( ( in @ SV804 @ ( powerset @ SV163 ) )
= $false )
| ( ( in @ SV459 @ ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3553]) ).
thf(3757,plain,
! [SV168: $i,SV464: $i,SV666: $i,SV877: $i] :
( ( ( ~ ( in @ ( sK79_SY4066 @ SV877 @ SV666 @ SV464 @ SV168 ) @ SV168 )
| ! [SY4154: $i] :
( ~ ( in @ SY4154 @ SV464 )
| ~ ( in @ ( kpair @ ( sK79_SY4066 @ SV877 @ SV666 @ SV464 @ SV168 ) @ SY4154 ) @ SV666 )
| ( in @ ( kpair @ ( sK79_SY4066 @ SV877 @ SV666 @ SV464 @ SV168 ) @ SY4154 ) @ SV877 ) ) )
= $false )
| ( ( subset @ SV666 @ SV877 )
= $true )
| ( ( breln @ SV168 @ SV464 @ SV877 )
= $false )
| ( ( breln @ SV168 @ SV464 @ SV666 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3555]) ).
thf(3758,plain,
! [SV175: $i,SV470: $i > $i,SV976: $i] :
( ( ~ ( ~ ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
| ~ ! [SY4135: $i] :
~ ~ ( ~ ( in @ SY4135 @ SV175 )
| ( SV976
!= ( SV470 @ SY4135 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3558]) ).
thf(3759,plain,
! [SV470: $i > $i,SV976: $i,SV175: $i] :
( ( ~ ( ~ ~ ! [SY4136: $i] :
~ ~ ( ~ ( in @ SY4136 @ SV175 )
| ( SV976
!= ( SV470 @ SY4136 ) ) )
| ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3558]) ).
thf(3760,plain,
! [SV470: $i > $i,SV175: $i,SV977: $i] :
( ( ( ! [SY4137: $i] :
~ ( ~ ( ~ ( in @ SY4137 @ SV977 )
| ~ ! [SY3468: $i] :
~ ~ ( ~ ( in @ SY3468 @ SV175 )
| ( SY4137
!= ( SV470 @ SY3468 ) ) ) )
| ~ ( ~ ~ ! [SY3469: $i] :
~ ~ ( ~ ( in @ SY3469 @ SV175 )
| ( SY4137
!= ( SV470 @ SY3469 ) ) )
| ( in @ SY4137 @ SV977 ) ) ) )
= $false )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3559]) ).
thf(3761,plain,
! [SV670: $i > $i > $o,SV180: $i,SV475: $i,SV978: $i] :
( ( ( in @ SV978 @ ( breln1Set @ SV475 ) )
= $false )
| ( ( ~ ( reflwellordering @ SV475 @ SV978 )
| ! [SY4140: $i] :
( ~ ( in @ SY4140 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY4141: $i] :
~ ( ~ ( SV670 @ SY4140 @ SY4141 )
| ~ ! [SY4142: $i] :
( ~ ( in @ SY4142 @ SV475 )
| ~ ( SV670 @ SY4140 @ SY4142 )
| ( in @ ( kpair @ SY4141 @ SY4142 ) @ SV978 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3560]) ).
thf(3762,plain,
! [SV180: $i,SV670: $i > $i > $o,SV475: $i,SV979: $i] :
( ( ( ~ ( in @ SV979 @ SV475 )
| ~ ( SV670 @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV979 ) )
= $true )
| ( ( ! [SY3807: $i] :
( ~ ( in @ SY3807 @ ( breln1Set @ SV475 ) )
| ~ ( reflwellordering @ SV475 @ SY3807 )
| ! [SY3808: $i] :
( ~ ( in @ SY3808 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY3809: $i] :
~ ( ~ ( SV670 @ SY3808 @ SY3809 )
| ~ ! [SY3810: $i] :
( ~ ( in @ SY3810 @ SV475 )
| ~ ( SV670 @ SY3808 @ SY3810 )
| ( in @ ( kpair @ SY3809 @ SY3810 ) @ SY3807 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3561]) ).
thf(3763,plain,
! [SV672: $i > $i,SV477: $i,SV182: $i,SV980: $i] :
( ( ( in @ SV980 @ SV182 )
= $false )
| ( ( ( ap @ SV182 @ SV477
@ ( lam @ SV182 @ SV477
@ ^ [SY3814: $i] : ( SV672 @ SY3814 ) )
@ SV980 )
= ( SV672 @ SV980 ) )
= $true )
| ( ( in @ ( sK30_SY3812 @ SV477 @ SV672 @ SV182 ) @ SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3562]) ).
thf(3764,plain,
! [SV186: $i,SV950: $i,SV812: $i,SV481: $i] :
( ( ( ~ ( in @ SV481 @ ( powerset @ SV812 ) ) )
= $true )
| ( ( ~ ( in @ SV950 @ SV481 )
| ( in @ SV950 @ SV812 ) )
= $true )
| ( ( in @ SV950 @ SV186 )
= $false )
| ( ( in @ SV812 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV481 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3564]) ).
thf(3765,plain,
! [SV189: $i,SV484: $i > $o,SV879: $i] :
( ( ( ~ ( ~ ( in @ ( sK65_SY3497 @ SV879 @ SV484 @ SV189 ) @ SV189 )
| ~ ~ ( SV484 @ ( sK65_SY3497 @ SV879 @ SV484 @ SV189 ) ) ) )
= $true )
| ( ( SV484 @ SV879 )
= $true )
| ( ( in @ SV879 @ SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3567]) ).
thf(3766,plain,
! [SV485: $i,SV190: $i,SV813: $o] :
( ( ( in @ ( sK46_SY4001 @ SV813 @ SV190 @ SV485 ) @ SV190 )
= $true )
| ( SV813 = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3569]) ).
thf(3767,plain,
! [SV485: $i,SV190: $i] :
( ( ( in @ ( sK47_SX0 @ SV190 @ SV485 ) @ SV190 )
= $true )
| ( $true = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3572]) ).
thf(3768,plain,
! [SV485: $i,SV190: $i] :
( ( ( in @ ( sK48_SX0 @ SV190 @ SV485 ) @ SV190 )
= $true )
| ( $false = $true )
| ( ( in @ SV485 @ ( setunion @ SV190 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3575]) ).
thf(3769,plain,
! [SV191: $i,SV676: $i,SV880: $i,SV486: $i,SV981: $i] :
( ( ( in @ SV981 @ SV486 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV880 @ SV981 ) @ SV676 )
| ( ( ap @ SV191 @ SV486 @ SV676 @ SV880 )
= SV981 ) )
= $true )
| ( ( in @ SV880 @ SV191 )
= $false )
| ( ( in @ SV676 @ ( funcSet @ SV191 @ SV486 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3577]) ).
thf(3770,plain,
! [SV193: $i,SV488: $i > $i,SV881: $i] :
( ( ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
= $false )
| ( ( ~ ! [SY4070: $i] :
~ ~ ( ~ ( in @ SY4070 @ SV193 )
| ( SV881
!= ( SV488 @ SY4070 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3578]) ).
thf(3771,plain,
! [SV488: $i > $i,SV881: $i,SV193: $i] :
( ( ( ~ ! [SY4071: $i] :
~ ~ ( ~ ( in @ SY4071 @ SV193 )
| ( SV881
!= ( SV488 @ SY4071 ) ) ) )
= $false )
| ( ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3579]) ).
thf(3772,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ ( sK80_SY4002 @ SV816 @ SV196 ) )
| ( SV816
= ( sK80_SY4002 @ SV816 @ SV196 ) ) )
= $false )
| ( ( SV196 @ SV816 )
= $false )
| ( ( ~ ! [SY2855: $i] :
~ ~ ( ~ ( SV196 @ SY2855 )
| ~ ! [SY2856: $i] :
( ~ ( SV196 @ SY2856 )
| ( SY2855 = SY2856 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3581]) ).
thf(3773,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3582]) ).
thf(3774,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3583]) ).
thf(3775,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) ) )
= $false )
| ( ( ~ ( ~ ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
| ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3584]) ).
thf(3776,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( ~ ( ~ ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
| ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3584]) ).
thf(3777,plain,
! [SV199: $i,SV492: $i,SV679: $i] :
( ( ( in @ ( sK39_SY3820 @ SV679 @ SV492 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3585]) ).
thf(3778,plain,
! [SV199: $i,SV679: $i,SV492: $i] :
( ( ( ~ ! [SY4093: $i] :
~ ~ ( ~ ( in @ SY4093 @ SV492 )
| ( SV679
!= ( kpair @ ( sK39_SY3820 @ SV679 @ SV492 @ SV199 ) @ SY4093 ) ) ) )
= $true )
| ( ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3586]) ).
thf(3779,plain,
! [SV200: $i,SV817: $i,SV493: $i,SV951: $i] :
( ( ( ~ ~ ( in @ SV951 @ ( binunion @ SV493 @ SV817 ) ) )
= $true )
| ( ( ~ ( in @ SV951 @ SV817 ) )
= $true )
| ( ( in @ SV951 @ SV200 )
= $false )
| ( ( in @ SV817 @ ( powerset @ SV200 ) )
= $false )
| ( ( in @ SV493 @ ( powerset @ SV200 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3587]) ).
thf(3780,plain,
! [SV885: $o,SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SV885 ) )
= $true )
| ( SV885 = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3588]) ).
thf(3781,plain,
! [SV885: $o,SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SV885 )
| SV885 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3589]) ).
thf(3782,plain,
! [SV885: $o,SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SV885 ) )
= $true )
| ( SV885 = $true )
| ( SV885 = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3590]) ).
thf(3783,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3591]) ).
thf(3784,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $true )
| $true )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3592]) ).
thf(3785,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3593]) ).
thf(3786,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3594]) ).
thf(3787,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $false )
| $false )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3595]) ).
thf(3788,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3596]) ).
thf(3789,plain,
! [SV207: $i,SV500: $i > $o] :
( ( ( in @ ( sK40_SY3540 @ SV500 @ SV207 ) @ SV207 )
= $true )
| ( ( ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SV207 )
| ~ ( SV500 @ SY3541 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3597]) ).
thf(3790,plain,
! [SV207: $i,SV500: $i > $o] :
( ( ( SV500 @ ( sK40_SY3540 @ SV500 @ SV207 ) )
= $true )
| ( ( ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SV207 )
| ~ ( SV500 @ SY3541 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3598]) ).
thf(3791,plain,
! [SV952: $o,SV818: $i,SV501: $i,SV208: $i,SV982: $i] :
( ( ( in @ SV982 @ SV208 )
= $false )
| ( ( ~ ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
| ~ ( ~ ( in @ SV982 @ SV501 )
| SV952 )
| ~ ( ~ ( in @ SV982 @ SV818 )
| SV952 )
| SV952 )
= $true )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3599]) ).
thf(3792,plain,
! [SV818: $i,SV501: $i,SV208: $i,SV983: $i] :
( ( ( in @ SV983 @ SV208 )
= $false )
| ( ( ~ ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
| ~ ( ~ ( in @ SV983 @ SV501 )
| $true )
| ~ ( ~ ( in @ SV983 @ SV818 )
| $true )
| $true )
= $true )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3600]) ).
thf(3793,plain,
! [SV818: $i,SV501: $i,SV208: $i,SV984: $i] :
( ( ( in @ SV984 @ SV208 )
= $false )
| ( ( ~ ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
| ~ ( ~ ( in @ SV984 @ SV501 )
| $false )
| ~ ( ~ ( in @ SV984 @ SV818 )
| $false )
| $false )
= $true )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3601]) ).
thf(3794,plain,
! [SV209: $i,SV502: $i,SV689: $i,SV889: $i > $o] :
( ( ( in @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ SV209 )
= $true )
| ( ( ! [SY4074: $i] :
( ~ ( in @ SY4074 @ SV689 )
| ( SV889 @ SY4074 ) ) )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3602]) ).
thf(3795,plain,
! [SV502: $i,SV889: $i > $o,SV689: $i,SV209: $i] :
( ( ( ~ ( in @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) @ SV502 )
| ~ ( in @ ( kpair @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) ) @ SV689 )
| ( SV889 @ ( kpair @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) ) ) )
= $false )
| ( ( ! [SY4074: $i] :
( ~ ( in @ SY4074 @ SV689 )
| ( SV889 @ SY4074 ) ) )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3603]) ).
thf(3796,plain,
! [SV819: $i,SV508: $i,SV953: $i,SV216: $i,SV1001: $i] :
( ( ( ~ ( in @ SV1001 @ SV216 )
| ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
| ! [SY4155: $o] :
( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
| SY4155 )
| ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| SY4155 )
| SY4155 ) )
= $true )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3607]) ).
thf(3797,plain,
! [SV820: $i,SV509: $i,SV217: $i,SV954: $i] :
( ( ( ~ ( in @ SV954 @ ( setminus @ SV217 @ ( binunion @ SV509 @ SV820 ) ) ) )
= $true )
| ( ( in @ SV954 @ ( binintersect @ ( setminus @ SV217 @ SV509 ) @ ( setminus @ SV217 @ SV820 ) ) )
= $true )
| ( ( in @ SV954 @ SV217 )
= $false )
| ( ( in @ SV820 @ ( powerset @ SV217 ) )
= $false )
| ( ( in @ SV509 @ ( powerset @ SV217 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3608]) ).
thf(3798,plain,
! [SV218: $i,SV696: $i,SV510: $i > $i] :
( ( ( in @ ( sK41_SY3843 @ SV510 @ SV696 @ SV218 ) @ SV218 )
= $true )
| ( ( in @ SV696
@ ( image1 @ SV218
@ ^ [SY3564: $i] : ( SV510 @ SY3564 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3609]) ).
thf(3799,plain,
! [SV218: $i,SV510: $i > $i,SV696: $i] :
( ( ( SV696
= ( SV510 @ ( sK41_SY3843 @ SV510 @ SV696 @ SV218 ) ) )
= $true )
| ( ( in @ SV696
@ ( image1 @ SV218
@ ^ [SY3564: $i] : ( SV510 @ SY3564 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3610]) ).
thf(3800,plain,
! [SV226: $i] :
( ( ~ ! [SY3851: $i] :
( ~ ( in @ SY3851 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY2945: $i] :
( ~ ( in @ SY2945 @ SY3851 )
| ( in @ SY2945 @ SV226 ) ) )
| ~ ! [SY3853: $i,SY3854: $i] :
( ~ ~ ( ~ ( in @ SY3853 @ SV226 )
| ~ ( in @ SY3854 @ SV226 ) )
| ~ ! [SY3855: $i] :
( ~ ( in @ SY3855 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SY3853 @ SY3855 )
| ( in @ SY3854 @ SY3855 ) )
| ~ ( ~ ( in @ SY3854 @ SY3855 )
| ( in @ SY3853 @ SY3855 ) ) ) )
| ( SY3853 = SY3854 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3611]) ).
thf(3801,plain,
! [SV226: $i,SV1002: $i] :
( ( ! [SY4156: $i] :
( ~ ~ ( ~ ( in @ SV1002 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4156 @ ( sK2_SY2943 @ SV226 ) ) )
| ! [SY4157: $i] :
( ~ ( in @ SY4157 @ SV1002 )
| ( in @ SY4157 @ SY4156 ) )
| ! [SY4158: $i] :
( ~ ( in @ SY4158 @ SY4156 )
| ( in @ SY4158 @ SV1002 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3612]) ).
thf(3802,plain,
! [SV226: $i,SV955: $i] :
( ( ( ~ ! [SY4114: $i] :
( ~ ( in @ SY4114 @ SV955 )
| ( in @ SY4114 @ SV226 ) )
| ~ ~ ! [SY4115: $i] :
~ ( in @ SY4115 @ SV955 ) )
= $true )
| ( ( ~ ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3613]) ).
thf(3803,plain,
! [SV703: $i > $i > $o,SV517: $i,SV227: $i,SV920: $i,SV752: $i] :
( ( ( in @ ( kpair @ SV752 @ SV920 )
@ ( dpsetconstr @ SV227 @ SV517
@ ^ [SY3870: $i,SY3871: $i] : ( SV703 @ SY3870 @ SY3871 ) ) )
= $false )
| ( ( SV703 @ SV752 @ SV920 )
= $true )
| ( ( in @ SV920 @ SV517 )
= $false )
| ( ( in @ SV752 @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3614]) ).
thf(3804,plain,
! [SV229: $i,SV822: $i,SV519: $i,SV956: $i] :
( ( ( ~ ~ ( in @ SV956 @ ( binunion @ SV519 @ SV822 ) ) )
= $true )
| ( ( ~ ( in @ SV956 @ SV519 ) )
= $true )
| ( ( in @ SV956 @ SV229 )
= $false )
| ( ( in @ SV822 @ ( powerset @ SV229 ) )
= $false )
| ( ( in @ SV519 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3615]) ).
thf(3805,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1003: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
| ~ ! [SY4159: $i] :
~ ~ ( ~ ( in @ SY4159 @ SV520 )
| ~ ( SV230 @ SY4159 @ SV1003 ) ) )
| ~ ( ~ ~ ! [SY4160: $i] :
~ ~ ( ~ ( in @ SY4160 @ SV520 )
| ~ ( SV230 @ SY4160 @ SV1003 ) )
| ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) ) ) ) )
= $true )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3616]) ).
thf(3806,plain,
! [SV957: $i,SV520: $i,SV230: $i > $i > $o] :
( ( ( ~ ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 ) )
= $true )
| ( ( ~ ! [SY4121: $i] :
( ~ ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SY4121 )
| ( SV957 = SY4121 ) ) )
= $true )
| ( ( ~ ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3617]) ).
thf(3807,plain,
! [SV231: $i,SV521: $i,SV705: $i,SV896: $i] :
( ( ( ~ ( in @ ( sK82_SY4081 @ SV896 @ SV705 @ SV521 @ SV231 ) @ SV231 )
| ( ( ap @ SV231 @ SV521 @ SV705 @ ( sK82_SY4081 @ SV896 @ SV705 @ SV521 @ SV231 ) )
= ( ap @ SV231 @ SV521 @ SV896 @ ( sK82_SY4081 @ SV896 @ SV705 @ SV521 @ SV231 ) ) ) )
= $false )
| ( ( SV705 = SV896 )
= $true )
| ( ( func @ SV231 @ SV521 @ SV896 )
= $false )
| ( ( func @ SV231 @ SV521 @ SV705 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3618]) ).
thf(3808,plain,
! [SV233: $i,SV823: $i > $o,SV523: $i,SV1004: $i] :
( ( ( ~ ( in @ SV1004 @ SV523 )
| ( SV823 @ SV1004 ) )
= $true )
| ( ( in @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ SV233 )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3622]) ).
thf(3809,plain,
! [SV233: $i,SV823: $i > $o,SV523: $i] :
( ( ( ~ ( in @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) @ SV233 ) )
= $false )
| ( ( ! [SY4016: $i] :
( ~ ( in @ SY4016 @ SV523 )
| ( SV823 @ SY4016 ) ) )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3623]) ).
thf(3810,plain,
! [SV233: $i,SV523: $i,SV823: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) ) @ SV523 )
| ( SV823 @ ( kpair @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) ) ) )
= $false )
| ( ( ! [SY4016: $i] :
( ~ ( in @ SY4016 @ SV523 )
| ( SV823 @ SY4016 ) ) )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3623]) ).
thf(3811,plain,
! [SV245: $i,SV901: $i,SV533: $i > $o] :
( ( ( SV533 @ SV901 )
= $false )
| ( ( in @ SV901 @ SV245 )
= $false )
| ( ( ( ( dsetconstr @ SV245
@ ^ [SY3609: $i] : ( SV533 @ SY3609 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3627]) ).
thf(3812,plain,
! [SV535: $i,SV247: $i,SV827: $i,SV959: $i] :
( ( ( ~ ( in @ ( kpair @ SV959 @ SV827 ) @ ( breln1invset @ SV247 @ SV535 ) ) )
= $true )
| ( ( in @ ( kpair @ SV827 @ SV959 ) @ SV535 )
= $true )
| ( ( in @ SV959 @ SV247 )
= $false )
| ( ( in @ SV827 @ SV247 )
= $false )
| ( ( breln1 @ SV247 @ SV535 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3628]) ).
thf(3813,plain,
! [SV251: $i,SV828: $i,SV538: $i,SV960: $i] :
( ( ( ~ ~ ( in @ SV960 @ SV538 ) )
= $true )
| ( ( ~ ~ ( in @ SV960 @ SV828 )
| ~ ( in @ SV960 @ ( binunion @ SV538 @ SV828 ) ) )
= $true )
| ( ( in @ SV960 @ SV251 )
= $false )
| ( ( in @ SV828 @ ( powerset @ SV251 ) )
= $false )
| ( ( in @ SV538 @ ( powerset @ SV251 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3629]) ).
thf(3814,plain,
! [SV259: $i,SV719: $i,SV908: $i,SV548: $i,SV985: $i] :
( ( ( in @ SV985 @ SV548 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV908 @ SV985 ) @ SV719 )
| ( ( ap @ SV259 @ SV548 @ SV719 @ SV908 )
= SV985 ) )
= $true )
| ( ( in @ SV908 @ SV259 )
= $false )
| ( ( func @ SV259 @ SV548 @ SV719 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3633]) ).
thf(3815,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SV260 ) )
= $false )
| ( ( ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) )
| ( SV549 = SV829 ) )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3634]) ).
thf(3816,plain,
! [SV549: $i,SV829: $i,SV260: $i] :
( ( ( ! [SY4150: $i] :
( ~ ( in @ SY4150 @ SV260 )
| ~ ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SY4150 ) @ SV549 )
| ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SY4150 ) @ SV829 ) ) )
= $false )
| ( ( ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) )
| ( SV549 = SV829 ) )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3634]) ).
thf(3817,plain,
! [SV830: $i,SV553: $i,SV961: $i,SV264: $i,SV1005: $i] :
( ( ( ~ ( in @ SV1005 @ SV264 )
| ~ ( ( in @ ( kpair @ SV961 @ SV1005 ) @ SV553 )
| ( in @ ( kpair @ SV961 @ SV1005 ) @ SV830 ) )
| ( in @ ( kpair @ SV961 @ SV1005 ) @ ( binunion @ SV553 @ SV830 ) ) )
= $true )
| ( ( in @ SV961 @ SV264 )
= $false )
| ( ( breln1 @ SV264 @ SV830 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3635]) ).
thf(3818,plain,
! [SV271: $i,SV833: $i > $o,SV559: $i,SV1006: $i] :
( ( ( ~ ( in @ SV1006 @ SV559 )
| ( SV833 @ SV1006 ) )
= $true )
| ( ( in @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ SV271 )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3636]) ).
thf(3819,plain,
! [SV271: $i,SV833: $i > $o,SV559: $i] :
( ( ( ~ ( in @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) @ SV271 ) )
= $false )
| ( ( ! [SY4028: $i] :
( ~ ( in @ SY4028 @ SV559 )
| ( SV833 @ SY4028 ) ) )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3637]) ).
thf(3820,plain,
! [SV271: $i,SV559: $i,SV833: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) ) @ SV559 )
| ( SV833 @ ( kpair @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) ) ) )
= $false )
| ( ( ! [SY4028: $i] :
( ~ ( in @ SY4028 @ SV559 )
| ( SV833 @ SY4028 ) ) )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3637]) ).
thf(3821,plain,
! [SV563: $i > $o,SV275: $i,SV989: $i] :
( ( ( ~ ( ~ ( in @ SV989 @ SV275 )
| ~ ( SV563 @ SV989 ) ) )
= $false )
| ( ( in @ ( sK16_SY3653 @ SV563 @ SV275 ) @ SV275 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3638]) ).
thf(3822,plain,
! [SV563: $i > $o,SV275: $i,SV990: $i] :
( ( ( ~ ( ~ ( in @ SV990 @ SV275 )
| ~ ( SV563 @ SV990 ) ) )
= $false )
| ( ( SV563 @ ( sK16_SY3653 @ SV563 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3639]) ).
thf(3823,plain,
! [SV835: $i,SV565: $i,SV277: $i,SV962: $i] :
( ( ( ~ ( in @ SV962 @ ( setminus @ SV277 @ ( binunion @ SV565 @ SV835 ) ) ) )
= $true )
| ( ( in @ SV962 @ ( setminus @ SV277 @ SV565 ) )
= $true )
| ( ( in @ SV962 @ SV277 )
= $false )
| ( ( in @ SV835 @ ( powerset @ SV277 ) )
= $false )
| ( ( in @ SV565 @ ( powerset @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3640]) ).
thf(3824,plain,
! [SV566: $i,SV278: $i] :
( ( ( ~ ( in @ ( sK69_SY3658 @ SV278 @ SV566 ) @ SV566 ) )
= $false )
| ( ( SV278 = SV566 )
= $true )
| ( ( in @ ( sK17_SY3657 @ SV566 @ SV278 ) @ SV278 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3641]) ).
thf(3825,plain,
! [SV566: $i,SV278: $i] :
( ( ( in @ ( sK69_SY3658 @ SV278 @ SV566 ) @ SV278 )
= $false )
| ( ( SV278 = SV566 )
= $true )
| ( ( in @ ( sK17_SY3657 @ SV566 @ SV278 ) @ SV278 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3641]) ).
thf(3826,plain,
! [SV566: $i,SV278: $i] :
( ( ( in @ ( sK57_SY3658 @ SV278 @ SV566 ) @ SV566 )
= $true )
| ( ( SV278 = SV566 )
= $true )
| ( ( in @ ( sK17_SY3657 @ SV566 @ SV278 ) @ SV566 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3642]) ).
thf(3827,plain,
! [SV836: $i,SV568: $i,SV963: $i,SV280: $i,SV1007: $i] :
( ( ( ~ ( in @ SV1007 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
| ! [SY4161: $o] :
( ~ ! [SY4162: $i] :
( ~ ( in @ SY4162 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SY4162 ) @ SV568 )
| ~ ( in @ ( kpair @ SY4162 @ SV1007 ) @ SV836 )
| SY4161 )
| SY4161 ) )
= $true )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3644]) ).
thf(3828,plain,
! [SV284: $i,SV572: $i] :
( ( ( in @ ( sK42_SY3668 @ SV572 @ SV284 ) @ SV284 )
= $true )
| ( ( ( binintersect @ SV284 @ SV572 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3645]) ).
thf(3829,plain,
! [SV284: $i,SV572: $i] :
( ( ( in @ ( sK42_SY3668 @ SV572 @ SV284 ) @ SV572 )
= $true )
| ( ( ( binintersect @ SV284 @ SV572 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3646]) ).
thf(3830,plain,
! [SV837: $i,SV288: $i > $o] :
( ( ( ~ ( SV288 @ ( sK83_SY4034 @ SV837 @ SV288 ) )
| ( SV837
= ( sK83_SY4034 @ SV837 @ SV288 ) ) )
= $false )
| ( ( SV288 @ SV837 )
= $false )
| ( ( ! [SY3119: $i,SY3120: $i] :
( ~ ( SV288 @ SY3119 )
| ~ ( SV288 @ SY3120 )
| ( SY3119 = SY3120 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3647]) ).
thf(3831,plain,
! [SV289: $i,SV575: $i > $o] :
( ( ( in @ ( sK43_SY3670 @ SV575 @ SV289 ) @ SV289 )
= $true )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV289 )
| ~ ( SV575 @ SY3671 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3648]) ).
thf(3832,plain,
! [SV289: $i,SV575: $i > $o] :
( ( ( SV575 @ ( sK43_SY3670 @ SV575 @ SV289 ) )
= $true )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV289 )
| ~ ( SV575 @ SY3671 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3649]) ).
thf(3833,plain,
! [SV579: $i,SV293: $i,SV922: $i,SV755: $i,SV732: $i > $i > $o] :
( ( ( SV732 @ SV755 @ SV922 )
= $false )
| ( ( in @ ( kpair @ SV755 @ SV922 )
@ ( dpsetconstr @ SV293 @ SV579
@ ^ [SY3897: $i,SY3898: $i] : ( SV732 @ SY3897 @ SY3898 ) ) )
= $true )
| ( ( in @ SV922 @ SV579 )
= $false )
| ( ( in @ SV755 @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3650]) ).
thf(3834,plain,
! [SV298: $i,SV757: $o,SV583: $i,SV733: $i] :
( ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| SV757 ) )
= $true )
| ( SV757 = $true )
| ( ( in @ SV733 @ SV298 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3651]) ).
thf(3835,plain,
! [SV298: $i,SV757: $o,SV583: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV583 )
| SV757 )
= $false )
| ( SV757 = $true )
| ( SV757 = $false )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3652]) ).
thf(3836,plain,
! [SV298: $i,SV583: $i,SV733: $i] :
( ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV733 @ SV298 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3653]) ).
thf(3837,plain,
! [SV298: $i,SV583: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV583 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3654]) ).
thf(3838,plain,
! [SV298: $i,SV583: $i,SV733: $i] :
( ( ( ~ ( ~ ( in @ SV733 @ SV583 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV733 @ SV298 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3655]) ).
thf(3839,plain,
! [SV298: $i,SV583: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV583 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3656]) ).
thf(3840,plain,
! [SV299: $i,SV584: $i,SV840: $i] :
( ( ( ~ ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV299 ) )
= $false )
| ( ( ~ ! [SY4036: $i] :
( ~ ( in @ SY4036 @ SV299 )
| ~ ( in @ SY4036 @ SV840 )
| ( in @ SY4036 @ SV584 ) )
| ( SV584 = SV840 ) )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3657]) ).
thf(3841,plain,
! [SV299: $i,SV584: $i,SV840: $i] :
( ( ( ~ ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV584 )
| ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV840 ) )
= $false )
| ( ( ~ ! [SY4036: $i] :
( ~ ( in @ SY4036 @ SV299 )
| ~ ( in @ SY4036 @ SV840 )
| ( in @ SY4036 @ SV584 ) )
| ( SV584 = SV840 ) )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3657]) ).
thf(3842,plain,
! [SV841: $i,SV585: $i,SV964: $i,SV300: $i,SV1008: $i] :
( ( ( ~ ( in @ SV1008 @ SV300 )
| ~ ( in @ ( kpair @ SV964 @ SV1008 ) @ SV585 )
| ( in @ ( kpair @ SV964 @ SV1008 ) @ ( binunion @ SV585 @ SV841 ) ) )
= $true )
| ( ( in @ SV964 @ SV300 )
= $false )
| ( ( breln1 @ SV300 @ SV841 )
= $false )
| ( ( breln1 @ SV300 @ SV585 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3658]) ).
thf(3843,plain,
! [SV301: $i,SV586: $i,SV734: $i,SV911: $i] :
( ( ( ~ ( in @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) @ SV301 )
| ( ( ap @ SV301 @ SV586 @ SV734 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) )
= ( ap @ SV301 @ SV586 @ SV911 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) ) ) )
= $false )
| ( ( ! [SY4088: $i] :
( ~ ( in @ SY4088 @ SV301 )
| ! [SY4089: $i] :
( ~ ( in @ SY4089 @ SV586 )
| ~ ( in @ ( kpair @ SY4088 @ SY4089 ) @ SV911 )
| ( in @ ( kpair @ SY4088 @ SY4089 ) @ SV734 ) ) ) )
= $true )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3659]) ).
thf(3844,plain,
! [SV842: $i,SV587: $i,SV302: $i,SV965: $i] :
( ( ( ~ ( in @ SV965 @ ( binunion @ ( setminus @ SV302 @ SV587 ) @ ( setminus @ SV302 @ SV842 ) ) ) )
= $true )
| ( ( in @ SV965 @ ( setminus @ SV302 @ ( binintersect @ SV587 @ SV842 ) ) )
= $true )
| ( ( in @ SV965 @ SV302 )
= $false )
| ( ( in @ SV842 @ ( powerset @ SV302 ) )
= $false )
| ( ( in @ SV587 @ ( powerset @ SV302 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3660]) ).
thf(3845,plain,
! [SV844: $i,SV590: $i,SV307: $i,SV967: $i] :
( ( ( ~ ( in @ SV967 @ ( binintersect @ ( setminus @ SV307 @ SV590 ) @ ( setminus @ SV307 @ SV844 ) ) ) )
= $true )
| ( ( in @ SV967 @ ( setminus @ SV307 @ ( binunion @ SV590 @ SV844 ) ) )
= $true )
| ( ( in @ SV967 @ SV307 )
= $false )
| ( ( in @ SV844 @ ( powerset @ SV307 ) )
= $false )
| ( ( in @ SV590 @ ( powerset @ SV307 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3662]) ).
thf(3846,plain,
! [SV308: $i,SV591: $i,SV845: $i] :
( ( ( ~ ( in @ ( sK71_SY4042 @ SV845 @ SV591 @ SV308 ) @ SV308 ) )
= $false )
| ( ( in @ SV591 @ ( powerset @ SV845 ) )
= $true )
| ( ( in @ SV845 @ ( powerset @ SV308 ) )
= $false )
| ( ( in @ SV591 @ ( powerset @ SV308 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3663]) ).
thf(3847,plain,
! [SV308: $i,SV591: $i,SV845: $i] :
( ( ( ~ ( in @ ( sK71_SY4042 @ SV845 @ SV591 @ SV308 ) @ SV591 )
| ( in @ ( sK71_SY4042 @ SV845 @ SV591 @ SV308 ) @ SV845 ) )
= $false )
| ( ( in @ SV591 @ ( powerset @ SV845 ) )
= $true )
| ( ( in @ SV845 @ ( powerset @ SV308 ) )
= $false )
| ( ( in @ SV591 @ ( powerset @ SV308 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3663]) ).
thf(3848,plain,
! [SV846: $i,SV592: $i,SV309: $i,SV968: $i] :
( ( ( ~ ( in @ SV968 @ ( setminus @ SV309 @ SV592 ) ) )
= $true )
| ( ( ~ ( in @ SV968 @ ( setminus @ SV309 @ SV846 ) )
| ( in @ SV968 @ ( setminus @ SV309 @ ( binunion @ SV592 @ SV846 ) ) ) )
= $true )
| ( ( in @ SV968 @ SV309 )
= $false )
| ( ( in @ SV846 @ ( powerset @ SV309 ) )
= $false )
| ( ( in @ SV592 @ ( powerset @ SV309 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3664]) ).
thf(3849,plain,
! [SV847: $i,SV598: $i,SV315: $i,SV969: $i] :
( ( ( ~ ( in @ SV969 @ ( setminus @ SV315 @ ( binunion @ SV598 @ SV847 ) ) ) )
= $true )
| ( ( ~ ( in @ SV969 @ SV598 ) )
= $true )
| ( ( in @ SV969 @ SV315 )
= $false )
| ( ( in @ SV847 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV598 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3665]) ).
thf(3850,plain,
! [SV848: $i,SV316: $i > $o] :
( ( ( ~ ( SV316 @ ( sK85_SY4045 @ SV848 @ SV316 ) )
| ( SV848
= ( sK85_SY4045 @ SV848 @ SV316 ) ) )
= $false )
| ( ( SV316 @ SV848 )
= $false )
| ( ( ~ ! [SY3190: $i] :
~ ! [SY3191: $i] :
~ ( ~ ( ~ ( SV316 @ SY3191 )
| ( SY3191 = SY3190 ) )
| ~ ( ( SY3191 != SY3190 )
| ( SV316 @ SY3191 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3666]) ).
thf(3851,plain,
! [SV849: $i,SV970: $i,SV599: $i,SV317: $i,SV1009: $i] :
( ( ( ~ ( in @ SV1009 @ ( powerset @ SV317 ) )
| ~ ( subset @ SV599 @ SV970 )
| ~ ( subset @ SV849 @ SV1009 )
| ( subset @ ( binintersect @ SV599 @ SV849 ) @ ( binintersect @ SV970 @ SV1009 ) ) )
= $true )
| ( ( in @ SV970 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV849 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3667]) ).
thf(3852,plain,
! [SV318: $i,SV600: $i,SV850: $i,SV971: $i] :
( ( ( ~ ~ ( in @ SV971 @ SV850 ) )
= $true )
| ( ( ~ ( in @ SV971 @ ( binintersect @ SV600 @ SV850 ) ) )
= $true )
| ( ( in @ SV971 @ SV318 )
= $false )
| ( ( in @ SV850 @ ( powerset @ SV318 ) )
= $false )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3668]) ).
thf(3853,plain,
! [SV319: $i,SV601: $i,SV738: $i,SV914: $i > $o] :
( ( ( in @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ SV319 )
= $true )
| ( ( ! [SY4092: $i] :
( ~ ( in @ SY4092 @ SV738 )
| ( SV914 @ SY4092 ) ) )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3669]) ).
thf(3854,plain,
! [SV601: $i,SV914: $i > $o,SV738: $i,SV319: $i] :
( ( ( ~ ( in @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) @ SV601 )
| ~ ( in @ ( kpair @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) ) @ SV738 )
| ( SV914 @ ( kpair @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) ) ) )
= $false )
| ( ( ! [SY4092: $i] :
( ~ ( in @ SY4092 @ SV738 )
| ( SV914 @ SY4092 ) ) )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3670]) ).
thf(3855,plain,
! [SV915: $i,SV739: $i,SV321: $i,SV603: $o] :
( ( SV603 = $true )
| ( ( ( if @ SV321 @ SV603 @ SV739 @ SV915 )
= SV915 )
= $true )
| ( ( in @ SV915 @ SV321 )
= $false )
| ( ( in @ SV739 @ SV321 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3671]) ).
thf(3856,plain,
! [SV916: $i,SV740: $i,SV321: $i] :
( ( $true = $true )
| ( ( ( if @ SV321 @ $true @ SV740 @ SV916 )
= SV916 )
= $true )
| ( ( in @ SV916 @ SV321 )
= $false )
| ( ( in @ SV740 @ SV321 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3672]) ).
thf(3857,plain,
! [SV917: $i,SV741: $i,SV321: $i] :
( ( $false = $true )
| ( ( ( if @ SV321 @ $false @ SV741 @ SV917 )
= SV917 )
= $true )
| ( ( in @ SV917 @ SV321 )
= $false )
| ( ( in @ SV741 @ SV321 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3673]) ).
thf(3858,plain,
! [SV322: $i,SV851: $i] :
( ( ( ~ ( in @ ( sK51_SY3211 @ SV851 @ SV322 ) @ SV322 ) )
= $false )
| ( ( in @ SV851 @ SV322 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3674]) ).
thf(3859,plain,
! [SV322: $i,SV851: $i] :
( ( ( ~ ~ ~ ! [SY4130: $i] :
~ ~ ( ~ ( in @ SY4130 @ ( sK51_SY3211 @ SV851 @ SV322 ) )
| ~ ( in @ SY4130 @ SV322 ) ) )
= $false )
| ( ( in @ SV851 @ SV322 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3674]) ).
thf(3860,plain,
! [SV325: $i,SV972: $i,SV852: $i,SV606: $i] :
( ( ( ~ ( subset @ SV606 @ SV852 ) )
= $true )
| ( ( ~ ( subset @ SV606 @ SV972 )
| ( subset @ SV606 @ ( binintersect @ SV852 @ SV972 ) ) )
= $true )
| ( ( in @ SV972 @ ( powerset @ SV325 ) )
= $false )
| ( ( in @ SV852 @ ( powerset @ SV325 ) )
= $false )
| ( ( in @ SV606 @ ( powerset @ SV325 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3675]) ).
thf(3861,plain,
! [SV759: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ ( sK72_SY3941 @ SV759 @ SV40 ) ) )
= $false )
| ( ( SV40 @ SV759 )
= $false )
| ( ( ~ ! [SY2411: $i] :
~ ( SV40 @ SY2411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3676]) ).
thf(3862,plain,
! [SV40: $i > $o,SV759: $i] :
( ( ( SV759
= ( sK72_SY3941 @ SV759 @ SV40 ) )
= $false )
| ( ( SV40 @ SV759 )
= $false )
| ( ( ~ ! [SY2411: $i] :
~ ( SV40 @ SY2411 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3676]) ).
thf(3863,plain,
! [SV760: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK73_SY3942 @ SV760 @ SV42 ) ) )
= $false )
| ( ( SV42 @ SV760 )
= $false )
| ( ( SV42
@ ( descr
@ ^ [SY2417: $i] : ( SV42 @ SY2417 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3677]) ).
thf(3864,plain,
! [SV42: $i > $o,SV760: $i] :
( ( ( SV760
= ( sK73_SY3942 @ SV760 @ SV42 ) )
= $false )
| ( ( SV42 @ SV760 )
= $false )
| ( ( SV42
@ ( descr
@ ^ [SY2417: $i] : ( SV42 @ SY2417 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3677]) ).
thf(3865,plain,
! [SV353: $i > $o,SV44: $i,SV991: $i] :
( ( ( ~ ( ~ ( in @ SV991 @ SV44 )
| ~ ( SV353 @ SV991 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( in @ ( sK9_SY3238 @ SV353 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3678]) ).
thf(3866,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ( ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( in @ ( sK36_SY3943 @ SV353 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3679]) ).
thf(3867,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ( ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( SV353 @ ( sK9_SY3238 @ SV353 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3680]) ).
thf(3868,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ( ~ ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( SV353 @ ( sK36_SY3943 @ SV353 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3681]) ).
thf(3869,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ( ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( ( sK9_SY3238 @ SV353 @ SV44 )
= ( sK36_SY3943 @ SV353 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3682]) ).
thf(3870,plain,
! [SV45: $i,SV354: $i,SV612: $i,SV854: $i] :
( ( ( ~ ( in @ ( sK74_SY4050 @ SV854 @ SV612 @ SV354 @ SV45 ) @ SV45 ) )
= $false )
| ( ( SV612 = SV854 )
= $true )
| ( ( in @ SV854 @ ( funcSet @ SV45 @ SV354 ) )
= $false )
| ( ( in @ SV612 @ ( funcSet @ SV45 @ SV354 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3683]) ).
thf(3871,plain,
! [SV854: $i,SV612: $i,SV354: $i,SV45: $i] :
( ( ( ( ap @ SV45 @ SV354 @ SV612 @ ( sK74_SY4050 @ SV854 @ SV612 @ SV354 @ SV45 ) )
= ( ap @ SV45 @ SV354 @ SV854 @ ( sK74_SY4050 @ SV854 @ SV612 @ SV354 @ SV45 ) ) )
= $false )
| ( ( SV612 = SV854 )
= $true )
| ( ( in @ SV854 @ ( funcSet @ SV45 @ SV354 ) )
= $false )
| ( ( in @ SV612 @ ( funcSet @ SV45 @ SV354 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3683]) ).
thf(3872,plain,
! [SV923: $i,SV762: $i,SV361: $i,SV52: $i,SV992: $i] :
( ( ( ~ ( in @ SV992 @ SV52 ) )
= $true )
| ( ( ~ ( in @ SV992 @ ( binintersect @ SV361 @ SV762 ) )
| ( in @ SV992 @ ( binunion @ SV762 @ SV923 ) ) )
= $true )
| ( ( in @ SV923 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV762 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3684]) ).
thf(3873,plain,
! [SV924: $i,SV764: $i,SV365: $i,SV56: $i,SV993: $i] :
( ( ( ~ ( in @ SV993 @ ( powerset @ SV56 ) ) )
= $true )
| ( ( ( setminus @ SV56 @ ( binintersect @ ( binunion @ SV365 @ SV764 ) @ ( binunion @ SV924 @ SV993 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV56 @ SV365 ) @ ( setminus @ SV56 @ SV764 ) ) @ ( binintersect @ ( setminus @ SV56 @ SV924 ) @ ( setminus @ SV56 @ SV993 ) ) ) )
= $true )
| ( ( in @ SV924 @ ( powerset @ SV56 ) )
= $false )
| ( ( in @ SV764 @ ( powerset @ SV56 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV56 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3685]) ).
thf(3874,plain,
! [SV57: $i,SV366: $i] :
( ( ( ~ ( in @ SV366 @ ( sK52_SY3265 @ SV57 @ SV366 ) ) )
= $false )
| ( ( in @ SV366 @ ( setunion @ SV57 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3686]) ).
thf(3875,plain,
! [SV366: $i,SV57: $i] :
( ( ( ~ ( in @ ( sK52_SY3265 @ SV57 @ SV366 ) @ SV57 ) )
= $false )
| ( ( in @ SV366 @ ( setunion @ SV57 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3686]) ).
thf(3876,plain,
! [SV57: $i,SV973: $i,SV366: $i] :
( ( ( ~ ( in @ SV366 @ SV973 ) )
= $true )
| ( ( ~ ( in @ SV973 @ SV57 ) )
= $true )
| ( ( in @ SV366 @ ( setunion @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3687]) ).
thf(3877,plain,
! [SV765: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK75_SY3949 @ SV765 @ SV58 ) ) )
= $false )
| ( ( SV58 @ SV765 )
= $false )
| ( ( ! [SY2464: $i,SY2465: $i] :
( ~ ( SV58 @ SY2464 )
| ~ ( SV58 @ SY2465 )
| ( SY2464 = SY2465 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3688]) ).
thf(3878,plain,
! [SV58: $i > $o,SV765: $i] :
( ( ( SV765
= ( sK75_SY3949 @ SV765 @ SV58 ) )
= $false )
| ( ( SV58 @ SV765 )
= $false )
| ( ( ! [SY2464: $i,SY2465: $i] :
( ~ ( SV58 @ SY2464 )
| ~ ( SV58 @ SY2465 )
| ( SY2464 = SY2465 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3688]) ).
thf(3879,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( ~ ( ( ( sK37_SY3950 @ SV766 @ SV59 )
!= SV766 )
| ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) ) ) )
= $true )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3689]) ).
thf(3880,plain,
! [SV59: $i > $o,SV766: $i] :
( ( ( ( ( sK37_SY3950 @ SV766 @ SV59 )
!= SV766 )
| ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) ) )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3690]) ).
thf(3881,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ~ ( SV60 @ ( sK76_SY3951 @ SV767 @ SV60 ) ) )
= $false )
| ( ( SV60 @ SV767 )
= $false )
| ( ( ~ ! [SY2472: $i] :
~ ~ ( ~ ( SV60 @ SY2472 )
| ~ ! [SY2473: $i] :
( ~ ( SV60 @ SY2473 )
| ( SY2472 = SY2473 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3691]) ).
thf(3882,plain,
! [SV60: $i > $o,SV767: $i] :
( ( ( SV767
= ( sK76_SY3951 @ SV767 @ SV60 ) )
= $false )
| ( ( SV60 @ SV767 )
= $false )
| ( ( ~ ! [SY2472: $i] :
~ ~ ( ~ ( SV60 @ SY2472 )
| ~ ! [SY2473: $i] :
( ~ ( SV60 @ SY2473 )
| ( SY2472 = SY2473 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3691]) ).
thf(3883,plain,
! [SV61: $i,SV367: $i > $o,SV858: $i] :
( ( ( ~ ( in @ ( sK59_SY3268 @ SV858 @ SV367 @ SV61 ) @ SV61 )
| ~ ~ ( SV367 @ ( sK59_SY3268 @ SV858 @ SV367 @ SV61 ) ) )
= $false )
| ( ( SV367 @ SV858 )
= $true )
| ( ( in @ SV858 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3692]) ).
thf(3884,plain,
! [SV65: $i,SV371: $i] :
( ( ( ~ ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 ) )
= $false )
| ( ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 )
= $true )
| ( ( SV65 = SV371 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3693]) ).
thf(3885,plain,
! [SV65: $i,SV371: $i] :
( ( ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 )
= $false )
| ( ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 )
= $true )
| ( ( SV65 = SV371 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3693]) ).
thf(3886,plain,
! [SV65: $i,SV371: $i] :
( ( ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 )
= $true )
| ( ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 )
= $false )
| ( ( SV65 = SV371 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3694]) ).
thf(3887,plain,
! [SV372: $i,SV768: $i,SV68: $i,SV986: $i] :
( ( ( in @ SV986 @ SV68 )
= $false )
| ( ( ~ ( in @ SV986 @ SV768 )
| ( in @ SV986 @ ( setminus @ SV68 @ SV372 ) ) )
= $true )
| ( ( subset @ SV372 @ ( setminus @ SV68 @ SV768 ) )
= $false )
| ( ( in @ SV768 @ ( powerset @ SV68 ) )
= $false )
| ( ( in @ SV372 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3696]) ).
thf(3888,plain,
! [SV769: $i,SV373: $i,SV69: $i,SV925: $i] :
( ( ( in @ SV925 @ ( setminus @ SV69 @ ( binintersect @ SV373 @ SV769 ) ) )
= $false )
| ( ( in @ SV925 @ ( binunion @ ( setminus @ SV69 @ SV373 ) @ ( setminus @ SV69 @ SV769 ) ) )
= $true )
| ( ( in @ SV925 @ SV69 )
= $false )
| ( ( in @ SV769 @ ( powerset @ SV69 ) )
= $false )
| ( ( in @ SV373 @ ( powerset @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3697]) ).
thf(3889,plain,
! [SV72: $i,SV860: $o,SV376: $i,SV621: $i] :
( ( ( ~ ( in @ SV621 @ SV376 )
| SV860 )
= $false )
| ( SV860 = $true )
| ( ( SV621 = SV72 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3698]) ).
thf(3890,plain,
! [SV72: $i,SV860: $o,SV376: $i,SV621: $i] :
( ( ( ~ ( in @ SV621 @ SV376 ) )
= $false )
| ( SV860 = $true )
| ( SV860 = $false )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3699]) ).
thf(3891,plain,
! [SV376: $i,SV72: $i,SV621: $i,SV860: $o] :
( ( SV860 = $false )
| ( SV860 = $true )
| ( SV860 = $false )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3699]) ).
thf(3892,plain,
! [SV72: $i,SV376: $i,SV621: $i] :
( ( ( ~ ( in @ SV621 @ SV376 )
| $true )
= $false )
| ( $true = $true )
| ( ( SV621 = SV72 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3700]) ).
thf(3893,plain,
! [SV72: $i,SV376: $i,SV621: $i] :
( ( ( ~ ( in @ SV621 @ SV376 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3701]) ).
thf(3894,plain,
! [SV376: $i,SV72: $i,SV621: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3701]) ).
thf(3895,plain,
! [SV72: $i,SV376: $i,SV621: $i] :
( ( ( ~ ( in @ SV621 @ SV376 )
| $false )
= $false )
| ( $false = $true )
| ( ( SV621 = SV72 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3702]) ).
thf(3896,plain,
! [SV72: $i,SV376: $i,SV621: $i] :
( ( ( ~ ( in @ SV621 @ SV376 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3703]) ).
thf(3897,plain,
! [SV376: $i,SV72: $i,SV621: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3703]) ).
thf(3898,plain,
! [SV772: $i,SV379: $i,SV75: $i,SV926: $i] :
( ( ( in @ SV926 @ ( setminus @ SV75 @ ( binunion @ SV379 @ SV772 ) ) )
= $false )
| ( ( in @ SV926 @ ( setminus @ SV75 @ SV772 ) )
= $true )
| ( ( in @ SV926 @ SV75 )
= $false )
| ( ( in @ SV772 @ ( powerset @ SV75 ) )
= $false )
| ( ( in @ SV379 @ ( powerset @ SV75 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3704]) ).
thf(3899,plain,
! [SV76: $i,SV622: $i,SV380: $i > $i] :
( ( ( ~ ( in @ ( sK60_SY3750 @ SV380 @ SV622 @ SV76 ) @ SV76 )
| ( SV622
!= ( SV380 @ ( sK60_SY3750 @ SV380 @ SV622 @ SV76 ) ) ) )
= $false )
| ( ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3287: $i] : ( SV380 @ SY3287 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3705]) ).
thf(3900,plain,
! [SV380: $i > $i,SV622: $i,SV76: $i,SV987: $i] :
( ( ( ~ ( in @ SV987 @ SV76 )
| ( SV622
!= ( SV380 @ SV987 ) ) )
= $true )
| ( ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3290: $i] : ( SV380 @ SY3290 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3706]) ).
thf(3901,plain,
! [SV77: $i,SV918: $i,SV381: $i > $i,SV623: $i] :
( ( ( SV623
= ( SV381 @ SV918 ) )
= $false )
| ( ( in @ SV918 @ SV77 )
= $false )
| ( ( in @ SV623
@ ( image1 @ SV77
@ ^ [SY3293: $i] : ( SV381 @ SY3293 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3707]) ).
thf(3902,plain,
! [SV773: $i,SV382: $i,SV927: $i,SV78: $i,SV994: $i] :
( ( ( ~ ( in @ SV994 @ SV78 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV927 @ SV994 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
| ~ ! [SY4151: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY4151 @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ SY4151 ) @ SV382 ) )
| ~ ( in @ ( kpair @ SY4151 @ SV994 ) @ SV773 ) ) )
= $true )
| ( ( in @ SV927 @ SV78 )
= $false )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3708]) ).
thf(3903,plain,
! [SV774: $i,SV386: $i,SV928: $i,SV82: $i,SV995: $i] :
( ( ( ~ ( in @ SV995 @ SV82 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV928 @ SV995 ) @ ( binunion @ SV386 @ SV774 ) )
| ( in @ ( kpair @ SV928 @ SV995 ) @ SV386 )
| ( in @ ( kpair @ SV928 @ SV995 ) @ SV774 ) )
= $true )
| ( ( in @ SV928 @ SV82 )
= $false )
| ( ( breln1 @ SV82 @ SV774 )
= $false )
| ( ( breln1 @ SV82 @ SV386 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3709]) ).
thf(3904,plain,
! [SV929: $i,SV776: $i,SV86: $i,SV389: $i] :
( ( ( subset @ SV389 @ ( setminus @ SV86 @ SV776 ) )
= $false )
| ( ( ~ ( in @ SV929 @ SV776 )
| ~ ( in @ SV929 @ SV389 ) )
= $true )
| ( ( in @ SV929 @ SV86 )
= $false )
| ( ( in @ SV776 @ ( powerset @ SV86 ) )
= $false )
| ( ( in @ SV389 @ ( powerset @ SV86 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3710]) ).
thf(3905,plain,
! [SV87: $i,SV930: $i,SV777: $i,SV390: $i] :
( ( ( subset @ SV390 @ SV777 )
= $false )
| ( ( ~ ~ ( in @ SV930 @ SV777 )
| ~ ( in @ SV930 @ SV390 ) )
= $true )
| ( ( in @ SV930 @ SV87 )
= $false )
| ( ( in @ SV777 @ ( powerset @ SV87 ) )
= $false )
| ( ( in @ SV390 @ ( powerset @ SV87 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3711]) ).
thf(3906,plain,
! [SV931: $i,SV779: $i,SV393: $i,SV90: $i,SV996: $i] :
( ( ( ~ ( in @ SV996 @ SV90 ) )
= $true )
| ( ( ~ ( in @ SV996 @ ( binintersect @ SV393 @ SV779 ) )
| ( in @ SV996 @ ( binintersect @ ( binunion @ SV393 @ SV931 ) @ ( binunion @ SV779 @ SV931 ) ) ) )
= $true )
| ( ( in @ SV931 @ ( powerset @ SV90 ) )
= $false )
| ( ( in @ SV779 @ ( powerset @ SV90 ) )
= $false )
| ( ( in @ SV393 @ ( powerset @ SV90 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3712]) ).
thf(3907,plain,
! [SV780: $i,SV400: $i,SV99: $i,SV932: $i] :
( ( ( in @ SV932 @ ( setminus @ SV99 @ ( binunion @ SV400 @ SV780 ) ) )
= $false )
| ( ( in @ SV932 @ ( setminus @ SV99 @ SV400 ) )
= $true )
| ( ( in @ SV932 @ SV99 )
= $false )
| ( ( in @ SV780 @ ( powerset @ SV99 ) )
= $false )
| ( ( in @ SV400 @ ( powerset @ SV99 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3713]) ).
thf(3908,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( SV100 @ ( sK53_SY2563 @ SV781 @ SV100 ) )
= $true )
| ( ( ~ ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3714]) ).
thf(3909,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK61_SY4131 @ SV781 @ SV100 ) ) )
= $false )
| ( ( ~ ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3715]) ).
thf(3910,plain,
! [SV100: $i > $o,SV781: $i] :
( ( ( ( sK53_SY2563 @ SV781 @ SV100 )
= ( sK61_SY4131 @ SV781 @ SV100 ) )
= $false )
| ( ( ~ ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3715]) ).
thf(3911,plain,
! [SV104: $i,SV862: $i,SV404: $i > $o] :
( ( ( SV404 @ SV862 )
= $true )
| ( ( in @ SV862 @ SV104 )
= $false )
| ( ( ~ ! [SY3324: $i] :
( ~ ( in @ SY3324 @ SV104 )
| ( SV404 @ SY3324 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3716]) ).
thf(3912,plain,
! [SV106: $i] :
( ( ( ~ ( in @ ( sK44_SY2577 @ SV106 ) @ omega ) )
= $false )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( ! [SY2578: $i] :
( ~ ( in @ SY2578 @ omega )
| ( in @ SY2578 @ SV106 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3717]) ).
thf(3913,plain,
! [SV106: $i] :
( ( ( ~ ( in @ ( sK44_SY2577 @ SV106 ) @ SV106 ) )
= $false )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( ! [SY2578: $i] :
( ~ ( in @ SY2578 @ omega )
| ( in @ SY2578 @ SV106 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3717]) ).
thf(3914,plain,
! [SV106: $i,SV988: $i] :
( ( ( in @ SV988 @ omega )
= $false )
| ( ( in @ SV988 @ SV106 )
= $true )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( in @ ( setadjoin @ ( sK44_SY2577 @ SV106 ) @ ( sK44_SY2577 @ SV106 ) ) @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3718]) ).
thf(3915,plain,
! [SV109: $i,SV407: $i,SV782: $i] :
( ( ( in @ ( sK62_SY3965 @ SV782 @ SV407 @ SV109 ) @ SV109 )
= $true )
| ( ( subset @ SV407 @ SV782 )
= $true )
| ( ( in @ SV782 @ ( powerset @ SV109 ) )
= $false )
| ( ( in @ SV407 @ ( powerset @ SV109 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3719]) ).
thf(3916,plain,
! [SV109: $i,SV407: $i,SV782: $i] :
( ( ( ~ ( in @ ( sK62_SY3965 @ SV782 @ SV407 @ SV109 ) @ SV407 ) )
= $false )
| ( ( subset @ SV407 @ SV782 )
= $true )
| ( ( in @ SV782 @ ( powerset @ SV109 ) )
= $false )
| ( ( in @ SV407 @ ( powerset @ SV109 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3720]) ).
thf(3917,plain,
! [SV109: $i,SV407: $i,SV782: $i] :
( ( ( in @ ( sK62_SY3965 @ SV782 @ SV407 @ SV109 ) @ SV782 )
= $false )
| ( ( subset @ SV407 @ SV782 )
= $true )
| ( ( in @ SV782 @ ( powerset @ SV109 ) )
= $false )
| ( ( in @ SV407 @ ( powerset @ SV109 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3720]) ).
thf(3918,plain,
! [SV110: $i,SV783: $i,SV408: $i,SV933: $i] :
( ( ( ~ ( in @ SV933 @ SV408 ) )
= $false )
| ( ( ~ ( in @ SV933 @ ( binintersect @ SV408 @ SV783 ) ) )
= $true )
| ( ( in @ SV933 @ SV110 )
= $false )
| ( ( in @ SV783 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV408 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3721]) ).
thf(3919,plain,
! [SV784: $i,SV411: $i,SV113: $i,SV934: $i] :
( ( ( in @ SV934 @ ( setminus @ SV113 @ SV411 ) )
= $false )
| ( ( in @ SV934 @ ( setminus @ SV113 @ ( binintersect @ SV411 @ SV784 ) ) )
= $true )
| ( ( in @ SV934 @ SV113 )
= $false )
| ( ( in @ SV784 @ ( powerset @ SV113 ) )
= $false )
| ( ( in @ SV411 @ ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3722]) ).
thf(3920,plain,
! [SV118: $i,SV416: $i > $o,SV639: $i] :
( ( ( in @ ( sK63_SY3768 @ SV639 @ SV416 @ SV118 ) @ SV118 )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY3351: $i] : ( SV416 @ SY3351 ) )
= $true )
| ( ( SV416 @ SV639 )
= $false )
| ( ( in @ SV639 @ SV118 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3723]) ).
thf(3921,plain,
! [SV118: $i,SV639: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK63_SY3768 @ SV639 @ SV416 @ SV118 ) ) )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY3351: $i] : ( SV416 @ SY3351 ) )
= $true )
| ( ( SV416 @ SV639 )
= $false )
| ( ( in @ SV639 @ SV118 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3724]) ).
thf(3922,plain,
! [SV118: $i,SV416: $i > $o,SV639: $i] :
( ( ( ( sK63_SY3768 @ SV639 @ SV416 @ SV118 )
= SV639 )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY3351: $i] : ( SV416 @ SY3351 ) )
= $true )
| ( ( SV416 @ SV639 )
= $false )
| ( ( in @ SV639 @ SV118 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3724]) ).
thf(3923,plain,
! [SV420: $i,SV865: $i > $o,SV788: $i > $o,SV122: $i] :
( ( ( ~ ( in @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) @ SV420 ) )
= $false )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3727]) ).
thf(3924,plain,
! [SV122: $i,SV420: $i,SV788: $i > $o,SV865: $i > $o] :
( ( ( ( ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 )
!= ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
| ~ ( ~ ( ~ ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) )
| ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) ) )
| ~ ( ~ ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
| ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3727]) ).
thf(3925,plain,
! [SV123: $i,SV936: $i,SV789: $i,SV421: $i > $o] :
( ( ( SV421 @ SV789 )
= $false )
| ( ( ~ ( SV421 @ SV936 )
| ( SV789 = SV936 ) )
= $true )
| ( ( in @ SV936 @ SV123 )
= $false )
| ( ( in @ SV789 @ SV123 )
= $false )
| ( ( ex1 @ SV123
@ ^ [SY3363: $i] : ( SV421 @ SY3363 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3728]) ).
thf(3926,plain,
! [SV423: $i,SV790: $i,SV937: $i,SV125: $i,SV997: $i] :
( ( ( ~ ( in @ SV997 @ SV125 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV937 @ SV997 ) @ SV790 )
| ( in @ ( kpair @ SV937 @ SV997 ) @ ( binunion @ SV423 @ SV790 ) ) )
= $true )
| ( ( in @ SV937 @ SV125 )
= $false )
| ( ( breln1 @ SV125 @ SV790 )
= $false )
| ( ( breln1 @ SV125 @ SV423 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3729]) ).
thf(3927,plain,
! [SV792: $i,SV428: $i,SV939: $i,SV131: $i,SV998: $i] :
( ( ( ~ ( in @ SV998 @ SV131 ) )
= $true )
| ( ( ! [SY4152: $i] :
( ~ ( in @ SY4152 @ SV131 )
| ~ ( in @ ( kpair @ SV939 @ SY4152 ) @ SV428 )
| ~ ( in @ ( kpair @ SY4152 @ SV998 ) @ SV792 )
| ( in @ ( kpair @ SV939 @ SV998 ) @ ( breln1compset @ SV131 @ SV428 @ SV792 ) ) ) )
= $true )
| ( ( in @ SV939 @ SV131 )
= $false )
| ( ( breln1 @ SV131 @ SV792 )
= $false )
| ( ( breln1 @ SV131 @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3733]) ).
thf(3928,plain,
! [SV135: $i,SV432: $i,SV794: $i] :
( ( ( in @ ( sK64_SY3983 @ SV794 @ SV432 @ SV135 ) @ SV135 )
= $true )
| ( ( subset @ SV432 @ SV794 )
= $true )
| ( ( breln1 @ SV135 @ SV794 )
= $false )
| ( ( breln1 @ SV135 @ SV432 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3734]) ).
thf(3929,plain,
! [SV135: $i,SV794: $i,SV432: $i] :
( ( ( ~ ( in @ ( sK87_SY4149 @ SV432 @ SV794 @ SV135 ) @ SV135 )
| ~ ( in @ ( kpair @ ( sK64_SY3983 @ SV794 @ SV432 @ SV135 ) @ ( sK87_SY4149 @ SV432 @ SV794 @ SV135 ) ) @ SV432 )
| ( in @ ( kpair @ ( sK64_SY3983 @ SV794 @ SV432 @ SV135 ) @ ( sK87_SY4149 @ SV432 @ SV794 @ SV135 ) ) @ SV794 ) )
= $false )
| ( ( subset @ SV432 @ SV794 )
= $true )
| ( ( breln1 @ SV135 @ SV794 )
= $false )
| ( ( breln1 @ SV135 @ SV432 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3735]) ).
thf(3930,plain,
! [SV434: $i,SV869: $i,SV138: $i,SV795: $i] :
( ( ( ~ ( in @ SV795 @ SV138 ) )
= $true )
| ( ( in @ SV869 @ SV434 )
= $true )
| ( ( SV795 = SV869 )
= $false )
| ( ( SV138 = SV434 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3736]) ).
thf(3931,plain,
! [SV138: $i,SV795: $i,SV434: $i,SV869: $i] :
( ( ( ~ ( in @ SV869 @ SV434 ) )
= $true )
| ( ( in @ SV795 @ SV138 )
= $true )
| ( ( SV795 = SV869 )
= $false )
| ( ( SV138 = SV434 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3737]) ).
thf(3932,plain,
! [SV139: $i,SV796: $i,SV940: $i,SV435: $i] :
( ( ( subset @ SV435 @ SV940 )
= $false )
| ( ( subset @ ( binintersect @ SV435 @ SV796 ) @ SV940 )
= $true )
| ( ( in @ SV940 @ ( powerset @ SV139 ) )
= $false )
| ( ( in @ SV796 @ ( powerset @ SV139 ) )
= $false )
| ( ( in @ SV435 @ ( powerset @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3738]) ).
thf(3933,plain,
! [SV140: $i,SV436: $i,SV650: $i,SV870: $i] :
( ( ( ~ ( in @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SV140 ) )
= $false )
| ( ( ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) )
| ( SV650 = SV870 ) )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3739]) ).
thf(3934,plain,
! [SV140: $i,SV650: $i,SV870: $i,SV436: $i] :
( ( ( ! [SY4153: $i] :
( ~ ( in @ SY4153 @ SV436 )
| ~ ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SY4153 ) @ SV650 )
| ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SY4153 ) @ SV870 ) ) )
= $false )
| ( ( ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) )
| ( SV650 = SV870 ) )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3739]) ).
thf(3935,plain,
! [SV654: $i > $i,SV975: $i,SV440: $i,SV144: $i] :
( ( ( ~ ! [SY4134: $i] :
( ~ ( in @ SY4134 @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SV975 @ ( SV654 @ SY4134 ) )
= SY4134 ) ) )
= $true )
| ( ( surjective @ SV440 @ SV144 @ SV975 )
= $true )
| ( ( in @ SV975 @ ( funcSet @ SV440 @ SV144 ) )
= $false )
| ( ( in @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) @ SV144 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3740]) ).
thf(3936,plain,
! [SV654: $i > $i,SV941: $i,SV440: $i,SV144: $i] :
( ( ( ! [SY4108: $i] :
( ~ ( in @ SY4108 @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SV941 @ ( SV654 @ SY4108 ) )
= SY4108 ) ) )
= $false )
| ( ( surjective @ SV440 @ SV144 @ SV941 )
= $true )
| ( ( in @ SV941 @ ( funcSet @ SV440 @ SV144 ) )
= $false )
| ( ( in @ ( SV654 @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) ) @ SV440 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3741]) ).
thf(3937,plain,
! [SV442: $i > $o,SV146: $i,SV999: $i] :
( ( ( ~ ( ~ ( in @ SV999 @ SV146 )
| ~ ( SV442 @ SV999 ) ) )
= $false )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( in @ ( sK11_SY3407 @ SV442 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3742]) ).
thf(3938,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ( ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( in @ ( sK38_SY3987 @ SV442 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3743]) ).
thf(3939,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ( ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) ) )
= $false )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( SV442 @ ( sK11_SY3407 @ SV442 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3744]) ).
thf(3940,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ( ~ ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( SV442 @ ( sK38_SY3987 @ SV442 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3745]) ).
thf(3941,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ( ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) ) )
= $false )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( ( sK11_SY3407 @ SV442 @ SV146 )
= ( sK38_SY3987 @ SV442 @ SV146 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3746]) ).
thf(3942,plain,
! [SV798: $i,SV443: $i,SV147: $i,SV942: $i] :
( ( ( in @ SV942 @ ( setminus @ SV147 @ SV443 ) )
= $false )
| ( ( ~ ( in @ SV942 @ ( binintersect @ SV443 @ SV798 ) ) )
= $true )
| ( ( in @ SV942 @ SV147 )
= $false )
| ( ( in @ SV798 @ ( powerset @ SV147 ) )
= $false )
| ( ( in @ SV443 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3747]) ).
thf(3943,plain,
! [SV943: $i,SV799: $i,SV444: $i,SV148: $i,SV1000: $i] :
( ( ( ~ ( in @ SV1000 @ SV148 ) )
= $true )
| ( ( ~ ( in @ SV1000 @ ( binintersect @ SV444 @ SV799 ) )
| ( in @ SV1000 @ ( binunion @ SV444 @ SV943 ) ) )
= $true )
| ( ( in @ SV943 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV799 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV444 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3748]) ).
thf(3944,plain,
! [SV448: $i > $o,SV1010: $i,SV152: $i > $o] :
( ( ( ~ ~ ( ~ ( SV152 @ SV1010 )
| ~ ! [SY4163: $i] :
( ~ ( SV152 @ SY4163 )
| ( SV1010 = SY4163 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3749]) ).
thf(3945,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( ~ ( ~ ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
| ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3750]) ).
thf(3946,plain,
! [SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
| ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3751]) ).
thf(3947,plain,
! [SV157: $i,SV453: $i,SV945: $i,SV802: $i] :
( ( ( in @ ( kpair @ SV802 @ SV945 ) @ SV453 )
= $false )
| ( ( in @ ( kpair @ SV945 @ SV802 ) @ ( breln1invset @ SV157 @ SV453 ) )
= $true )
| ( ( in @ SV945 @ SV157 )
= $false )
| ( ( in @ SV802 @ SV157 )
= $false )
| ( ( breln1 @ SV157 @ SV453 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3755]) ).
thf(3948,plain,
! [SV163: $i,SV459: $i,SV946: $i,SV804: $i] :
( ( ( subset @ SV804 @ SV946 )
= $false )
| ( ( subset @ ( binintersect @ SV459 @ SV804 ) @ SV946 )
= $true )
| ( ( in @ SV946 @ ( powerset @ SV163 ) )
= $false )
| ( ( in @ SV804 @ ( powerset @ SV163 ) )
= $false )
| ( ( in @ SV459 @ ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3756]) ).
thf(3949,plain,
! [SV168: $i,SV464: $i,SV666: $i,SV877: $i] :
( ( ( ~ ( in @ ( sK79_SY4066 @ SV877 @ SV666 @ SV464 @ SV168 ) @ SV168 ) )
= $false )
| ( ( subset @ SV666 @ SV877 )
= $true )
| ( ( breln @ SV168 @ SV464 @ SV877 )
= $false )
| ( ( breln @ SV168 @ SV464 @ SV666 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3757]) ).
thf(3950,plain,
! [SV168: $i,SV666: $i,SV877: $i,SV464: $i] :
( ( ( ! [SY4154: $i] :
( ~ ( in @ SY4154 @ SV464 )
| ~ ( in @ ( kpair @ ( sK79_SY4066 @ SV877 @ SV666 @ SV464 @ SV168 ) @ SY4154 ) @ SV666 )
| ( in @ ( kpair @ ( sK79_SY4066 @ SV877 @ SV666 @ SV464 @ SV168 ) @ SY4154 ) @ SV877 ) ) )
= $false )
| ( ( subset @ SV666 @ SV877 )
= $true )
| ( ( breln @ SV168 @ SV464 @ SV877 )
= $false )
| ( ( breln @ SV168 @ SV464 @ SV666 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3757]) ).
thf(3951,plain,
! [SV175: $i,SV470: $i > $i,SV976: $i] :
( ( ~ ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
| ~ ! [SY4135: $i] :
~ ~ ( ~ ( in @ SY4135 @ SV175 )
| ( SV976
!= ( SV470 @ SY4135 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3758]) ).
thf(3952,plain,
! [SV470: $i > $i,SV976: $i,SV175: $i] :
( ( ~ ~ ! [SY4136: $i] :
~ ~ ( ~ ( in @ SY4136 @ SV175 )
| ( SV976
!= ( SV470 @ SY4136 ) ) )
| ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3759]) ).
thf(3953,plain,
! [SV977: $i,SV175: $i,SV470: $i > $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
| ~ ! [SY4164: $i] :
~ ~ ( ~ ( in @ SY4164 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4164 ) ) ) )
| ~ ( ~ ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) )
| ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 ) ) ) )
= $false )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3760]) ).
thf(3954,plain,
! [SV670: $i > $i > $o,SV180: $i,SV978: $i,SV475: $i] :
( ( ( ~ ( reflwellordering @ SV475 @ SV978 ) )
= $true )
| ( ( ! [SY4140: $i] :
( ~ ( in @ SY4140 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY4141: $i] :
~ ( ~ ( SV670 @ SY4140 @ SY4141 )
| ~ ! [SY4142: $i] :
( ~ ( in @ SY4142 @ SV475 )
| ~ ( SV670 @ SY4140 @ SY4142 )
| ( in @ ( kpair @ SY4141 @ SY4142 ) @ SV978 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV978 @ ( breln1Set @ SV475 ) )
= $false )
| ( ( in @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV180 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3761]) ).
thf(3955,plain,
! [SV180: $i,SV670: $i > $i > $o,SV475: $i,SV979: $i] :
( ( ( ~ ( in @ SV979 @ SV475 ) )
= $true )
| ( ( ~ ( SV670 @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV979 ) )
= $true )
| ( ( ! [SY3807: $i] :
( ~ ( in @ SY3807 @ ( breln1Set @ SV475 ) )
| ~ ( reflwellordering @ SV475 @ SY3807 )
| ! [SY3808: $i] :
( ~ ( in @ SY3808 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY3809: $i] :
~ ( ~ ( SV670 @ SY3808 @ SY3809 )
| ~ ! [SY3810: $i] :
( ~ ( in @ SY3810 @ SV475 )
| ~ ( SV670 @ SY3808 @ SY3810 )
| ( in @ ( kpair @ SY3809 @ SY3810 ) @ SY3807 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3762]) ).
thf(3956,plain,
! [SV186: $i,SV950: $i,SV812: $i,SV481: $i] :
( ( ( in @ SV481 @ ( powerset @ SV812 ) )
= $false )
| ( ( ~ ( in @ SV950 @ SV481 )
| ( in @ SV950 @ SV812 ) )
= $true )
| ( ( in @ SV950 @ SV186 )
= $false )
| ( ( in @ SV812 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV481 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3764]) ).
thf(3957,plain,
! [SV189: $i,SV484: $i > $o,SV879: $i] :
( ( ( ~ ( in @ ( sK65_SY3497 @ SV879 @ SV484 @ SV189 ) @ SV189 )
| ~ ~ ( SV484 @ ( sK65_SY3497 @ SV879 @ SV484 @ SV189 ) ) )
= $false )
| ( ( SV484 @ SV879 )
= $true )
| ( ( in @ SV879 @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3765]) ).
thf(3958,plain,
! [SV486: $i,SV191: $i,SV676: $i,SV981: $i,SV880: $i] :
( ( ( ~ ( in @ ( kpair @ SV880 @ SV981 ) @ SV676 ) )
= $true )
| ( ( ( ap @ SV191 @ SV486 @ SV676 @ SV880 )
= SV981 )
= $true )
| ( ( in @ SV981 @ SV486 )
= $false )
| ( ( in @ SV880 @ SV191 )
= $false )
| ( ( in @ SV676 @ ( funcSet @ SV191 @ SV486 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3769]) ).
thf(3959,plain,
! [SV488: $i > $i,SV881: $i,SV193: $i] :
( ( ( ! [SY4070: $i] :
~ ~ ( ~ ( in @ SY4070 @ SV193 )
| ( SV881
!= ( SV488 @ SY4070 ) ) ) )
= $false )
| ( ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3770]) ).
thf(3960,plain,
! [SV488: $i > $i,SV881: $i,SV193: $i] :
( ( ( ! [SY4071: $i] :
~ ~ ( ~ ( in @ SY4071 @ SV193 )
| ( SV881
!= ( SV488 @ SY4071 ) ) ) )
= $true )
| ( ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3771]) ).
thf(3961,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ ( sK80_SY4002 @ SV816 @ SV196 ) ) )
= $false )
| ( ( SV196 @ SV816 )
= $false )
| ( ( ~ ! [SY2855: $i] :
~ ~ ( ~ ( SV196 @ SY2855 )
| ~ ! [SY2856: $i] :
( ~ ( SV196 @ SY2856 )
| ( SY2855 = SY2856 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3772]) ).
thf(3962,plain,
! [SV196: $i > $o,SV816: $i] :
( ( ( SV816
= ( sK80_SY4002 @ SV816 @ SV196 ) )
= $false )
| ( ( SV196 @ SV816 )
= $false )
| ( ( ~ ! [SY2855: $i] :
~ ~ ( ~ ( SV196 @ SY2855 )
| ~ ! [SY2856: $i] :
( ~ ( SV196 @ SY2856 )
| ( SY2855 = SY2856 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3772]) ).
thf(3963,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3773]) ).
thf(3964,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3774]) ).
thf(3965,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( ~ ( ~ ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
| ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3775]) ).
thf(3966,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
| ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3776]) ).
thf(3967,plain,
! [SV199: $i,SV679: $i,SV492: $i] :
( ( ( ! [SY4093: $i] :
~ ~ ( ~ ( in @ SY4093 @ SV492 )
| ( SV679
!= ( kpair @ ( sK39_SY3820 @ SV679 @ SV492 @ SV199 ) @ SY4093 ) ) ) )
= $false )
| ( ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3778]) ).
thf(3968,plain,
! [SV200: $i,SV817: $i,SV493: $i,SV951: $i] :
( ( ( ~ ( in @ SV951 @ ( binunion @ SV493 @ SV817 ) ) )
= $false )
| ( ( ~ ( in @ SV951 @ SV817 ) )
= $true )
| ( ( in @ SV951 @ SV200 )
= $false )
| ( ( in @ SV817 @ ( powerset @ SV200 ) )
= $false )
| ( ( in @ SV493 @ ( powerset @ SV200 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3779]) ).
thf(3969,plain,
! [SV885: $o,SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SV885 )
= $false )
| ( SV885 = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3780]) ).
thf(3970,plain,
! [SV885: $o,SV203: $i,SV496: $i,SV683: $i] :
( ( ( in @ SV683 @ SV496 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SV885 )
| SV885 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3781]) ).
thf(3971,plain,
! [SV885: $o,SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SV885 )
= $false )
| ( SV885 = $true )
| ( SV885 = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3782]) ).
thf(3972,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3783]) ).
thf(3973,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( in @ SV683 @ SV496 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $true )
| $true )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3784]) ).
thf(3974,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3785]) ).
thf(3975,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3786]) ).
thf(3976,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( in @ SV683 @ SV496 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $false )
| $false )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3787]) ).
thf(3977,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3788]) ).
thf(3978,plain,
! [SV500: $i > $o,SV207: $i,SV1011: $i] :
( ( ( ~ ( in @ SV1011 @ SV207 )
| ~ ( SV500 @ SV1011 ) )
= $true )
| ( ( in @ ( sK40_SY3540 @ SV500 @ SV207 ) @ SV207 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3789]) ).
thf(3979,plain,
! [SV500: $i > $o,SV207: $i,SV1012: $i] :
( ( ( ~ ( in @ SV1012 @ SV207 )
| ~ ( SV500 @ SV1012 ) )
= $true )
| ( ( SV500 @ ( sK40_SY3540 @ SV500 @ SV207 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3790]) ).
thf(3980,plain,
! [SV208: $i,SV952: $o,SV818: $i,SV501: $i,SV982: $i] :
( ( ( ~ ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV982 @ SV501 )
| SV952 )
| ~ ( ~ ( in @ SV982 @ SV818 )
| SV952 )
| SV952 )
= $true )
| ( ( in @ SV982 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3791]) ).
thf(3981,plain,
! [SV208: $i,SV818: $i,SV501: $i,SV983: $i] :
( ( ( ~ ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV983 @ SV501 )
| $true )
| ~ ( ~ ( in @ SV983 @ SV818 )
| $true )
| $true )
= $true )
| ( ( in @ SV983 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3792]) ).
thf(3982,plain,
! [SV208: $i,SV818: $i,SV501: $i,SV984: $i] :
( ( ( ~ ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV984 @ SV501 )
| $false )
| ~ ( ~ ( in @ SV984 @ SV818 )
| $false )
| $false )
= $true )
| ( ( in @ SV984 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3793]) ).
thf(3983,plain,
! [SV209: $i,SV502: $i,SV889: $i > $o,SV689: $i,SV1013: $i] :
( ( ( ~ ( in @ SV1013 @ SV689 )
| ( SV889 @ SV1013 ) )
= $true )
| ( ( in @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ SV209 )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3794]) ).
thf(3984,plain,
! [SV502: $i,SV889: $i > $o,SV689: $i,SV209: $i] :
( ( ( ~ ( in @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) @ SV502 ) )
= $false )
| ( ( ! [SY4074: $i] :
( ~ ( in @ SY4074 @ SV689 )
| ( SV889 @ SY4074 ) ) )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3795]) ).
thf(3985,plain,
! [SV209: $i,SV502: $i,SV689: $i,SV889: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) ) @ SV689 )
| ( SV889 @ ( kpair @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) ) ) )
= $false )
| ( ( ! [SY4074: $i] :
( ~ ( in @ SY4074 @ SV689 )
| ( SV889 @ SY4074 ) ) )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3795]) ).
thf(3986,plain,
! [SV819: $i,SV508: $i,SV953: $i,SV216: $i,SV1001: $i] :
( ( ( ~ ( in @ SV1001 @ SV216 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
| ! [SY4155: $o] :
( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
| SY4155 )
| ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| SY4155 )
| SY4155 ) )
= $true )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3796]) ).
thf(3987,plain,
! [SV820: $i,SV509: $i,SV217: $i,SV954: $i] :
( ( ( in @ SV954 @ ( setminus @ SV217 @ ( binunion @ SV509 @ SV820 ) ) )
= $false )
| ( ( in @ SV954 @ ( binintersect @ ( setminus @ SV217 @ SV509 ) @ ( setminus @ SV217 @ SV820 ) ) )
= $true )
| ( ( in @ SV954 @ SV217 )
= $false )
| ( ( in @ SV820 @ ( powerset @ SV217 ) )
= $false )
| ( ( in @ SV509 @ ( powerset @ SV217 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3797]) ).
thf(3988,plain,
! [SV226: $i] :
( ( ~ ! [SY3851: $i] :
( ~ ( in @ SY3851 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY2945: $i] :
( ~ ( in @ SY2945 @ SY3851 )
| ( in @ SY2945 @ SV226 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3800]) ).
thf(3989,plain,
! [SV226: $i] :
( ( ~ ! [SY3853: $i,SY3854: $i] :
( ~ ~ ( ~ ( in @ SY3853 @ SV226 )
| ~ ( in @ SY3854 @ SV226 ) )
| ~ ! [SY3855: $i] :
( ~ ( in @ SY3855 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SY3853 @ SY3855 )
| ( in @ SY3854 @ SY3855 ) )
| ~ ( ~ ( in @ SY3854 @ SY3855 )
| ( in @ SY3853 @ SY3855 ) ) ) )
| ( SY3853 = SY3854 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3800]) ).
thf(3990,plain,
! [SV1014: $i,SV226: $i,SV1002: $i] :
( ( ~ ~ ( ~ ( in @ SV1002 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SV1014 @ ( sK2_SY2943 @ SV226 ) ) )
| ! [SY4166: $i] :
( ~ ( in @ SY4166 @ SV1002 )
| ( in @ SY4166 @ SV1014 ) )
| ! [SY4167: $i] :
( ~ ( in @ SY4167 @ SV1014 )
| ( in @ SY4167 @ SV1002 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3801]) ).
thf(3991,plain,
! [SV226: $i,SV955: $i] :
( ( ( ~ ! [SY4114: $i] :
( ~ ( in @ SY4114 @ SV955 )
| ( in @ SY4114 @ SV226 ) ) )
= $true )
| ( ( ~ ~ ! [SY4115: $i] :
~ ( in @ SY4115 @ SV955 ) )
= $true )
| ( ( ~ ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3802]) ).
thf(3992,plain,
! [SV229: $i,SV822: $i,SV519: $i,SV956: $i] :
( ( ( ~ ( in @ SV956 @ ( binunion @ SV519 @ SV822 ) ) )
= $false )
| ( ( ~ ( in @ SV956 @ SV519 ) )
= $true )
| ( ( in @ SV956 @ SV229 )
= $false )
| ( ( in @ SV822 @ ( powerset @ SV229 ) )
= $false )
| ( ( in @ SV519 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3804]) ).
thf(3993,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1003: $i] :
( ( ( ~ ( ~ ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
| ~ ! [SY4159: $i] :
~ ~ ( ~ ( in @ SY4159 @ SV520 )
| ~ ( SV230 @ SY4159 @ SV1003 ) ) )
| ~ ( ~ ~ ! [SY4160: $i] :
~ ~ ( ~ ( in @ SY4160 @ SV520 )
| ~ ( SV230 @ SY4160 @ SV1003 ) )
| ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3805]) ).
thf(3994,plain,
! [SV957: $i,SV520: $i,SV230: $i > $i > $o] :
( ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( ~ ! [SY4121: $i] :
( ~ ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SY4121 )
| ( SV957 = SY4121 ) ) )
= $true )
| ( ( ~ ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3806]) ).
thf(3995,plain,
! [SV231: $i,SV521: $i,SV705: $i,SV896: $i] :
( ( ( ~ ( in @ ( sK82_SY4081 @ SV896 @ SV705 @ SV521 @ SV231 ) @ SV231 ) )
= $false )
| ( ( SV705 = SV896 )
= $true )
| ( ( func @ SV231 @ SV521 @ SV896 )
= $false )
| ( ( func @ SV231 @ SV521 @ SV705 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3807]) ).
thf(3996,plain,
! [SV896: $i,SV705: $i,SV521: $i,SV231: $i] :
( ( ( ( ap @ SV231 @ SV521 @ SV705 @ ( sK82_SY4081 @ SV896 @ SV705 @ SV521 @ SV231 ) )
= ( ap @ SV231 @ SV521 @ SV896 @ ( sK82_SY4081 @ SV896 @ SV705 @ SV521 @ SV231 ) ) )
= $false )
| ( ( SV705 = SV896 )
= $true )
| ( ( func @ SV231 @ SV521 @ SV896 )
= $false )
| ( ( func @ SV231 @ SV521 @ SV705 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3807]) ).
thf(3997,plain,
! [SV233: $i,SV823: $i > $o,SV523: $i,SV1004: $i] :
( ( ( ~ ( in @ SV1004 @ SV523 ) )
= $true )
| ( ( SV823 @ SV1004 )
= $true )
| ( ( in @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ SV233 )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3808]) ).
thf(3998,plain,
! [SV233: $i,SV823: $i > $o,SV523: $i] :
( ( ( in @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) @ SV233 )
= $true )
| ( ( ! [SY4016: $i] :
( ~ ( in @ SY4016 @ SV523 )
| ( SV823 @ SY4016 ) ) )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3809]) ).
thf(3999,plain,
! [SV233: $i,SV523: $i,SV823: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) ) @ SV523 ) )
= $false )
| ( ( ! [SY4016: $i] :
( ~ ( in @ SY4016 @ SV523 )
| ( SV823 @ SY4016 ) ) )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3810]) ).
thf(4000,plain,
! [SV233: $i,SV523: $i,SV823: $i > $o] :
( ( ( SV823 @ ( kpair @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) ) )
= $false )
| ( ( ! [SY4016: $i] :
( ~ ( in @ SY4016 @ SV523 )
| ( SV823 @ SY4016 ) ) )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3810]) ).
thf(4001,plain,
! [SV901: $i,SV533: $i > $o,SV245: $i] :
( ( ( ( dsetconstr @ SV245
@ ^ [SY3609: $i] : ( SV533 @ SY3609 ) )
!= emptyset )
= $true )
| ( $false = $true )
| ( ( in @ SV901 @ SV245 )
= $false )
| ( ( SV533 @ SV901 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3811]) ).
thf(4002,plain,
! [SV535: $i,SV247: $i,SV827: $i,SV959: $i] :
( ( ( in @ ( kpair @ SV959 @ SV827 ) @ ( breln1invset @ SV247 @ SV535 ) )
= $false )
| ( ( in @ ( kpair @ SV827 @ SV959 ) @ SV535 )
= $true )
| ( ( in @ SV959 @ SV247 )
= $false )
| ( ( in @ SV827 @ SV247 )
= $false )
| ( ( breln1 @ SV247 @ SV535 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3812]) ).
thf(4003,plain,
! [SV251: $i,SV828: $i,SV538: $i,SV960: $i] :
( ( ( ~ ( in @ SV960 @ SV538 ) )
= $false )
| ( ( ~ ~ ( in @ SV960 @ SV828 )
| ~ ( in @ SV960 @ ( binunion @ SV538 @ SV828 ) ) )
= $true )
| ( ( in @ SV960 @ SV251 )
= $false )
| ( ( in @ SV828 @ ( powerset @ SV251 ) )
= $false )
| ( ( in @ SV538 @ ( powerset @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3813]) ).
thf(4004,plain,
! [SV548: $i,SV259: $i,SV719: $i,SV985: $i,SV908: $i] :
( ( ( ~ ( in @ ( kpair @ SV908 @ SV985 ) @ SV719 ) )
= $true )
| ( ( ( ap @ SV259 @ SV548 @ SV719 @ SV908 )
= SV985 )
= $true )
| ( ( in @ SV985 @ SV548 )
= $false )
| ( ( in @ SV908 @ SV259 )
= $false )
| ( ( func @ SV259 @ SV548 @ SV719 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3814]) ).
thf(4005,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( in @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SV260 )
= $true )
| ( ( ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) )
| ( SV549 = SV829 ) )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3815]) ).
thf(4006,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( ~ ( in @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) @ SV260 )
| ~ ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV549 )
| ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV829 ) )
= $false )
| ( ( ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) )
| ( SV549 = SV829 ) )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3816]) ).
thf(4007,plain,
! [SV830: $i,SV553: $i,SV961: $i,SV264: $i,SV1005: $i] :
( ( ( ~ ( in @ SV1005 @ SV264 ) )
= $true )
| ( ( ~ ( ( in @ ( kpair @ SV961 @ SV1005 ) @ SV553 )
| ( in @ ( kpair @ SV961 @ SV1005 ) @ SV830 ) )
| ( in @ ( kpair @ SV961 @ SV1005 ) @ ( binunion @ SV553 @ SV830 ) ) )
= $true )
| ( ( in @ SV961 @ SV264 )
= $false )
| ( ( breln1 @ SV264 @ SV830 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3817]) ).
thf(4008,plain,
! [SV271: $i,SV833: $i > $o,SV559: $i,SV1006: $i] :
( ( ( ~ ( in @ SV1006 @ SV559 ) )
= $true )
| ( ( SV833 @ SV1006 )
= $true )
| ( ( in @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ SV271 )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3818]) ).
thf(4009,plain,
! [SV271: $i,SV833: $i > $o,SV559: $i] :
( ( ( in @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) @ SV271 )
= $true )
| ( ( ! [SY4028: $i] :
( ~ ( in @ SY4028 @ SV559 )
| ( SV833 @ SY4028 ) ) )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3819]) ).
thf(4010,plain,
! [SV271: $i,SV559: $i,SV833: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) ) @ SV559 ) )
= $false )
| ( ( ! [SY4028: $i] :
( ~ ( in @ SY4028 @ SV559 )
| ( SV833 @ SY4028 ) ) )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3820]) ).
thf(4011,plain,
! [SV271: $i,SV559: $i,SV833: $i > $o] :
( ( ( SV833 @ ( kpair @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) ) )
= $false )
| ( ( ! [SY4028: $i] :
( ~ ( in @ SY4028 @ SV559 )
| ( SV833 @ SY4028 ) ) )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3820]) ).
thf(4012,plain,
! [SV563: $i > $o,SV275: $i,SV989: $i] :
( ( ( ~ ( in @ SV989 @ SV275 )
| ~ ( SV563 @ SV989 ) )
= $true )
| ( ( in @ ( sK16_SY3653 @ SV563 @ SV275 ) @ SV275 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3821]) ).
thf(4013,plain,
! [SV563: $i > $o,SV275: $i,SV990: $i] :
( ( ( ~ ( in @ SV990 @ SV275 )
| ~ ( SV563 @ SV990 ) )
= $true )
| ( ( SV563 @ ( sK16_SY3653 @ SV563 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3822]) ).
thf(4014,plain,
! [SV835: $i,SV565: $i,SV277: $i,SV962: $i] :
( ( ( in @ SV962 @ ( setminus @ SV277 @ ( binunion @ SV565 @ SV835 ) ) )
= $false )
| ( ( in @ SV962 @ ( setminus @ SV277 @ SV565 ) )
= $true )
| ( ( in @ SV962 @ SV277 )
= $false )
| ( ( in @ SV835 @ ( powerset @ SV277 ) )
= $false )
| ( ( in @ SV565 @ ( powerset @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3823]) ).
thf(4015,plain,
! [SV566: $i,SV278: $i] :
( ( ( in @ ( sK69_SY3658 @ SV278 @ SV566 ) @ SV566 )
= $true )
| ( ( SV278 = SV566 )
= $true )
| ( ( in @ ( sK17_SY3657 @ SV566 @ SV278 ) @ SV278 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3824]) ).
thf(4016,plain,
! [SV836: $i,SV568: $i,SV963: $i,SV280: $i,SV1007: $i] :
( ( ( ~ ( in @ SV1007 @ SV280 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
| ! [SY4161: $o] :
( ~ ! [SY4162: $i] :
( ~ ( in @ SY4162 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SY4162 ) @ SV568 )
| ~ ( in @ ( kpair @ SY4162 @ SV1007 ) @ SV836 )
| SY4161 )
| SY4161 ) )
= $true )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3827]) ).
thf(4017,plain,
! [SV837: $i,SV288: $i > $o] :
( ( ( ~ ( SV288 @ ( sK83_SY4034 @ SV837 @ SV288 ) ) )
= $false )
| ( ( SV288 @ SV837 )
= $false )
| ( ( ! [SY3119: $i,SY3120: $i] :
( ~ ( SV288 @ SY3119 )
| ~ ( SV288 @ SY3120 )
| ( SY3119 = SY3120 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3830]) ).
thf(4018,plain,
! [SV288: $i > $o,SV837: $i] :
( ( ( SV837
= ( sK83_SY4034 @ SV837 @ SV288 ) )
= $false )
| ( ( SV288 @ SV837 )
= $false )
| ( ( ! [SY3119: $i,SY3120: $i] :
( ~ ( SV288 @ SY3119 )
| ~ ( SV288 @ SY3120 )
| ( SY3119 = SY3120 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3830]) ).
thf(4019,plain,
! [SV575: $i > $o,SV289: $i,SV1015: $i] :
( ( ( ~ ( in @ SV1015 @ SV289 )
| ~ ( SV575 @ SV1015 ) )
= $true )
| ( ( in @ ( sK43_SY3670 @ SV575 @ SV289 ) @ SV289 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3831]) ).
thf(4020,plain,
! [SV575: $i > $o,SV289: $i,SV1016: $i] :
( ( ( ~ ( in @ SV1016 @ SV289 )
| ~ ( SV575 @ SV1016 ) )
= $true )
| ( ( SV575 @ ( sK43_SY3670 @ SV575 @ SV289 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3832]) ).
thf(4021,plain,
! [SV298: $i,SV757: $o,SV583: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV583 )
| SV757 )
= $false )
| ( SV757 = $true )
| ( ( in @ SV733 @ SV298 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3834]) ).
thf(4022,plain,
! [SV298: $i,SV757: $o,SV583: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV583 ) )
= $false )
| ( SV757 = $true )
| ( SV757 = $false )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3835]) ).
thf(4023,plain,
! [SV583: $i,SV298: $i,SV733: $i,SV757: $o] :
( ( SV757 = $false )
| ( SV757 = $true )
| ( SV757 = $false )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3835]) ).
thf(4024,plain,
! [SV298: $i,SV583: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV583 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV733 @ SV298 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3836]) ).
thf(4025,plain,
! [SV298: $i,SV583: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV583 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3837]) ).
thf(4026,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3837]) ).
thf(4027,plain,
! [SV298: $i,SV583: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV583 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV733 @ SV298 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3838]) ).
thf(4028,plain,
! [SV298: $i,SV583: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV583 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3839]) ).
thf(4029,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3839]) ).
thf(4030,plain,
! [SV299: $i,SV584: $i,SV840: $i] :
( ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV299 )
= $true )
| ( ( ~ ! [SY4036: $i] :
( ~ ( in @ SY4036 @ SV299 )
| ~ ( in @ SY4036 @ SV840 )
| ( in @ SY4036 @ SV584 ) )
| ( SV584 = SV840 ) )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3840]) ).
thf(4031,plain,
! [SV299: $i,SV584: $i,SV840: $i] :
( ( ( ~ ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV584 ) )
= $false )
| ( ( ~ ! [SY4036: $i] :
( ~ ( in @ SY4036 @ SV299 )
| ~ ( in @ SY4036 @ SV840 )
| ( in @ SY4036 @ SV584 ) )
| ( SV584 = SV840 ) )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3841]) ).
thf(4032,plain,
! [SV299: $i,SV584: $i,SV840: $i] :
( ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV840 )
= $false )
| ( ( ~ ! [SY4036: $i] :
( ~ ( in @ SY4036 @ SV299 )
| ~ ( in @ SY4036 @ SV840 )
| ( in @ SY4036 @ SV584 ) )
| ( SV584 = SV840 ) )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3841]) ).
thf(4033,plain,
! [SV841: $i,SV585: $i,SV964: $i,SV300: $i,SV1008: $i] :
( ( ( ~ ( in @ SV1008 @ SV300 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV964 @ SV1008 ) @ SV585 )
| ( in @ ( kpair @ SV964 @ SV1008 ) @ ( binunion @ SV585 @ SV841 ) ) )
= $true )
| ( ( in @ SV964 @ SV300 )
= $false )
| ( ( breln1 @ SV300 @ SV841 )
= $false )
| ( ( breln1 @ SV300 @ SV585 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3842]) ).
thf(4034,plain,
! [SV301: $i,SV586: $i,SV734: $i,SV911: $i] :
( ( ( ~ ( in @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) @ SV301 ) )
= $false )
| ( ( ! [SY4088: $i] :
( ~ ( in @ SY4088 @ SV301 )
| ! [SY4089: $i] :
( ~ ( in @ SY4089 @ SV586 )
| ~ ( in @ ( kpair @ SY4088 @ SY4089 ) @ SV911 )
| ( in @ ( kpair @ SY4088 @ SY4089 ) @ SV734 ) ) ) )
= $true )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3843]) ).
thf(4035,plain,
! [SV911: $i,SV734: $i,SV586: $i,SV301: $i] :
( ( ( ( ap @ SV301 @ SV586 @ SV734 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) )
= ( ap @ SV301 @ SV586 @ SV911 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) ) )
= $false )
| ( ( ! [SY4088: $i] :
( ~ ( in @ SY4088 @ SV301 )
| ! [SY4089: $i] :
( ~ ( in @ SY4089 @ SV586 )
| ~ ( in @ ( kpair @ SY4088 @ SY4089 ) @ SV911 )
| ( in @ ( kpair @ SY4088 @ SY4089 ) @ SV734 ) ) ) )
= $true )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3843]) ).
thf(4036,plain,
! [SV842: $i,SV587: $i,SV302: $i,SV965: $i] :
( ( ( in @ SV965 @ ( binunion @ ( setminus @ SV302 @ SV587 ) @ ( setminus @ SV302 @ SV842 ) ) )
= $false )
| ( ( in @ SV965 @ ( setminus @ SV302 @ ( binintersect @ SV587 @ SV842 ) ) )
= $true )
| ( ( in @ SV965 @ SV302 )
= $false )
| ( ( in @ SV842 @ ( powerset @ SV302 ) )
= $false )
| ( ( in @ SV587 @ ( powerset @ SV302 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3844]) ).
thf(4037,plain,
! [SV844: $i,SV590: $i,SV307: $i,SV967: $i] :
( ( ( in @ SV967 @ ( binintersect @ ( setminus @ SV307 @ SV590 ) @ ( setminus @ SV307 @ SV844 ) ) )
= $false )
| ( ( in @ SV967 @ ( setminus @ SV307 @ ( binunion @ SV590 @ SV844 ) ) )
= $true )
| ( ( in @ SV967 @ SV307 )
= $false )
| ( ( in @ SV844 @ ( powerset @ SV307 ) )
= $false )
| ( ( in @ SV590 @ ( powerset @ SV307 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3845]) ).
thf(4038,plain,
! [SV308: $i,SV591: $i,SV845: $i] :
( ( ( in @ ( sK71_SY4042 @ SV845 @ SV591 @ SV308 ) @ SV308 )
= $true )
| ( ( in @ SV591 @ ( powerset @ SV845 ) )
= $true )
| ( ( in @ SV845 @ ( powerset @ SV308 ) )
= $false )
| ( ( in @ SV591 @ ( powerset @ SV308 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3846]) ).
thf(4039,plain,
! [SV308: $i,SV591: $i,SV845: $i] :
( ( ( ~ ( in @ ( sK71_SY4042 @ SV845 @ SV591 @ SV308 ) @ SV591 ) )
= $false )
| ( ( in @ SV591 @ ( powerset @ SV845 ) )
= $true )
| ( ( in @ SV845 @ ( powerset @ SV308 ) )
= $false )
| ( ( in @ SV591 @ ( powerset @ SV308 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3847]) ).
thf(4040,plain,
! [SV308: $i,SV591: $i,SV845: $i] :
( ( ( in @ ( sK71_SY4042 @ SV845 @ SV591 @ SV308 ) @ SV845 )
= $false )
| ( ( in @ SV591 @ ( powerset @ SV845 ) )
= $true )
| ( ( in @ SV845 @ ( powerset @ SV308 ) )
= $false )
| ( ( in @ SV591 @ ( powerset @ SV308 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3847]) ).
thf(4041,plain,
! [SV846: $i,SV592: $i,SV309: $i,SV968: $i] :
( ( ( in @ SV968 @ ( setminus @ SV309 @ SV592 ) )
= $false )
| ( ( ~ ( in @ SV968 @ ( setminus @ SV309 @ SV846 ) )
| ( in @ SV968 @ ( setminus @ SV309 @ ( binunion @ SV592 @ SV846 ) ) ) )
= $true )
| ( ( in @ SV968 @ SV309 )
= $false )
| ( ( in @ SV846 @ ( powerset @ SV309 ) )
= $false )
| ( ( in @ SV592 @ ( powerset @ SV309 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3848]) ).
thf(4042,plain,
! [SV847: $i,SV598: $i,SV315: $i,SV969: $i] :
( ( ( in @ SV969 @ ( setminus @ SV315 @ ( binunion @ SV598 @ SV847 ) ) )
= $false )
| ( ( ~ ( in @ SV969 @ SV598 ) )
= $true )
| ( ( in @ SV969 @ SV315 )
= $false )
| ( ( in @ SV847 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV598 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3849]) ).
thf(4043,plain,
! [SV848: $i,SV316: $i > $o] :
( ( ( ~ ( SV316 @ ( sK85_SY4045 @ SV848 @ SV316 ) ) )
= $false )
| ( ( SV316 @ SV848 )
= $false )
| ( ( ~ ! [SY3190: $i] :
~ ! [SY3191: $i] :
~ ( ~ ( ~ ( SV316 @ SY3191 )
| ( SY3191 = SY3190 ) )
| ~ ( ( SY3191 != SY3190 )
| ( SV316 @ SY3191 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3850]) ).
thf(4044,plain,
! [SV316: $i > $o,SV848: $i] :
( ( ( SV848
= ( sK85_SY4045 @ SV848 @ SV316 ) )
= $false )
| ( ( SV316 @ SV848 )
= $false )
| ( ( ~ ! [SY3190: $i] :
~ ! [SY3191: $i] :
~ ( ~ ( ~ ( SV316 @ SY3191 )
| ( SY3191 = SY3190 ) )
| ~ ( ( SY3191 != SY3190 )
| ( SV316 @ SY3191 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3850]) ).
thf(4045,plain,
! [SV849: $i,SV970: $i,SV599: $i,SV317: $i,SV1009: $i] :
( ( ( ~ ( in @ SV1009 @ ( powerset @ SV317 ) ) )
= $true )
| ( ( ~ ( subset @ SV599 @ SV970 )
| ~ ( subset @ SV849 @ SV1009 )
| ( subset @ ( binintersect @ SV599 @ SV849 ) @ ( binintersect @ SV970 @ SV1009 ) ) )
= $true )
| ( ( in @ SV970 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV849 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3851]) ).
thf(4046,plain,
! [SV318: $i,SV600: $i,SV850: $i,SV971: $i] :
( ( ( ~ ( in @ SV971 @ SV850 ) )
= $false )
| ( ( ~ ( in @ SV971 @ ( binintersect @ SV600 @ SV850 ) ) )
= $true )
| ( ( in @ SV971 @ SV318 )
= $false )
| ( ( in @ SV850 @ ( powerset @ SV318 ) )
= $false )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3852]) ).
thf(4047,plain,
! [SV319: $i,SV601: $i,SV914: $i > $o,SV738: $i,SV1017: $i] :
( ( ( ~ ( in @ SV1017 @ SV738 )
| ( SV914 @ SV1017 ) )
= $true )
| ( ( in @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ SV319 )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3853]) ).
thf(4048,plain,
! [SV601: $i,SV914: $i > $o,SV738: $i,SV319: $i] :
( ( ( ~ ( in @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) @ SV601 ) )
= $false )
| ( ( ! [SY4092: $i] :
( ~ ( in @ SY4092 @ SV738 )
| ( SV914 @ SY4092 ) ) )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3854]) ).
thf(4049,plain,
! [SV319: $i,SV601: $i,SV738: $i,SV914: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) ) @ SV738 )
| ( SV914 @ ( kpair @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) ) ) )
= $false )
| ( ( ! [SY4092: $i] :
( ~ ( in @ SY4092 @ SV738 )
| ( SV914 @ SY4092 ) ) )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3854]) ).
thf(4050,plain,
! [SV322: $i,SV851: $i] :
( ( ( in @ ( sK51_SY3211 @ SV851 @ SV322 ) @ SV322 )
= $true )
| ( ( in @ SV851 @ SV322 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3858]) ).
thf(4051,plain,
! [SV322: $i,SV851: $i] :
( ( ( ~ ~ ! [SY4130: $i] :
~ ~ ( ~ ( in @ SY4130 @ ( sK51_SY3211 @ SV851 @ SV322 ) )
| ~ ( in @ SY4130 @ SV322 ) ) )
= $true )
| ( ( in @ SV851 @ SV322 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3859]) ).
thf(4052,plain,
! [SV325: $i,SV972: $i,SV852: $i,SV606: $i] :
( ( ( subset @ SV606 @ SV852 )
= $false )
| ( ( ~ ( subset @ SV606 @ SV972 )
| ( subset @ SV606 @ ( binintersect @ SV852 @ SV972 ) ) )
= $true )
| ( ( in @ SV972 @ ( powerset @ SV325 ) )
= $false )
| ( ( in @ SV852 @ ( powerset @ SV325 ) )
= $false )
| ( ( in @ SV606 @ ( powerset @ SV325 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3860]) ).
thf(4053,plain,
! [SV759: $i,SV40: $i > $o] :
( ( ( SV40 @ ( sK72_SY3941 @ SV759 @ SV40 ) )
= $true )
| ( ( SV40 @ SV759 )
= $false )
| ( ( ~ ! [SY2411: $i] :
~ ( SV40 @ SY2411 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3861]) ).
thf(4054,plain,
! [SV759: $i,SV40: $i > $o] :
( ( ( ! [SY2411: $i] :
~ ( SV40 @ SY2411 ) )
= $false )
| ( ( SV40 @ SV759 )
= $false )
| ( ( SV759
= ( sK72_SY3941 @ SV759 @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3862]) ).
thf(4055,plain,
! [SV760: $i,SV42: $i > $o] :
( ( ( SV42 @ ( sK73_SY3942 @ SV760 @ SV42 ) )
= $true )
| ( ( SV42 @ SV760 )
= $false )
| ( ( SV42
@ ( descr
@ ^ [SY2417: $i] : ( SV42 @ SY2417 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3863]) ).
thf(4056,plain,
! [SV353: $i > $o,SV44: $i,SV991: $i] :
( ( ( ~ ( in @ SV991 @ SV44 )
| ~ ( SV353 @ SV991 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( in @ ( sK9_SY3238 @ SV353 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3865]) ).
thf(4057,plain,
! [SV353: $i > $o,SV44: $i,SV1018: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1018 @ SV44 )
| ~ ( SV353 @ SV1018 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( in @ ( sK36_SY3943 @ SV353 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3866]) ).
thf(4058,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ( ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( SV353 @ ( sK9_SY3238 @ SV353 @ SV44 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3867]) ).
thf(4059,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ( ~ ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( SV353 @ ( sK36_SY3943 @ SV353 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3868]) ).
thf(4060,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ( ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( ( sK9_SY3238 @ SV353 @ SV44 )
= ( sK36_SY3943 @ SV353 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3869]) ).
thf(4061,plain,
! [SV45: $i,SV354: $i,SV612: $i,SV854: $i] :
( ( ( in @ ( sK74_SY4050 @ SV854 @ SV612 @ SV354 @ SV45 ) @ SV45 )
= $true )
| ( ( SV612 = SV854 )
= $true )
| ( ( in @ SV854 @ ( funcSet @ SV45 @ SV354 ) )
= $false )
| ( ( in @ SV612 @ ( funcSet @ SV45 @ SV354 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3870]) ).
thf(4062,plain,
! [SV923: $i,SV762: $i,SV361: $i,SV52: $i,SV992: $i] :
( ( ( in @ SV992 @ SV52 )
= $false )
| ( ( ~ ( in @ SV992 @ ( binintersect @ SV361 @ SV762 ) )
| ( in @ SV992 @ ( binunion @ SV762 @ SV923 ) ) )
= $true )
| ( ( in @ SV923 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV762 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3872]) ).
thf(4063,plain,
! [SV924: $i,SV764: $i,SV365: $i,SV56: $i,SV993: $i] :
( ( ( in @ SV993 @ ( powerset @ SV56 ) )
= $false )
| ( ( ( setminus @ SV56 @ ( binintersect @ ( binunion @ SV365 @ SV764 ) @ ( binunion @ SV924 @ SV993 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV56 @ SV365 ) @ ( setminus @ SV56 @ SV764 ) ) @ ( binintersect @ ( setminus @ SV56 @ SV924 ) @ ( setminus @ SV56 @ SV993 ) ) ) )
= $true )
| ( ( in @ SV924 @ ( powerset @ SV56 ) )
= $false )
| ( ( in @ SV764 @ ( powerset @ SV56 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3873]) ).
thf(4064,plain,
! [SV57: $i,SV366: $i] :
( ( ( in @ SV366 @ ( sK52_SY3265 @ SV57 @ SV366 ) )
= $true )
| ( ( in @ SV366 @ ( setunion @ SV57 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3874]) ).
thf(4065,plain,
! [SV366: $i,SV57: $i] :
( ( ( in @ ( sK52_SY3265 @ SV57 @ SV366 ) @ SV57 )
= $true )
| ( ( in @ SV366 @ ( setunion @ SV57 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3875]) ).
thf(4066,plain,
! [SV57: $i,SV973: $i,SV366: $i] :
( ( ( in @ SV366 @ SV973 )
= $false )
| ( ( ~ ( in @ SV973 @ SV57 ) )
= $true )
| ( ( in @ SV366 @ ( setunion @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3876]) ).
thf(4067,plain,
! [SV765: $i,SV58: $i > $o] :
( ( ( SV58 @ ( sK75_SY3949 @ SV765 @ SV58 ) )
= $true )
| ( ( SV58 @ SV765 )
= $false )
| ( ( ! [SY2464: $i,SY2465: $i] :
( ~ ( SV58 @ SY2464 )
| ~ ( SV58 @ SY2465 )
| ( SY2464 = SY2465 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3877]) ).
thf(4068,plain,
! [SV765: $i,SV1019: $i,SV58: $i > $o] :
( ( ( ! [SY4168: $i] :
( ~ ( SV58 @ SV1019 )
| ~ ( SV58 @ SY4168 )
| ( SV1019 = SY4168 ) ) )
= $true )
| ( ( SV58 @ SV765 )
= $false )
| ( ( SV765
= ( sK75_SY3949 @ SV765 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3878]) ).
thf(4069,plain,
! [SV59: $i > $o,SV766: $i] :
( ( ( ( ( sK37_SY3950 @ SV766 @ SV59 )
!= SV766 )
| ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) ) )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3879]) ).
thf(4070,plain,
! [SV59: $i > $o,SV766: $i] :
( ( ( ( sK37_SY3950 @ SV766 @ SV59 )
!= SV766 )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3880]) ).
thf(4071,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3880]) ).
thf(4072,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( SV60 @ ( sK76_SY3951 @ SV767 @ SV60 ) )
= $true )
| ( ( SV60 @ SV767 )
= $false )
| ( ( ~ ! [SY2472: $i] :
~ ~ ( ~ ( SV60 @ SY2472 )
| ~ ! [SY2473: $i] :
( ~ ( SV60 @ SY2473 )
| ( SY2472 = SY2473 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3881]) ).
thf(4073,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ! [SY2472: $i] :
~ ~ ( ~ ( SV60 @ SY2472 )
| ~ ! [SY2473: $i] :
( ~ ( SV60 @ SY2473 )
| ( SY2472 = SY2473 ) ) ) )
= $false )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV767
= ( sK76_SY3951 @ SV767 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3882]) ).
thf(4074,plain,
! [SV61: $i,SV367: $i > $o,SV858: $i] :
( ( ( ~ ( in @ ( sK59_SY3268 @ SV858 @ SV367 @ SV61 ) @ SV61 ) )
= $false )
| ( ( SV367 @ SV858 )
= $true )
| ( ( in @ SV858 @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3883]) ).
thf(4075,plain,
! [SV61: $i,SV858: $i,SV367: $i > $o] :
( ( ( ~ ~ ( SV367 @ ( sK59_SY3268 @ SV858 @ SV367 @ SV61 ) ) )
= $false )
| ( ( SV367 @ SV858 )
= $true )
| ( ( in @ SV858 @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3883]) ).
thf(4076,plain,
! [SV65: $i,SV371: $i] :
( ( ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV371 )
= $true )
| ( ( in @ ( sK10_SY3275 @ SV371 @ SV65 ) @ SV65 )
= $true )
| ( ( SV65 = SV371 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3884]) ).
thf(4077,plain,
! [SV372: $i,SV68: $i,SV768: $i,SV986: $i] :
( ( ( ~ ( in @ SV986 @ SV768 ) )
= $true )
| ( ( in @ SV986 @ ( setminus @ SV68 @ SV372 ) )
= $true )
| ( ( in @ SV986 @ SV68 )
= $false )
| ( ( subset @ SV372 @ ( setminus @ SV68 @ SV768 ) )
= $false )
| ( ( in @ SV768 @ ( powerset @ SV68 ) )
= $false )
| ( ( in @ SV372 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3887]) ).
thf(4078,plain,
! [SV72: $i,SV860: $o,SV376: $i,SV621: $i] :
( ( ( ~ ( in @ SV621 @ SV376 ) )
= $false )
| ( SV860 = $true )
| ( ( SV621 = SV72 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3889]) ).
thf(4079,plain,
! [SV376: $i,SV72: $i,SV621: $i,SV860: $o] :
( ( SV860 = $false )
| ( SV860 = $true )
| ( ( SV621 = SV72 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3889]) ).
thf(4080,plain,
! [SV72: $i,SV860: $o,SV376: $i,SV621: $i] :
( ( ( in @ SV621 @ SV376 )
= $true )
| ( SV860 = $true )
| ( SV860 = $false )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3890]) ).
thf(4081,plain,
! [SV72: $i,SV376: $i,SV621: $i] :
( ( ( ~ ( in @ SV621 @ SV376 ) )
= $false )
| ( $true = $true )
| ( ( SV621 = SV72 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3892]) ).
thf(4082,plain,
! [SV376: $i,SV72: $i,SV621: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( SV621 = SV72 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3892]) ).
thf(4083,plain,
! [SV72: $i,SV376: $i,SV621: $i] :
( ( ( in @ SV621 @ SV376 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3893]) ).
thf(4084,plain,
! [SV72: $i,SV376: $i,SV621: $i] :
( ( ( ~ ( in @ SV621 @ SV376 ) )
= $false )
| ( $false = $true )
| ( ( SV621 = SV72 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3895]) ).
thf(4085,plain,
! [SV376: $i,SV72: $i,SV621: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( SV621 = SV72 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3895]) ).
thf(4086,plain,
! [SV72: $i,SV376: $i,SV621: $i] :
( ( ( in @ SV621 @ SV376 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3896]) ).
thf(4087,plain,
! [SV76: $i,SV622: $i,SV380: $i > $i] :
( ( ( ~ ( in @ ( sK60_SY3750 @ SV380 @ SV622 @ SV76 ) @ SV76 ) )
= $false )
| ( ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3287: $i] : ( SV380 @ SY3287 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3899]) ).
thf(4088,plain,
! [SV76: $i,SV380: $i > $i,SV622: $i] :
( ( ( SV622
!= ( SV380 @ ( sK60_SY3750 @ SV380 @ SV622 @ SV76 ) ) )
= $false )
| ( ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3287: $i] : ( SV380 @ SY3287 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3899]) ).
thf(4089,plain,
! [SV380: $i > $i,SV622: $i,SV76: $i,SV987: $i] :
( ( ( ~ ( in @ SV987 @ SV76 ) )
= $true )
| ( ( SV622
!= ( SV380 @ SV987 ) )
= $true )
| ( ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3290: $i] : ( SV380 @ SY3290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3900]) ).
thf(4090,plain,
! [SV773: $i,SV382: $i,SV927: $i,SV78: $i,SV994: $i] :
( ( ( in @ SV994 @ SV78 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV927 @ SV994 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
| ~ ! [SY4151: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY4151 @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ SY4151 ) @ SV382 ) )
| ~ ( in @ ( kpair @ SY4151 @ SV994 ) @ SV773 ) ) )
= $true )
| ( ( in @ SV927 @ SV78 )
= $false )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3902]) ).
thf(4091,plain,
! [SV774: $i,SV386: $i,SV928: $i,SV82: $i,SV995: $i] :
( ( ( in @ SV995 @ SV82 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV928 @ SV995 ) @ ( binunion @ SV386 @ SV774 ) )
| ( in @ ( kpair @ SV928 @ SV995 ) @ SV386 )
| ( in @ ( kpair @ SV928 @ SV995 ) @ SV774 ) )
= $true )
| ( ( in @ SV928 @ SV82 )
= $false )
| ( ( breln1 @ SV82 @ SV774 )
= $false )
| ( ( breln1 @ SV82 @ SV386 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3903]) ).
thf(4092,plain,
! [SV86: $i,SV389: $i,SV776: $i,SV929: $i] :
( ( ( ~ ( in @ SV929 @ SV776 ) )
= $true )
| ( ( ~ ( in @ SV929 @ SV389 ) )
= $true )
| ( ( subset @ SV389 @ ( setminus @ SV86 @ SV776 ) )
= $false )
| ( ( in @ SV929 @ SV86 )
= $false )
| ( ( in @ SV776 @ ( powerset @ SV86 ) )
= $false )
| ( ( in @ SV389 @ ( powerset @ SV86 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3904]) ).
thf(4093,plain,
! [SV87: $i,SV390: $i,SV777: $i,SV930: $i] :
( ( ( ~ ~ ( in @ SV930 @ SV777 ) )
= $true )
| ( ( ~ ( in @ SV930 @ SV390 ) )
= $true )
| ( ( subset @ SV390 @ SV777 )
= $false )
| ( ( in @ SV930 @ SV87 )
= $false )
| ( ( in @ SV777 @ ( powerset @ SV87 ) )
= $false )
| ( ( in @ SV390 @ ( powerset @ SV87 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3905]) ).
thf(4094,plain,
! [SV931: $i,SV779: $i,SV393: $i,SV90: $i,SV996: $i] :
( ( ( in @ SV996 @ SV90 )
= $false )
| ( ( ~ ( in @ SV996 @ ( binintersect @ SV393 @ SV779 ) )
| ( in @ SV996 @ ( binintersect @ ( binunion @ SV393 @ SV931 ) @ ( binunion @ SV779 @ SV931 ) ) ) )
= $true )
| ( ( in @ SV931 @ ( powerset @ SV90 ) )
= $false )
| ( ( in @ SV779 @ ( powerset @ SV90 ) )
= $false )
| ( ( in @ SV393 @ ( powerset @ SV90 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3906]) ).
thf(4095,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $false )
| ( ( SV100 @ ( sK53_SY2563 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3908]) ).
thf(4096,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( SV100 @ ( sK61_SY4131 @ SV781 @ SV100 ) )
= $true )
| ( ( ~ ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3909]) ).
thf(4097,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $false )
| ( ( ( sK53_SY2563 @ SV781 @ SV100 )
= ( sK61_SY4131 @ SV781 @ SV100 ) )
= $false )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3910]) ).
thf(4098,plain,
! [SV862: $i,SV404: $i > $o,SV104: $i] :
( ( ( ! [SY3324: $i] :
( ~ ( in @ SY3324 @ SV104 )
| ( SV404 @ SY3324 ) ) )
= $false )
| ( ( in @ SV862 @ SV104 )
= $false )
| ( ( SV404 @ SV862 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3911]) ).
thf(4099,plain,
! [SV106: $i] :
( ( ( in @ ( sK44_SY2577 @ SV106 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( ! [SY2578: $i] :
( ~ ( in @ SY2578 @ omega )
| ( in @ SY2578 @ SV106 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3912]) ).
thf(4100,plain,
! [SV106: $i] :
( ( ( in @ ( sK44_SY2577 @ SV106 ) @ SV106 )
= $true )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( ! [SY2578: $i] :
( ~ ( in @ SY2578 @ omega )
| ( in @ SY2578 @ SV106 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3913]) ).
thf(4101,plain,
! [SV109: $i,SV407: $i,SV782: $i] :
( ( ( in @ ( sK62_SY3965 @ SV782 @ SV407 @ SV109 ) @ SV407 )
= $true )
| ( ( subset @ SV407 @ SV782 )
= $true )
| ( ( in @ SV782 @ ( powerset @ SV109 ) )
= $false )
| ( ( in @ SV407 @ ( powerset @ SV109 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3916]) ).
thf(4102,plain,
! [SV110: $i,SV783: $i,SV408: $i,SV933: $i] :
( ( ( in @ SV933 @ SV408 )
= $true )
| ( ( ~ ( in @ SV933 @ ( binintersect @ SV408 @ SV783 ) ) )
= $true )
| ( ( in @ SV933 @ SV110 )
= $false )
| ( ( in @ SV783 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV408 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3918]) ).
thf(4103,plain,
! [SV118: $i,SV639: $i,SV416: $i > $o] :
( ( ( SV416 @ ( sK63_SY3768 @ SV639 @ SV416 @ SV118 ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY3351: $i] : ( SV416 @ SY3351 ) )
= $true )
| ( ( SV416 @ SV639 )
= $false )
| ( ( in @ SV639 @ SV118 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3921]) ).
thf(4104,plain,
! [SV420: $i,SV865: $i > $o,SV788: $i > $o,SV122: $i] :
( ( ( in @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) @ SV420 )
= $true )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3923]) ).
thf(4105,plain,
! [SV122: $i,SV420: $i,SV788: $i > $o,SV865: $i > $o] :
( ( ( ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 )
!= ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
= $false )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3924]) ).
thf(4106,plain,
! [SV122: $i,SV420: $i,SV865: $i > $o,SV788: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) )
| ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) ) )
| ~ ( ~ ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
| ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3924]) ).
thf(4107,plain,
! [SV123: $i,SV789: $i,SV936: $i,SV421: $i > $o] :
( ( ( ~ ( SV421 @ SV936 ) )
= $true )
| ( ( SV789 = SV936 )
= $true )
| ( ( SV421 @ SV789 )
= $false )
| ( ( in @ SV936 @ SV123 )
= $false )
| ( ( in @ SV789 @ SV123 )
= $false )
| ( ( ex1 @ SV123
@ ^ [SY3363: $i] : ( SV421 @ SY3363 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3925]) ).
thf(4108,plain,
! [SV423: $i,SV790: $i,SV937: $i,SV125: $i,SV997: $i] :
( ( ( in @ SV997 @ SV125 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV937 @ SV997 ) @ SV790 )
| ( in @ ( kpair @ SV937 @ SV997 ) @ ( binunion @ SV423 @ SV790 ) ) )
= $true )
| ( ( in @ SV937 @ SV125 )
= $false )
| ( ( breln1 @ SV125 @ SV790 )
= $false )
| ( ( breln1 @ SV125 @ SV423 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3926]) ).
thf(4109,plain,
! [SV792: $i,SV428: $i,SV939: $i,SV131: $i,SV998: $i] :
( ( ( in @ SV998 @ SV131 )
= $false )
| ( ( ! [SY4152: $i] :
( ~ ( in @ SY4152 @ SV131 )
| ~ ( in @ ( kpair @ SV939 @ SY4152 ) @ SV428 )
| ~ ( in @ ( kpair @ SY4152 @ SV998 ) @ SV792 )
| ( in @ ( kpair @ SV939 @ SV998 ) @ ( breln1compset @ SV131 @ SV428 @ SV792 ) ) ) )
= $true )
| ( ( in @ SV939 @ SV131 )
= $false )
| ( ( breln1 @ SV131 @ SV792 )
= $false )
| ( ( breln1 @ SV131 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3927]) ).
thf(4110,plain,
! [SV135: $i,SV794: $i,SV432: $i] :
( ( ( ~ ( in @ ( sK87_SY4149 @ SV432 @ SV794 @ SV135 ) @ SV135 ) )
= $false )
| ( ( subset @ SV432 @ SV794 )
= $true )
| ( ( breln1 @ SV135 @ SV794 )
= $false )
| ( ( breln1 @ SV135 @ SV432 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3929]) ).
thf(4111,plain,
! [SV135: $i,SV432: $i,SV794: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK64_SY3983 @ SV794 @ SV432 @ SV135 ) @ ( sK87_SY4149 @ SV432 @ SV794 @ SV135 ) ) @ SV432 )
| ( in @ ( kpair @ ( sK64_SY3983 @ SV794 @ SV432 @ SV135 ) @ ( sK87_SY4149 @ SV432 @ SV794 @ SV135 ) ) @ SV794 ) )
= $false )
| ( ( subset @ SV432 @ SV794 )
= $true )
| ( ( breln1 @ SV135 @ SV794 )
= $false )
| ( ( breln1 @ SV135 @ SV432 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3929]) ).
thf(4112,plain,
! [SV434: $i,SV869: $i,SV138: $i,SV795: $i] :
( ( ( in @ SV795 @ SV138 )
= $false )
| ( ( in @ SV869 @ SV434 )
= $true )
| ( ( SV795 = SV869 )
= $false )
| ( ( SV138 = SV434 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3930]) ).
thf(4113,plain,
! [SV138: $i,SV795: $i,SV434: $i,SV869: $i] :
( ( ( in @ SV869 @ SV434 )
= $false )
| ( ( in @ SV795 @ SV138 )
= $true )
| ( ( SV795 = SV869 )
= $false )
| ( ( SV138 = SV434 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3931]) ).
thf(4114,plain,
! [SV140: $i,SV436: $i,SV650: $i,SV870: $i] :
( ( ( in @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SV140 )
= $true )
| ( ( ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) )
| ( SV650 = SV870 ) )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3933]) ).
thf(4115,plain,
! [SV436: $i,SV870: $i,SV650: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) @ SV436 )
| ~ ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV650 )
| ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV870 ) )
= $false )
| ( ( ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) )
| ( SV650 = SV870 ) )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3934]) ).
thf(4116,plain,
! [SV654: $i > $i,SV975: $i,SV440: $i,SV144: $i] :
( ( ( ! [SY4134: $i] :
( ~ ( in @ SY4134 @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SV975 @ ( SV654 @ SY4134 ) )
= SY4134 ) ) )
= $false )
| ( ( surjective @ SV440 @ SV144 @ SV975 )
= $true )
| ( ( in @ SV975 @ ( funcSet @ SV440 @ SV144 ) )
= $false )
| ( ( in @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) @ SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3935]) ).
thf(4117,plain,
! [SV144: $i,SV440: $i,SV941: $i,SV654: $i > $i] :
( ( ( ~ ( in @ ( sK91_SY4108 @ SV654 @ SV941 @ SV440 @ SV144 ) @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SV941 @ ( SV654 @ ( sK91_SY4108 @ SV654 @ SV941 @ SV440 @ SV144 ) ) )
= ( sK91_SY4108 @ SV654 @ SV941 @ SV440 @ SV144 ) ) )
= $false )
| ( ( surjective @ SV440 @ SV144 @ SV941 )
= $true )
| ( ( in @ SV941 @ ( funcSet @ SV440 @ SV144 ) )
= $false )
| ( ( in @ ( SV654 @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) ) @ SV440 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3936]) ).
thf(4118,plain,
! [SV442: $i > $o,SV146: $i,SV999: $i] :
( ( ( ~ ( in @ SV999 @ SV146 )
| ~ ( SV442 @ SV999 ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( in @ ( sK11_SY3407 @ SV442 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3937]) ).
thf(4119,plain,
! [SV442: $i > $o,SV146: $i,SV1020: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1020 @ SV146 )
| ~ ( SV442 @ SV1020 ) ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( in @ ( sK38_SY3987 @ SV442 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3938]) ).
thf(4120,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ( ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( SV442 @ ( sK11_SY3407 @ SV442 @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3939]) ).
thf(4121,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ( ~ ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) ) )
= $false )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( SV442 @ ( sK38_SY3987 @ SV442 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3940]) ).
thf(4122,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ( ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( ( sK11_SY3407 @ SV442 @ SV146 )
= ( sK38_SY3987 @ SV442 @ SV146 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3941]) ).
thf(4123,plain,
! [SV147: $i,SV798: $i,SV443: $i,SV942: $i] :
( ( ( in @ SV942 @ ( binintersect @ SV443 @ SV798 ) )
= $false )
| ( ( in @ SV942 @ ( setminus @ SV147 @ SV443 ) )
= $false )
| ( ( in @ SV942 @ SV147 )
= $false )
| ( ( in @ SV798 @ ( powerset @ SV147 ) )
= $false )
| ( ( in @ SV443 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3942]) ).
thf(4124,plain,
! [SV943: $i,SV799: $i,SV444: $i,SV148: $i,SV1000: $i] :
( ( ( in @ SV1000 @ SV148 )
= $false )
| ( ( ~ ( in @ SV1000 @ ( binintersect @ SV444 @ SV799 ) )
| ( in @ SV1000 @ ( binunion @ SV444 @ SV943 ) ) )
= $true )
| ( ( in @ SV943 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV799 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV444 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3943]) ).
thf(4125,plain,
! [SV448: $i > $o,SV1010: $i,SV152: $i > $o] :
( ( ( ~ ( ~ ( SV152 @ SV1010 )
| ~ ! [SY4163: $i] :
( ~ ( SV152 @ SY4163 )
| ( SV1010 = SY4163 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3944]) ).
thf(4126,plain,
! [SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
| ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3945]) ).
thf(4127,plain,
! [SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3946]) ).
thf(4128,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3946]) ).
thf(4129,plain,
! [SV168: $i,SV464: $i,SV666: $i,SV877: $i] :
( ( ( in @ ( sK79_SY4066 @ SV877 @ SV666 @ SV464 @ SV168 ) @ SV168 )
= $true )
| ( ( subset @ SV666 @ SV877 )
= $true )
| ( ( breln @ SV168 @ SV464 @ SV877 )
= $false )
| ( ( breln @ SV168 @ SV464 @ SV666 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3949]) ).
thf(4130,plain,
! [SV464: $i,SV877: $i,SV666: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK92_SY4154 @ SV168 @ SV666 @ SV877 @ SV464 ) @ SV464 )
| ~ ( in @ ( kpair @ ( sK79_SY4066 @ SV877 @ SV666 @ SV464 @ SV168 ) @ ( sK92_SY4154 @ SV168 @ SV666 @ SV877 @ SV464 ) ) @ SV666 )
| ( in @ ( kpair @ ( sK79_SY4066 @ SV877 @ SV666 @ SV464 @ SV168 ) @ ( sK92_SY4154 @ SV168 @ SV666 @ SV877 @ SV464 ) ) @ SV877 ) )
= $false )
| ( ( subset @ SV666 @ SV877 )
= $true )
| ( ( breln @ SV168 @ SV464 @ SV877 )
= $false )
| ( ( breln @ SV168 @ SV464 @ SV666 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3950]) ).
thf(4131,plain,
! [SV175: $i,SV470: $i > $i,SV976: $i] :
( ( ( ~ ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) ) )
= $true )
| ( ( ~ ! [SY4135: $i] :
~ ~ ( ~ ( in @ SY4135 @ SV175 )
| ( SV976
!= ( SV470 @ SY4135 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3951]) ).
thf(4132,plain,
! [SV470: $i > $i,SV976: $i,SV175: $i] :
( ( ( ~ ~ ! [SY4136: $i] :
~ ~ ( ~ ( in @ SY4136 @ SV175 )
| ( SV976
!= ( SV470 @ SY4136 ) ) ) )
= $true )
| ( ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3952]) ).
thf(4133,plain,
! [SV977: $i,SV175: $i,SV470: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
| ~ ! [SY4164: $i] :
~ ~ ( ~ ( in @ SY4164 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4164 ) ) ) )
| ~ ( ~ ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) )
| ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 ) ) )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3953]) ).
thf(4134,plain,
! [SV670: $i > $i > $o,SV180: $i,SV978: $i,SV475: $i] :
( ( ( reflwellordering @ SV475 @ SV978 )
= $false )
| ( ( ! [SY4140: $i] :
( ~ ( in @ SY4140 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY4141: $i] :
~ ( ~ ( SV670 @ SY4140 @ SY4141 )
| ~ ! [SY4142: $i] :
( ~ ( in @ SY4142 @ SV475 )
| ~ ( SV670 @ SY4140 @ SY4142 )
| ( in @ ( kpair @ SY4141 @ SY4142 ) @ SV978 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV978 @ ( breln1Set @ SV475 ) )
= $false )
| ( ( in @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3954]) ).
thf(4135,plain,
! [SV180: $i,SV670: $i > $i > $o,SV475: $i,SV979: $i] :
( ( ( in @ SV979 @ SV475 )
= $false )
| ( ( ~ ( SV670 @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV979 ) )
= $true )
| ( ( ! [SY3807: $i] :
( ~ ( in @ SY3807 @ ( breln1Set @ SV475 ) )
| ~ ( reflwellordering @ SV475 @ SY3807 )
| ! [SY3808: $i] :
( ~ ( in @ SY3808 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY3809: $i] :
~ ( ~ ( SV670 @ SY3808 @ SY3809 )
| ~ ! [SY3810: $i] :
( ~ ( in @ SY3810 @ SV475 )
| ~ ( SV670 @ SY3808 @ SY3810 )
| ( in @ ( kpair @ SY3809 @ SY3810 ) @ SY3807 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3955]) ).
thf(4136,plain,
! [SV186: $i,SV812: $i,SV481: $i,SV950: $i] :
( ( ( ~ ( in @ SV950 @ SV481 ) )
= $true )
| ( ( in @ SV950 @ SV812 )
= $true )
| ( ( in @ SV481 @ ( powerset @ SV812 ) )
= $false )
| ( ( in @ SV950 @ SV186 )
= $false )
| ( ( in @ SV812 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV481 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3956]) ).
thf(4137,plain,
! [SV189: $i,SV484: $i > $o,SV879: $i] :
( ( ( ~ ( in @ ( sK65_SY3497 @ SV879 @ SV484 @ SV189 ) @ SV189 ) )
= $false )
| ( ( SV484 @ SV879 )
= $true )
| ( ( in @ SV879 @ SV189 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3957]) ).
thf(4138,plain,
! [SV189: $i,SV879: $i,SV484: $i > $o] :
( ( ( ~ ~ ( SV484 @ ( sK65_SY3497 @ SV879 @ SV484 @ SV189 ) ) )
= $false )
| ( ( SV484 @ SV879 )
= $true )
| ( ( in @ SV879 @ SV189 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3957]) ).
thf(4139,plain,
! [SV486: $i,SV191: $i,SV676: $i,SV981: $i,SV880: $i] :
( ( ( in @ ( kpair @ SV880 @ SV981 ) @ SV676 )
= $false )
| ( ( ( ap @ SV191 @ SV486 @ SV676 @ SV880 )
= SV981 )
= $true )
| ( ( in @ SV981 @ SV486 )
= $false )
| ( ( in @ SV880 @ SV191 )
= $false )
| ( ( in @ SV676 @ ( funcSet @ SV191 @ SV486 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3958]) ).
thf(4140,plain,
! [SV193: $i,SV881: $i,SV488: $i > $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK93_SY4070 @ SV488 @ SV881 @ SV193 ) @ SV193 )
| ( SV881
!= ( SV488 @ ( sK93_SY4070 @ SV488 @ SV881 @ SV193 ) ) ) ) )
= $false )
| ( ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3959]) ).
thf(4141,plain,
! [SV488: $i > $i,SV881: $i,SV193: $i,SV1021: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1021 @ SV193 )
| ( SV881
!= ( SV488 @ SV1021 ) ) ) )
= $true )
| ( ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3960]) ).
thf(4142,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( SV196 @ ( sK80_SY4002 @ SV816 @ SV196 ) )
= $true )
| ( ( SV196 @ SV816 )
= $false )
| ( ( ~ ! [SY2855: $i] :
~ ~ ( ~ ( SV196 @ SY2855 )
| ~ ! [SY2856: $i] :
( ~ ( SV196 @ SY2856 )
| ( SY2855 = SY2856 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3961]) ).
thf(4143,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ! [SY2855: $i] :
~ ~ ( ~ ( SV196 @ SY2855 )
| ~ ! [SY2856: $i] :
( ~ ( SV196 @ SY2856 )
| ( SY2855 = SY2856 ) ) ) )
= $false )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV816
= ( sK80_SY4002 @ SV816 @ SV196 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3962]) ).
thf(4144,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) ) )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3963]) ).
thf(4145,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) ) )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3964]) ).
thf(4146,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
| ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3965]) ).
thf(4147,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3966]) ).
thf(4148,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3966]) ).
thf(4149,plain,
! [SV492: $i,SV679: $i,SV199: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK94_SY4093 @ SV199 @ SV679 @ SV492 ) @ SV492 )
| ( SV679
!= ( kpair @ ( sK39_SY3820 @ SV679 @ SV492 @ SV199 ) @ ( sK94_SY4093 @ SV199 @ SV679 @ SV492 ) ) ) ) )
= $false )
| ( ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3967]) ).
thf(4150,plain,
! [SV200: $i,SV817: $i,SV493: $i,SV951: $i] :
( ( ( in @ SV951 @ ( binunion @ SV493 @ SV817 ) )
= $true )
| ( ( ~ ( in @ SV951 @ SV817 ) )
= $true )
| ( ( in @ SV951 @ SV200 )
= $false )
| ( ( in @ SV817 @ ( powerset @ SV200 ) )
= $false )
| ( ( in @ SV493 @ ( powerset @ SV200 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3968]) ).
thf(4151,plain,
! [SV496: $i,SV885: $o,SV203: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV203 ) )
= $false )
| ( SV885 = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3969]) ).
thf(4152,plain,
! [SV203: $i,SV885: $o,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 )
| SV885 )
= $false )
| ( SV885 = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3969]) ).
thf(4153,plain,
! [SV885: $o,SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SV885 ) )
= $true )
| ( SV885 = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3970]) ).
thf(4154,plain,
! [SV496: $i,SV885: $o,SV203: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV203 ) )
= $false )
| ( SV885 = $true )
| ( SV885 = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3971]) ).
thf(4155,plain,
! [SV203: $i,SV885: $o,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 )
| SV885 )
= $false )
| ( SV885 = $true )
| ( SV885 = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3971]) ).
thf(4156,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV203 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3972]) ).
thf(4157,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3972]) ).
thf(4158,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3973]) ).
thf(4159,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV203 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3974]) ).
thf(4160,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3974]) ).
thf(4161,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV203 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3975]) ).
thf(4162,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3975]) ).
thf(4163,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3976]) ).
thf(4164,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV203 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3977]) ).
thf(4165,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3977]) ).
thf(4166,plain,
! [SV500: $i > $o,SV207: $i,SV1011: $i] :
( ( ( ~ ( in @ SV1011 @ SV207 ) )
= $true )
| ( ( ~ ( SV500 @ SV1011 ) )
= $true )
| ( ( in @ ( sK40_SY3540 @ SV500 @ SV207 ) @ SV207 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3978]) ).
thf(4167,plain,
! [SV500: $i > $o,SV207: $i,SV1012: $i] :
( ( ( ~ ( in @ SV1012 @ SV207 ) )
= $true )
| ( ( ~ ( SV500 @ SV1012 ) )
= $true )
| ( ( SV500 @ ( sK40_SY3540 @ SV500 @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3979]) ).
thf(4168,plain,
! [SV208: $i,SV952: $o,SV818: $i,SV501: $i,SV982: $i] :
( ( ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV982 @ SV501 )
| SV952 )
| ~ ( ~ ( in @ SV982 @ SV818 )
| SV952 )
| SV952 )
= $true )
| ( ( in @ SV982 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3980]) ).
thf(4169,plain,
! [SV208: $i,SV818: $i,SV501: $i,SV983: $i] :
( ( ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV983 @ SV501 )
| $true )
| ~ ( ~ ( in @ SV983 @ SV818 )
| $true )
| $true )
= $true )
| ( ( in @ SV983 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3981]) ).
thf(4170,plain,
! [SV208: $i,SV818: $i,SV501: $i,SV984: $i] :
( ( ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV984 @ SV501 )
| $false )
| ~ ( ~ ( in @ SV984 @ SV818 )
| $false )
| $false )
= $true )
| ( ( in @ SV984 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3982]) ).
thf(4171,plain,
! [SV209: $i,SV502: $i,SV889: $i > $o,SV689: $i,SV1013: $i] :
( ( ( ~ ( in @ SV1013 @ SV689 ) )
= $true )
| ( ( SV889 @ SV1013 )
= $true )
| ( ( in @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ SV209 )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3983]) ).
thf(4172,plain,
! [SV502: $i,SV889: $i > $o,SV689: $i,SV209: $i] :
( ( ( in @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) @ SV502 )
= $true )
| ( ( ! [SY4074: $i] :
( ~ ( in @ SY4074 @ SV689 )
| ( SV889 @ SY4074 ) ) )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3984]) ).
thf(4173,plain,
! [SV209: $i,SV502: $i,SV689: $i,SV889: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) ) @ SV689 ) )
= $false )
| ( ( ! [SY4074: $i] :
( ~ ( in @ SY4074 @ SV689 )
| ( SV889 @ SY4074 ) ) )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3985]) ).
thf(4174,plain,
! [SV209: $i,SV502: $i,SV689: $i,SV889: $i > $o] :
( ( ( SV889 @ ( kpair @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) ) )
= $false )
| ( ( ! [SY4074: $i] :
( ~ ( in @ SY4074 @ SV689 )
| ( SV889 @ SY4074 ) ) )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3985]) ).
thf(4175,plain,
! [SV819: $i,SV508: $i,SV953: $i,SV216: $i,SV1001: $i] :
( ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
| ! [SY4155: $o] :
( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
| SY4155 )
| ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| SY4155 )
| SY4155 ) )
= $true )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3986]) ).
thf(4176,plain,
! [SV226: $i] :
( ( ! [SY3851: $i] :
( ~ ( in @ SY3851 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY2945: $i] :
( ~ ( in @ SY2945 @ SY3851 )
| ( in @ SY2945 @ SV226 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3988]) ).
thf(4177,plain,
! [SV226: $i] :
( ( ! [SY3853: $i,SY3854: $i] :
( ~ ~ ( ~ ( in @ SY3853 @ SV226 )
| ~ ( in @ SY3854 @ SV226 ) )
| ~ ! [SY3855: $i] :
( ~ ( in @ SY3855 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SY3853 @ SY3855 )
| ( in @ SY3854 @ SY3855 ) )
| ~ ( ~ ( in @ SY3854 @ SY3855 )
| ( in @ SY3853 @ SY3855 ) ) ) )
| ( SY3853 = SY3854 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3989]) ).
thf(4178,plain,
! [SV1014: $i,SV226: $i,SV1002: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1002 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SV1014 @ ( sK2_SY2943 @ SV226 ) ) ) )
= $true )
| ( ( ! [SY4166: $i] :
( ~ ( in @ SY4166 @ SV1002 )
| ( in @ SY4166 @ SV1014 ) )
| ! [SY4167: $i] :
( ~ ( in @ SY4167 @ SV1014 )
| ( in @ SY4167 @ SV1002 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3990]) ).
thf(4179,plain,
! [SV226: $i,SV955: $i] :
( ( ( ! [SY4114: $i] :
( ~ ( in @ SY4114 @ SV955 )
| ( in @ SY4114 @ SV226 ) ) )
= $false )
| ( ( ~ ~ ! [SY4115: $i] :
~ ( in @ SY4115 @ SV955 ) )
= $true )
| ( ( ~ ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3991]) ).
thf(4180,plain,
! [SV229: $i,SV822: $i,SV519: $i,SV956: $i] :
( ( ( in @ SV956 @ ( binunion @ SV519 @ SV822 ) )
= $true )
| ( ( ~ ( in @ SV956 @ SV519 ) )
= $true )
| ( ( in @ SV956 @ SV229 )
= $false )
| ( ( in @ SV822 @ ( powerset @ SV229 ) )
= $false )
| ( ( in @ SV519 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3992]) ).
thf(4181,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1003: $i] :
( ( ( ~ ( ~ ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
| ~ ! [SY4159: $i] :
~ ~ ( ~ ( in @ SY4159 @ SV520 )
| ~ ( SV230 @ SY4159 @ SV1003 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3993]) ).
thf(4182,plain,
! [SV1003: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ~ ( ~ ~ ! [SY4160: $i] :
~ ~ ( ~ ( in @ SY4160 @ SV520 )
| ~ ( SV230 @ SY4160 @ SV1003 ) )
| ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3993]) ).
thf(4183,plain,
! [SV957: $i,SV520: $i,SV230: $i > $i > $o] :
( ( ( ! [SY4121: $i] :
( ~ ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SY4121 )
| ( SV957 = SY4121 ) ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( ~ ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3994]) ).
thf(4184,plain,
! [SV231: $i,SV521: $i,SV705: $i,SV896: $i] :
( ( ( in @ ( sK82_SY4081 @ SV896 @ SV705 @ SV521 @ SV231 ) @ SV231 )
= $true )
| ( ( SV705 = SV896 )
= $true )
| ( ( func @ SV231 @ SV521 @ SV896 )
= $false )
| ( ( func @ SV231 @ SV521 @ SV705 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3995]) ).
thf(4185,plain,
! [SV233: $i,SV823: $i > $o,SV523: $i,SV1004: $i] :
( ( ( in @ SV1004 @ SV523 )
= $false )
| ( ( SV823 @ SV1004 )
= $true )
| ( ( in @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ SV233 )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3997]) ).
thf(4186,plain,
! [SV233: $i,SV823: $i > $o,SV523: $i,SV1022: $i] :
( ( ( ~ ( in @ SV1022 @ SV523 )
| ( SV823 @ SV1022 ) )
= $true )
| ( ( in @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) @ SV233 )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3998]) ).
thf(4187,plain,
! [SV233: $i,SV523: $i,SV823: $i > $o] :
( ( ( in @ ( kpair @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) ) @ SV523 )
= $true )
| ( ( ! [SY4016: $i] :
( ~ ( in @ SY4016 @ SV523 )
| ( SV823 @ SY4016 ) ) )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3999]) ).
thf(4188,plain,
! [SV233: $i,SV823: $i > $o,SV523: $i,SV1023: $i] :
( ( ( ~ ( in @ SV1023 @ SV523 )
| ( SV823 @ SV1023 ) )
= $true )
| ( ( SV823 @ ( kpair @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) ) )
= $false )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4000]) ).
thf(4189,plain,
! [SV901: $i,SV533: $i > $o,SV245: $i] :
( ( ( ( dsetconstr @ SV245
@ ^ [SY3609: $i] : ( SV533 @ SY3609 ) )
= emptyset )
= $false )
| ( $false = $true )
| ( ( in @ SV901 @ SV245 )
= $false )
| ( ( SV533 @ SV901 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4001]) ).
thf(4190,plain,
! [SV251: $i,SV828: $i,SV538: $i,SV960: $i] :
( ( ( in @ SV960 @ SV538 )
= $true )
| ( ( ~ ~ ( in @ SV960 @ SV828 )
| ~ ( in @ SV960 @ ( binunion @ SV538 @ SV828 ) ) )
= $true )
| ( ( in @ SV960 @ SV251 )
= $false )
| ( ( in @ SV828 @ ( powerset @ SV251 ) )
= $false )
| ( ( in @ SV538 @ ( powerset @ SV251 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4003]) ).
thf(4191,plain,
! [SV548: $i,SV259: $i,SV719: $i,SV985: $i,SV908: $i] :
( ( ( in @ ( kpair @ SV908 @ SV985 ) @ SV719 )
= $false )
| ( ( ( ap @ SV259 @ SV548 @ SV719 @ SV908 )
= SV985 )
= $true )
| ( ( in @ SV985 @ SV548 )
= $false )
| ( ( in @ SV908 @ SV259 )
= $false )
| ( ( func @ SV259 @ SV548 @ SV719 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4004]) ).
thf(4192,plain,
! [SV549: $i,SV829: $i,SV260: $i] :
( ( ( ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) ) )
= $true )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4005]) ).
thf(4193,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( ~ ( in @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) @ SV260 ) )
= $false )
| ( ( ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) )
| ( SV549 = SV829 ) )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4006]) ).
thf(4194,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV549 )
| ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV829 ) )
= $false )
| ( ( ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) )
| ( SV549 = SV829 ) )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4006]) ).
thf(4195,plain,
! [SV830: $i,SV553: $i,SV961: $i,SV264: $i,SV1005: $i] :
( ( ( in @ SV1005 @ SV264 )
= $false )
| ( ( ~ ( ( in @ ( kpair @ SV961 @ SV1005 ) @ SV553 )
| ( in @ ( kpair @ SV961 @ SV1005 ) @ SV830 ) )
| ( in @ ( kpair @ SV961 @ SV1005 ) @ ( binunion @ SV553 @ SV830 ) ) )
= $true )
| ( ( in @ SV961 @ SV264 )
= $false )
| ( ( breln1 @ SV264 @ SV830 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4007]) ).
thf(4196,plain,
! [SV271: $i,SV833: $i > $o,SV559: $i,SV1006: $i] :
( ( ( in @ SV1006 @ SV559 )
= $false )
| ( ( SV833 @ SV1006 )
= $true )
| ( ( in @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ SV271 )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4008]) ).
thf(4197,plain,
! [SV271: $i,SV833: $i > $o,SV559: $i,SV1024: $i] :
( ( ( ~ ( in @ SV1024 @ SV559 )
| ( SV833 @ SV1024 ) )
= $true )
| ( ( in @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) @ SV271 )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4009]) ).
thf(4198,plain,
! [SV271: $i,SV559: $i,SV833: $i > $o] :
( ( ( in @ ( kpair @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) ) @ SV559 )
= $true )
| ( ( ! [SY4028: $i] :
( ~ ( in @ SY4028 @ SV559 )
| ( SV833 @ SY4028 ) ) )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4010]) ).
thf(4199,plain,
! [SV271: $i,SV833: $i > $o,SV559: $i,SV1025: $i] :
( ( ( ~ ( in @ SV1025 @ SV559 )
| ( SV833 @ SV1025 ) )
= $true )
| ( ( SV833 @ ( kpair @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) ) )
= $false )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4011]) ).
thf(4200,plain,
! [SV563: $i > $o,SV275: $i,SV989: $i] :
( ( ( ~ ( in @ SV989 @ SV275 ) )
= $true )
| ( ( ~ ( SV563 @ SV989 ) )
= $true )
| ( ( in @ ( sK16_SY3653 @ SV563 @ SV275 ) @ SV275 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4012]) ).
thf(4201,plain,
! [SV563: $i > $o,SV275: $i,SV990: $i] :
( ( ( ~ ( in @ SV990 @ SV275 ) )
= $true )
| ( ( ~ ( SV563 @ SV990 ) )
= $true )
| ( ( SV563 @ ( sK16_SY3653 @ SV563 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4013]) ).
thf(4202,plain,
! [SV836: $i,SV568: $i,SV963: $i,SV280: $i,SV1007: $i] :
( ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
| ! [SY4161: $o] :
( ~ ! [SY4162: $i] :
( ~ ( in @ SY4162 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SY4162 ) @ SV568 )
| ~ ( in @ ( kpair @ SY4162 @ SV1007 ) @ SV836 )
| SY4161 )
| SY4161 ) )
= $true )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4016]) ).
thf(4203,plain,
! [SV837: $i,SV288: $i > $o] :
( ( ( SV288 @ ( sK83_SY4034 @ SV837 @ SV288 ) )
= $true )
| ( ( SV288 @ SV837 )
= $false )
| ( ( ! [SY3119: $i,SY3120: $i] :
( ~ ( SV288 @ SY3119 )
| ~ ( SV288 @ SY3120 )
| ( SY3119 = SY3120 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4017]) ).
thf(4204,plain,
! [SV837: $i,SV1026: $i,SV288: $i > $o] :
( ( ( ! [SY4169: $i] :
( ~ ( SV288 @ SV1026 )
| ~ ( SV288 @ SY4169 )
| ( SV1026 = SY4169 ) ) )
= $true )
| ( ( SV288 @ SV837 )
= $false )
| ( ( SV837
= ( sK83_SY4034 @ SV837 @ SV288 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4018]) ).
thf(4205,plain,
! [SV575: $i > $o,SV289: $i,SV1015: $i] :
( ( ( ~ ( in @ SV1015 @ SV289 ) )
= $true )
| ( ( ~ ( SV575 @ SV1015 ) )
= $true )
| ( ( in @ ( sK43_SY3670 @ SV575 @ SV289 ) @ SV289 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4019]) ).
thf(4206,plain,
! [SV575: $i > $o,SV289: $i,SV1016: $i] :
( ( ( ~ ( in @ SV1016 @ SV289 ) )
= $true )
| ( ( ~ ( SV575 @ SV1016 ) )
= $true )
| ( ( SV575 @ ( sK43_SY3670 @ SV575 @ SV289 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4020]) ).
thf(4207,plain,
! [SV298: $i,SV757: $o,SV583: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV583 ) )
= $false )
| ( SV757 = $true )
| ( ( in @ SV733 @ SV298 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4021]) ).
thf(4208,plain,
! [SV583: $i,SV298: $i,SV733: $i,SV757: $o] :
( ( SV757 = $false )
| ( SV757 = $true )
| ( ( in @ SV733 @ SV298 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4021]) ).
thf(4209,plain,
! [SV298: $i,SV757: $o,SV583: $i,SV733: $i] :
( ( ( in @ SV733 @ SV583 )
= $true )
| ( SV757 = $true )
| ( SV757 = $false )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4022]) ).
thf(4210,plain,
! [SV298: $i,SV583: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV583 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV733 @ SV298 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4024]) ).
thf(4211,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV733 @ SV298 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4024]) ).
thf(4212,plain,
! [SV298: $i,SV583: $i,SV733: $i] :
( ( ( in @ SV733 @ SV583 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4025]) ).
thf(4213,plain,
! [SV298: $i,SV583: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV583 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV733 @ SV298 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4027]) ).
thf(4214,plain,
! [SV583: $i,SV298: $i,SV733: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV733 @ SV298 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4027]) ).
thf(4215,plain,
! [SV298: $i,SV583: $i,SV733: $i] :
( ( ( in @ SV733 @ SV583 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4028]) ).
thf(4216,plain,
! [SV584: $i,SV840: $i,SV299: $i] :
( ( ( ~ ! [SY4036: $i] :
( ~ ( in @ SY4036 @ SV299 )
| ~ ( in @ SY4036 @ SV840 )
| ( in @ SY4036 @ SV584 ) ) )
= $true )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV299 )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4030]) ).
thf(4217,plain,
! [SV299: $i,SV584: $i,SV840: $i] :
( ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV584 )
= $true )
| ( ( ~ ! [SY4036: $i] :
( ~ ( in @ SY4036 @ SV299 )
| ~ ( in @ SY4036 @ SV840 )
| ( in @ SY4036 @ SV584 ) )
| ( SV584 = SV840 ) )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4031]) ).
thf(4218,plain,
! [SV584: $i,SV840: $i,SV299: $i] :
( ( ( ~ ! [SY4036: $i] :
( ~ ( in @ SY4036 @ SV299 )
| ~ ( in @ SY4036 @ SV840 )
| ( in @ SY4036 @ SV584 ) ) )
= $true )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV840 )
= $false )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4032]) ).
thf(4219,plain,
! [SV841: $i,SV585: $i,SV964: $i,SV300: $i,SV1008: $i] :
( ( ( in @ SV1008 @ SV300 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV964 @ SV1008 ) @ SV585 )
| ( in @ ( kpair @ SV964 @ SV1008 ) @ ( binunion @ SV585 @ SV841 ) ) )
= $true )
| ( ( in @ SV964 @ SV300 )
= $false )
| ( ( breln1 @ SV300 @ SV841 )
= $false )
| ( ( breln1 @ SV300 @ SV585 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4033]) ).
thf(4220,plain,
! [SV301: $i,SV586: $i,SV734: $i,SV911: $i] :
( ( ( in @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) @ SV301 )
= $true )
| ( ( ! [SY4088: $i] :
( ~ ( in @ SY4088 @ SV301 )
| ! [SY4089: $i] :
( ~ ( in @ SY4089 @ SV586 )
| ~ ( in @ ( kpair @ SY4088 @ SY4089 ) @ SV911 )
| ( in @ ( kpair @ SY4088 @ SY4089 ) @ SV734 ) ) ) )
= $true )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4034]) ).
thf(4221,plain,
! [SV734: $i,SV911: $i,SV586: $i,SV301: $i,SV1027: $i] :
( ( ( ~ ( in @ SV1027 @ SV301 )
| ! [SY4170: $i] :
( ~ ( in @ SY4170 @ SV586 )
| ~ ( in @ ( kpair @ SV1027 @ SY4170 ) @ SV911 )
| ( in @ ( kpair @ SV1027 @ SY4170 ) @ SV734 ) ) )
= $true )
| ( ( ( ap @ SV301 @ SV586 @ SV734 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) )
= ( ap @ SV301 @ SV586 @ SV911 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) ) )
= $false )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4035]) ).
thf(4222,plain,
! [SV308: $i,SV591: $i,SV845: $i] :
( ( ( in @ ( sK71_SY4042 @ SV845 @ SV591 @ SV308 ) @ SV591 )
= $true )
| ( ( in @ SV591 @ ( powerset @ SV845 ) )
= $true )
| ( ( in @ SV845 @ ( powerset @ SV308 ) )
= $false )
| ( ( in @ SV591 @ ( powerset @ SV308 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4039]) ).
thf(4223,plain,
! [SV592: $i,SV846: $i,SV309: $i,SV968: $i] :
( ( ( ~ ( in @ SV968 @ ( setminus @ SV309 @ SV846 ) ) )
= $true )
| ( ( in @ SV968 @ ( setminus @ SV309 @ ( binunion @ SV592 @ SV846 ) ) )
= $true )
| ( ( in @ SV968 @ ( setminus @ SV309 @ SV592 ) )
= $false )
| ( ( in @ SV968 @ SV309 )
= $false )
| ( ( in @ SV846 @ ( powerset @ SV309 ) )
= $false )
| ( ( in @ SV592 @ ( powerset @ SV309 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4041]) ).
thf(4224,plain,
! [SV847: $i,SV315: $i,SV598: $i,SV969: $i] :
( ( ( in @ SV969 @ SV598 )
= $false )
| ( ( in @ SV969 @ ( setminus @ SV315 @ ( binunion @ SV598 @ SV847 ) ) )
= $false )
| ( ( in @ SV969 @ SV315 )
= $false )
| ( ( in @ SV847 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV598 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4042]) ).
thf(4225,plain,
! [SV848: $i,SV316: $i > $o] :
( ( ( SV316 @ ( sK85_SY4045 @ SV848 @ SV316 ) )
= $true )
| ( ( SV316 @ SV848 )
= $false )
| ( ( ~ ! [SY3190: $i] :
~ ! [SY3191: $i] :
~ ( ~ ( ~ ( SV316 @ SY3191 )
| ( SY3191 = SY3190 ) )
| ~ ( ( SY3191 != SY3190 )
| ( SV316 @ SY3191 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4043]) ).
thf(4226,plain,
! [SV848: $i,SV316: $i > $o] :
( ( ( ! [SY3190: $i] :
~ ! [SY3191: $i] :
~ ( ~ ( ~ ( SV316 @ SY3191 )
| ( SY3191 = SY3190 ) )
| ~ ( ( SY3191 != SY3190 )
| ( SV316 @ SY3191 ) ) ) )
= $false )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV848
= ( sK85_SY4045 @ SV848 @ SV316 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4044]) ).
thf(4227,plain,
! [SV849: $i,SV970: $i,SV599: $i,SV317: $i,SV1009: $i] :
( ( ( in @ SV1009 @ ( powerset @ SV317 ) )
= $false )
| ( ( ~ ( subset @ SV599 @ SV970 )
| ~ ( subset @ SV849 @ SV1009 )
| ( subset @ ( binintersect @ SV599 @ SV849 ) @ ( binintersect @ SV970 @ SV1009 ) ) )
= $true )
| ( ( in @ SV970 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV849 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4045]) ).
thf(4228,plain,
! [SV318: $i,SV600: $i,SV850: $i,SV971: $i] :
( ( ( in @ SV971 @ SV850 )
= $true )
| ( ( ~ ( in @ SV971 @ ( binintersect @ SV600 @ SV850 ) ) )
= $true )
| ( ( in @ SV971 @ SV318 )
= $false )
| ( ( in @ SV850 @ ( powerset @ SV318 ) )
= $false )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4046]) ).
thf(4229,plain,
! [SV319: $i,SV601: $i,SV914: $i > $o,SV738: $i,SV1017: $i] :
( ( ( ~ ( in @ SV1017 @ SV738 ) )
= $true )
| ( ( SV914 @ SV1017 )
= $true )
| ( ( in @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ SV319 )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4047]) ).
thf(4230,plain,
! [SV601: $i,SV914: $i > $o,SV738: $i,SV319: $i] :
( ( ( in @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) @ SV601 )
= $true )
| ( ( ! [SY4092: $i] :
( ~ ( in @ SY4092 @ SV738 )
| ( SV914 @ SY4092 ) ) )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4048]) ).
thf(4231,plain,
! [SV319: $i,SV601: $i,SV738: $i,SV914: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) ) @ SV738 ) )
= $false )
| ( ( ! [SY4092: $i] :
( ~ ( in @ SY4092 @ SV738 )
| ( SV914 @ SY4092 ) ) )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4049]) ).
thf(4232,plain,
! [SV319: $i,SV601: $i,SV738: $i,SV914: $i > $o] :
( ( ( SV914 @ ( kpair @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) ) )
= $false )
| ( ( ! [SY4092: $i] :
( ~ ( in @ SY4092 @ SV738 )
| ( SV914 @ SY4092 ) ) )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4049]) ).
thf(4233,plain,
! [SV322: $i,SV851: $i] :
( ( ( ~ ! [SY4130: $i] :
~ ~ ( ~ ( in @ SY4130 @ ( sK51_SY3211 @ SV851 @ SV322 ) )
| ~ ( in @ SY4130 @ SV322 ) ) )
= $false )
| ( ( in @ SV851 @ SV322 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4051]) ).
thf(4234,plain,
! [SV325: $i,SV852: $i,SV972: $i,SV606: $i] :
( ( ( ~ ( subset @ SV606 @ SV972 ) )
= $true )
| ( ( subset @ SV606 @ ( binintersect @ SV852 @ SV972 ) )
= $true )
| ( ( subset @ SV606 @ SV852 )
= $false )
| ( ( in @ SV972 @ ( powerset @ SV325 ) )
= $false )
| ( ( in @ SV852 @ ( powerset @ SV325 ) )
= $false )
| ( ( in @ SV606 @ ( powerset @ SV325 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4052]) ).
thf(4235,plain,
! [SV759: $i,SV40: $i > $o] :
( ( ( ! [SY2411: $i] :
~ ( SV40 @ SY2411 ) )
= $false )
| ( ( SV40 @ SV759 )
= $false )
| ( ( SV40 @ ( sK72_SY3941 @ SV759 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4053]) ).
thf(4236,plain,
! [SV759: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ ( sK95_SY2411 @ SV759 @ SV40 ) ) )
= $false )
| ( ( SV40 @ SV759 )
= $false )
| ( ( SV759
= ( sK72_SY3941 @ SV759 @ SV40 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4054]) ).
thf(4237,plain,
! [SV353: $i > $o,SV44: $i,SV991: $i] :
( ( ( ~ ( in @ SV991 @ SV44 ) )
= $true )
| ( ( ~ ( SV353 @ SV991 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( in @ ( sK9_SY3238 @ SV353 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4056]) ).
thf(4238,plain,
! [SV353: $i > $o,SV44: $i,SV1018: $i] :
( ( ( ~ ( ~ ( in @ SV1018 @ SV44 )
| ~ ( SV353 @ SV1018 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( in @ ( sK36_SY3943 @ SV353 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4057]) ).
thf(4239,plain,
! [SV353: $i > $o,SV44: $i,SV1028: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1028 @ SV44 )
| ~ ( SV353 @ SV1028 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( SV353 @ ( sK9_SY3238 @ SV353 @ SV44 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4058]) ).
thf(4240,plain,
! [SV353: $i > $o,SV44: $i] :
( ( ( ! [SY3240: $i] :
~ ~ ( ~ ( in @ SY3240 @ SV44 )
| ~ ( SV353 @ SY3240 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( SV353 @ ( sK36_SY3943 @ SV353 @ SV44 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4059]) ).
thf(4241,plain,
! [SV353: $i > $o,SV44: $i,SV1029: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1029 @ SV44 )
| ~ ( SV353 @ SV1029 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( ( sK9_SY3238 @ SV353 @ SV44 )
= ( sK36_SY3943 @ SV353 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4060]) ).
thf(4242,plain,
! [SV52: $i,SV923: $i,SV762: $i,SV361: $i,SV992: $i] :
( ( ( ~ ( in @ SV992 @ ( binintersect @ SV361 @ SV762 ) ) )
= $true )
| ( ( in @ SV992 @ ( binunion @ SV762 @ SV923 ) )
= $true )
| ( ( in @ SV992 @ SV52 )
= $false )
| ( ( in @ SV923 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV762 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4062]) ).
thf(4243,plain,
! [SV366: $i,SV57: $i,SV973: $i] :
( ( ( in @ SV973 @ SV57 )
= $false )
| ( ( in @ SV366 @ SV973 )
= $false )
| ( ( in @ SV366 @ ( setunion @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4066]) ).
thf(4244,plain,
! [SV765: $i,SV1030: $i,SV58: $i > $o] :
( ( ( ! [SY4171: $i] :
( ~ ( SV58 @ SV1030 )
| ~ ( SV58 @ SY4171 )
| ( SV1030 = SY4171 ) ) )
= $true )
| ( ( SV58 @ SV765 )
= $false )
| ( ( SV58 @ ( sK75_SY3949 @ SV765 @ SV58 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4067]) ).
thf(4245,plain,
! [SV765: $i,SV1031: $i,SV1019: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV1019 )
| ~ ( SV58 @ SV1031 )
| ( SV1019 = SV1031 ) )
= $true )
| ( ( SV58 @ SV765 )
= $false )
| ( ( SV765
= ( sK75_SY3949 @ SV765 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4068]) ).
thf(4246,plain,
! [SV59: $i > $o,SV766: $i] :
( ( ( ( sK37_SY3950 @ SV766 @ SV59 )
!= SV766 )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4069]) ).
thf(4247,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4069]) ).
thf(4248,plain,
! [SV59: $i > $o,SV766: $i] :
( ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4070]) ).
thf(4249,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4071]) ).
thf(4250,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ! [SY2472: $i] :
~ ~ ( ~ ( SV60 @ SY2472 )
| ~ ! [SY2473: $i] :
( ~ ( SV60 @ SY2473 )
| ( SY2472 = SY2473 ) ) ) )
= $false )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV60 @ ( sK76_SY3951 @ SV767 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4072]) ).
thf(4251,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ~ ~ ( ~ ( SV60 @ ( sK96_SY2472 @ SV767 @ SV60 ) )
| ~ ! [SY4172: $i] :
( ~ ( SV60 @ SY4172 )
| ( ( sK96_SY2472 @ SV767 @ SV60 )
= SY4172 ) ) ) )
= $false )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV767
= ( sK76_SY3951 @ SV767 @ SV60 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4073]) ).
thf(4252,plain,
! [SV61: $i,SV367: $i > $o,SV858: $i] :
( ( ( in @ ( sK59_SY3268 @ SV858 @ SV367 @ SV61 ) @ SV61 )
= $true )
| ( ( SV367 @ SV858 )
= $true )
| ( ( in @ SV858 @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4074]) ).
thf(4253,plain,
! [SV61: $i,SV858: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ ( sK59_SY3268 @ SV858 @ SV367 @ SV61 ) ) )
= $true )
| ( ( SV367 @ SV858 )
= $true )
| ( ( in @ SV858 @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4075]) ).
thf(4254,plain,
! [SV372: $i,SV68: $i,SV768: $i,SV986: $i] :
( ( ( in @ SV986 @ SV768 )
= $false )
| ( ( in @ SV986 @ ( setminus @ SV68 @ SV372 ) )
= $true )
| ( ( in @ SV986 @ SV68 )
= $false )
| ( ( subset @ SV372 @ ( setminus @ SV68 @ SV768 ) )
= $false )
| ( ( in @ SV768 @ ( powerset @ SV68 ) )
= $false )
| ( ( in @ SV372 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4077]) ).
thf(4255,plain,
! [SV72: $i,SV860: $o,SV376: $i,SV621: $i] :
( ( ( in @ SV621 @ SV376 )
= $true )
| ( SV860 = $true )
| ( ( SV621 = SV72 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4078]) ).
thf(4256,plain,
! [SV72: $i,SV376: $i,SV621: $i] :
( ( ( in @ SV621 @ SV376 )
= $true )
| ( $true = $true )
| ( ( SV621 = SV72 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4081]) ).
thf(4257,plain,
! [SV72: $i,SV376: $i,SV621: $i] :
( ( ( in @ SV621 @ SV376 )
= $true )
| ( $false = $true )
| ( ( SV621 = SV72 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV72 @ SV376 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4084]) ).
thf(4258,plain,
! [SV76: $i,SV622: $i,SV380: $i > $i] :
( ( ( in @ ( sK60_SY3750 @ SV380 @ SV622 @ SV76 ) @ SV76 )
= $true )
| ( ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3287: $i] : ( SV380 @ SY3287 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4087]) ).
thf(4259,plain,
! [SV76: $i,SV380: $i > $i,SV622: $i] :
( ( ( SV622
= ( SV380 @ ( sK60_SY3750 @ SV380 @ SV622 @ SV76 ) ) )
= $true )
| ( ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3287: $i] : ( SV380 @ SY3287 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4088]) ).
thf(4260,plain,
! [SV380: $i > $i,SV622: $i,SV76: $i,SV987: $i] :
( ( ( in @ SV987 @ SV76 )
= $false )
| ( ( SV622
!= ( SV380 @ SV987 ) )
= $true )
| ( ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3290: $i] : ( SV380 @ SY3290 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4089]) ).
thf(4261,plain,
! [SV773: $i,SV382: $i,SV78: $i,SV994: $i,SV927: $i] :
( ( ( ~ ( in @ ( kpair @ SV927 @ SV994 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) ) )
= $true )
| ( ( ~ ! [SY4151: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY4151 @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ SY4151 ) @ SV382 ) )
| ~ ( in @ ( kpair @ SY4151 @ SV994 ) @ SV773 ) ) )
= $true )
| ( ( in @ SV994 @ SV78 )
= $false )
| ( ( in @ SV927 @ SV78 )
= $false )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4090]) ).
thf(4262,plain,
! [SV82: $i,SV774: $i,SV386: $i,SV995: $i,SV928: $i] :
( ( ( ~ ( in @ ( kpair @ SV928 @ SV995 ) @ ( binunion @ SV386 @ SV774 ) ) )
= $true )
| ( ( ( in @ ( kpair @ SV928 @ SV995 ) @ SV386 )
| ( in @ ( kpair @ SV928 @ SV995 ) @ SV774 ) )
= $true )
| ( ( in @ SV995 @ SV82 )
= $false )
| ( ( in @ SV928 @ SV82 )
= $false )
| ( ( breln1 @ SV82 @ SV774 )
= $false )
| ( ( breln1 @ SV82 @ SV386 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4091]) ).
thf(4263,plain,
! [SV86: $i,SV389: $i,SV776: $i,SV929: $i] :
( ( ( in @ SV929 @ SV776 )
= $false )
| ( ( ~ ( in @ SV929 @ SV389 ) )
= $true )
| ( ( subset @ SV389 @ ( setminus @ SV86 @ SV776 ) )
= $false )
| ( ( in @ SV929 @ SV86 )
= $false )
| ( ( in @ SV776 @ ( powerset @ SV86 ) )
= $false )
| ( ( in @ SV389 @ ( powerset @ SV86 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4092]) ).
thf(4264,plain,
! [SV87: $i,SV390: $i,SV777: $i,SV930: $i] :
( ( ( ~ ( in @ SV930 @ SV777 ) )
= $false )
| ( ( ~ ( in @ SV930 @ SV390 ) )
= $true )
| ( ( subset @ SV390 @ SV777 )
= $false )
| ( ( in @ SV930 @ SV87 )
= $false )
| ( ( in @ SV777 @ ( powerset @ SV87 ) )
= $false )
| ( ( in @ SV390 @ ( powerset @ SV87 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4093]) ).
thf(4265,plain,
! [SV90: $i,SV931: $i,SV779: $i,SV393: $i,SV996: $i] :
( ( ( ~ ( in @ SV996 @ ( binintersect @ SV393 @ SV779 ) ) )
= $true )
| ( ( in @ SV996 @ ( binintersect @ ( binunion @ SV393 @ SV931 ) @ ( binunion @ SV779 @ SV931 ) ) )
= $true )
| ( ( in @ SV996 @ SV90 )
= $false )
| ( ( in @ SV931 @ ( powerset @ SV90 ) )
= $false )
| ( ( in @ SV779 @ ( powerset @ SV90 ) )
= $false )
| ( ( in @ SV393 @ ( powerset @ SV90 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4094]) ).
thf(4266,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ~ ( ~ ( SV100 @ ( sK97_SY2565 @ SV781 @ SV100 ) )
| ~ ! [SY4173: $i] :
( ~ ( SV100 @ SY4173 )
| ( ( sK97_SY2565 @ SV781 @ SV100 )
= SY4173 ) ) ) )
= $false )
| ( ( SV100 @ ( sK53_SY2563 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4095]) ).
thf(4267,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ! [SY2565: $i] :
~ ~ ( ~ ( SV100 @ SY2565 )
| ~ ! [SY2566: $i] :
( ~ ( SV100 @ SY2566 )
| ( SY2565 = SY2566 ) ) ) )
= $false )
| ( ( SV100 @ ( sK61_SY4131 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4096]) ).
thf(4268,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ~ ( ~ ( SV100 @ ( sK98_SY2565 @ SV781 @ SV100 ) )
| ~ ! [SY4174: $i] :
( ~ ( SV100 @ SY4174 )
| ( ( sK98_SY2565 @ SV781 @ SV100 )
= SY4174 ) ) ) )
= $false )
| ( ( ( sK53_SY2563 @ SV781 @ SV100 )
= ( sK61_SY4131 @ SV781 @ SV100 ) )
= $false )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4097]) ).
thf(4269,plain,
! [SV104: $i,SV404: $i > $o,SV862: $i] :
( ( ( ~ ( in @ ( sK99_SY3324 @ SV862 @ SV404 @ SV104 ) @ SV104 )
| ( SV404 @ ( sK99_SY3324 @ SV862 @ SV404 @ SV104 ) ) )
= $false )
| ( ( in @ SV862 @ SV104 )
= $false )
| ( ( SV404 @ SV862 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4098]) ).
thf(4270,plain,
! [SV106: $i,SV1032: $i] :
( ( ( ~ ( in @ SV1032 @ omega )
| ( in @ SV1032 @ SV106 ) )
= $true )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( in @ ( sK44_SY2577 @ SV106 ) @ omega )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4099]) ).
thf(4271,plain,
! [SV106: $i,SV1033: $i] :
( ( ( ~ ( in @ SV1033 @ omega )
| ( in @ SV1033 @ SV106 ) )
= $true )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( in @ ( sK44_SY2577 @ SV106 ) @ SV106 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4100]) ).
thf(4272,plain,
! [SV110: $i,SV783: $i,SV408: $i,SV933: $i] :
( ( ( in @ SV933 @ ( binintersect @ SV408 @ SV783 ) )
= $false )
| ( ( in @ SV933 @ SV408 )
= $true )
| ( ( in @ SV933 @ SV110 )
= $false )
| ( ( in @ SV783 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV408 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4102]) ).
thf(4273,plain,
! [SV122: $i,SV420: $i,SV788: $i > $o,SV865: $i > $o] :
( ( ( ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 )
= ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
= $true )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4105]) ).
thf(4274,plain,
! [SV122: $i,SV420: $i,SV865: $i > $o,SV788: $i > $o] :
( ( ( ~ ( ~ ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) )
| ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) ) )
| ~ ( ~ ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
| ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4106]) ).
thf(4275,plain,
! [SV123: $i,SV789: $i,SV936: $i,SV421: $i > $o] :
( ( ( SV421 @ SV936 )
= $false )
| ( ( SV789 = SV936 )
= $true )
| ( ( SV421 @ SV789 )
= $false )
| ( ( in @ SV936 @ SV123 )
= $false )
| ( ( in @ SV789 @ SV123 )
= $false )
| ( ( ex1 @ SV123
@ ^ [SY3363: $i] : ( SV421 @ SY3363 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4107]) ).
thf(4276,plain,
! [SV125: $i,SV423: $i,SV790: $i,SV997: $i,SV937: $i] :
( ( ( ~ ( in @ ( kpair @ SV937 @ SV997 ) @ SV790 ) )
= $true )
| ( ( in @ ( kpair @ SV937 @ SV997 ) @ ( binunion @ SV423 @ SV790 ) )
= $true )
| ( ( in @ SV997 @ SV125 )
= $false )
| ( ( in @ SV937 @ SV125 )
= $false )
| ( ( breln1 @ SV125 @ SV790 )
= $false )
| ( ( breln1 @ SV125 @ SV423 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4108]) ).
thf(4277,plain,
! [SV792: $i,SV998: $i,SV428: $i,SV939: $i,SV131: $i,SV1034: $i] :
( ( ( ~ ( in @ SV1034 @ SV131 )
| ~ ( in @ ( kpair @ SV939 @ SV1034 ) @ SV428 )
| ~ ( in @ ( kpair @ SV1034 @ SV998 ) @ SV792 )
| ( in @ ( kpair @ SV939 @ SV998 ) @ ( breln1compset @ SV131 @ SV428 @ SV792 ) ) )
= $true )
| ( ( in @ SV998 @ SV131 )
= $false )
| ( ( in @ SV939 @ SV131 )
= $false )
| ( ( breln1 @ SV131 @ SV792 )
= $false )
| ( ( breln1 @ SV131 @ SV428 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4109]) ).
thf(4278,plain,
! [SV135: $i,SV794: $i,SV432: $i] :
( ( ( in @ ( sK87_SY4149 @ SV432 @ SV794 @ SV135 ) @ SV135 )
= $true )
| ( ( subset @ SV432 @ SV794 )
= $true )
| ( ( breln1 @ SV135 @ SV794 )
= $false )
| ( ( breln1 @ SV135 @ SV432 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4110]) ).
thf(4279,plain,
! [SV135: $i,SV432: $i,SV794: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK64_SY3983 @ SV794 @ SV432 @ SV135 ) @ ( sK87_SY4149 @ SV432 @ SV794 @ SV135 ) ) @ SV432 ) )
= $false )
| ( ( subset @ SV432 @ SV794 )
= $true )
| ( ( breln1 @ SV135 @ SV794 )
= $false )
| ( ( breln1 @ SV135 @ SV432 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4111]) ).
thf(4280,plain,
! [SV135: $i,SV432: $i,SV794: $i] :
( ( ( in @ ( kpair @ ( sK64_SY3983 @ SV794 @ SV432 @ SV135 ) @ ( sK87_SY4149 @ SV432 @ SV794 @ SV135 ) ) @ SV794 )
= $false )
| ( ( subset @ SV432 @ SV794 )
= $true )
| ( ( breln1 @ SV135 @ SV794 )
= $false )
| ( ( breln1 @ SV135 @ SV432 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4111]) ).
thf(4281,plain,
! [SV650: $i,SV870: $i,SV436: $i,SV140: $i] :
( ( ( ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) ) )
= $true )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SV140 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4114]) ).
thf(4282,plain,
! [SV436: $i,SV870: $i,SV650: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) @ SV436 ) )
= $false )
| ( ( ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) )
| ( SV650 = SV870 ) )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4115]) ).
thf(4283,plain,
! [SV140: $i,SV436: $i,SV650: $i,SV870: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV650 )
| ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV870 ) )
= $false )
| ( ( ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) )
| ( SV650 = SV870 ) )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4115]) ).
thf(4284,plain,
! [SV144: $i,SV440: $i,SV975: $i,SV654: $i > $i] :
( ( ( ~ ( in @ ( sK100_SY4134 @ SV654 @ SV975 @ SV440 @ SV144 ) @ SV144 )
| ( ( ap @ SV440 @ SV144 @ SV975 @ ( SV654 @ ( sK100_SY4134 @ SV654 @ SV975 @ SV440 @ SV144 ) ) )
= ( sK100_SY4134 @ SV654 @ SV975 @ SV440 @ SV144 ) ) )
= $false )
| ( ( surjective @ SV440 @ SV144 @ SV975 )
= $true )
| ( ( in @ SV975 @ ( funcSet @ SV440 @ SV144 ) )
= $false )
| ( ( in @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) @ SV144 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4116]) ).
thf(4285,plain,
! [SV144: $i,SV440: $i,SV941: $i,SV654: $i > $i] :
( ( ( ~ ( in @ ( sK91_SY4108 @ SV654 @ SV941 @ SV440 @ SV144 ) @ SV144 ) )
= $false )
| ( ( surjective @ SV440 @ SV144 @ SV941 )
= $true )
| ( ( in @ SV941 @ ( funcSet @ SV440 @ SV144 ) )
= $false )
| ( ( in @ ( SV654 @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) ) @ SV440 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4117]) ).
thf(4286,plain,
! [SV654: $i > $i,SV941: $i,SV144: $i,SV440: $i] :
( ( ( ( ap @ SV440 @ SV144 @ SV941 @ ( SV654 @ ( sK91_SY4108 @ SV654 @ SV941 @ SV440 @ SV144 ) ) )
= ( sK91_SY4108 @ SV654 @ SV941 @ SV440 @ SV144 ) )
= $false )
| ( ( surjective @ SV440 @ SV144 @ SV941 )
= $true )
| ( ( in @ SV941 @ ( funcSet @ SV440 @ SV144 ) )
= $false )
| ( ( in @ ( SV654 @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) ) @ SV440 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4117]) ).
thf(4287,plain,
! [SV442: $i > $o,SV146: $i,SV999: $i] :
( ( ( ~ ( in @ SV999 @ SV146 ) )
= $true )
| ( ( ~ ( SV442 @ SV999 ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( in @ ( sK11_SY3407 @ SV442 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4118]) ).
thf(4288,plain,
! [SV442: $i > $o,SV146: $i,SV1020: $i] :
( ( ( ~ ( ~ ( in @ SV1020 @ SV146 )
| ~ ( SV442 @ SV1020 ) ) )
= $false )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( in @ ( sK38_SY3987 @ SV442 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4119]) ).
thf(4289,plain,
! [SV442: $i > $o,SV146: $i,SV1035: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1035 @ SV146 )
| ~ ( SV442 @ SV1035 ) ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( SV442 @ ( sK11_SY3407 @ SV442 @ SV146 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4120]) ).
thf(4290,plain,
! [SV442: $i > $o,SV146: $i] :
( ( ( ! [SY3409: $i] :
~ ~ ( ~ ( in @ SY3409 @ SV146 )
| ~ ( SV442 @ SY3409 ) ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( SV442 @ ( sK38_SY3987 @ SV442 @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4121]) ).
thf(4291,plain,
! [SV442: $i > $o,SV146: $i,SV1036: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1036 @ SV146 )
| ~ ( SV442 @ SV1036 ) ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( ( sK11_SY3407 @ SV442 @ SV146 )
= ( sK38_SY3987 @ SV442 @ SV146 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4122]) ).
thf(4292,plain,
! [SV148: $i,SV943: $i,SV799: $i,SV444: $i,SV1000: $i] :
( ( ( ~ ( in @ SV1000 @ ( binintersect @ SV444 @ SV799 ) ) )
= $true )
| ( ( in @ SV1000 @ ( binunion @ SV444 @ SV943 ) )
= $true )
| ( ( in @ SV1000 @ SV148 )
= $false )
| ( ( in @ SV943 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV799 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV444 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4124]) ).
thf(4293,plain,
! [SV448: $i > $o,SV1010: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ SV1010 )
| ~ ! [SY4163: $i] :
( ~ ( SV152 @ SY4163 )
| ( SV1010 = SY4163 ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4125]) ).
thf(4294,plain,
! [SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4126]) ).
thf(4295,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4126]) ).
thf(4296,plain,
! [SV152: $i > $o,SV448: $i > $o] :
( ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4127]) ).
thf(4297,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4128]) ).
thf(4298,plain,
! [SV464: $i,SV877: $i,SV666: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK92_SY4154 @ SV168 @ SV666 @ SV877 @ SV464 ) @ SV464 ) )
= $false )
| ( ( subset @ SV666 @ SV877 )
= $true )
| ( ( breln @ SV168 @ SV464 @ SV877 )
= $false )
| ( ( breln @ SV168 @ SV464 @ SV666 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4130]) ).
thf(4299,plain,
! [SV168: $i,SV464: $i,SV666: $i,SV877: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK79_SY4066 @ SV877 @ SV666 @ SV464 @ SV168 ) @ ( sK92_SY4154 @ SV168 @ SV666 @ SV877 @ SV464 ) ) @ SV666 )
| ( in @ ( kpair @ ( sK79_SY4066 @ SV877 @ SV666 @ SV464 @ SV168 ) @ ( sK92_SY4154 @ SV168 @ SV666 @ SV877 @ SV464 ) ) @ SV877 ) )
= $false )
| ( ( subset @ SV666 @ SV877 )
= $true )
| ( ( breln @ SV168 @ SV464 @ SV877 )
= $false )
| ( ( breln @ SV168 @ SV464 @ SV666 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4130]) ).
thf(4300,plain,
! [SV175: $i,SV470: $i > $i,SV976: $i] :
( ( ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
= $false )
| ( ( ~ ! [SY4135: $i] :
~ ~ ( ~ ( in @ SY4135 @ SV175 )
| ( SV976
!= ( SV470 @ SY4135 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4131]) ).
thf(4301,plain,
! [SV470: $i > $i,SV976: $i,SV175: $i] :
( ( ( ~ ! [SY4136: $i] :
~ ~ ( ~ ( in @ SY4136 @ SV175 )
| ( SV976
!= ( SV470 @ SY4136 ) ) ) )
= $false )
| ( ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4132]) ).
thf(4302,plain,
! [SV977: $i,SV175: $i,SV470: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
| ~ ! [SY4164: $i] :
~ ~ ( ~ ( in @ SY4164 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4164 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) )
| ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 ) ) )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4133]) ).
thf(4303,plain,
! [SV978: $i,SV670: $i > $i > $o,SV475: $i,SV180: $i,SV1037: $i] :
( ( ( ~ ( in @ SV1037 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY4175: $i] :
~ ( ~ ( SV670 @ SV1037 @ SY4175 )
| ~ ! [SY4176: $i] :
( ~ ( in @ SY4176 @ SV475 )
| ~ ( SV670 @ SV1037 @ SY4176 )
| ( in @ ( kpair @ SY4175 @ SY4176 ) @ SV978 ) ) ) ) ) )
= $true )
| ( ( reflwellordering @ SV475 @ SV978 )
= $false )
| ( ( in @ SV978 @ ( breln1Set @ SV475 ) )
= $false )
| ( ( in @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV180 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4134]) ).
thf(4304,plain,
! [SV979: $i,SV180: $i,SV475: $i,SV670: $i > $i > $o] :
( ( ( SV670 @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV979 )
= $false )
| ( ( in @ SV979 @ SV475 )
= $false )
| ( ( ! [SY3807: $i] :
( ~ ( in @ SY3807 @ ( breln1Set @ SV475 ) )
| ~ ( reflwellordering @ SV475 @ SY3807 )
| ! [SY3808: $i] :
( ~ ( in @ SY3808 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY3809: $i] :
~ ( ~ ( SV670 @ SY3808 @ SY3809 )
| ~ ! [SY3810: $i] :
( ~ ( in @ SY3810 @ SV475 )
| ~ ( SV670 @ SY3808 @ SY3810 )
| ( in @ ( kpair @ SY3809 @ SY3810 ) @ SY3807 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4135]) ).
thf(4305,plain,
! [SV186: $i,SV812: $i,SV481: $i,SV950: $i] :
( ( ( in @ SV950 @ SV481 )
= $false )
| ( ( in @ SV950 @ SV812 )
= $true )
| ( ( in @ SV481 @ ( powerset @ SV812 ) )
= $false )
| ( ( in @ SV950 @ SV186 )
= $false )
| ( ( in @ SV812 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ SV481 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4136]) ).
thf(4306,plain,
! [SV189: $i,SV484: $i > $o,SV879: $i] :
( ( ( in @ ( sK65_SY3497 @ SV879 @ SV484 @ SV189 ) @ SV189 )
= $true )
| ( ( SV484 @ SV879 )
= $true )
| ( ( in @ SV879 @ SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4137]) ).
thf(4307,plain,
! [SV189: $i,SV879: $i,SV484: $i > $o] :
( ( ( ~ ( SV484 @ ( sK65_SY3497 @ SV879 @ SV484 @ SV189 ) ) )
= $true )
| ( ( SV484 @ SV879 )
= $true )
| ( ( in @ SV879 @ SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4138]) ).
thf(4308,plain,
! [SV193: $i,SV881: $i,SV488: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK93_SY4070 @ SV488 @ SV881 @ SV193 ) @ SV193 )
| ( SV881
!= ( SV488 @ ( sK93_SY4070 @ SV488 @ SV881 @ SV193 ) ) ) ) )
= $true )
| ( ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4140]) ).
thf(4309,plain,
! [SV488: $i > $i,SV881: $i,SV193: $i,SV1021: $i] :
( ( ( ~ ( ~ ( in @ SV1021 @ SV193 )
| ( SV881
!= ( SV488 @ SV1021 ) ) ) )
= $false )
| ( ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4141]) ).
thf(4310,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ! [SY2855: $i] :
~ ~ ( ~ ( SV196 @ SY2855 )
| ~ ! [SY2856: $i] :
( ~ ( SV196 @ SY2856 )
| ( SY2855 = SY2856 ) ) ) )
= $false )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV196 @ ( sK80_SY4002 @ SV816 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4142]) ).
thf(4311,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ~ ~ ( ~ ( SV196 @ ( sK101_SY2855 @ SV816 @ SV196 ) )
| ~ ! [SY4177: $i] :
( ~ ( SV196 @ SY4177 )
| ( ( sK101_SY2855 @ SV816 @ SV196 )
= SY4177 ) ) ) )
= $false )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV816
= ( sK80_SY4002 @ SV816 @ SV196 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4143]) ).
thf(4312,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4144]) ).
thf(4313,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4145]) ).
thf(4314,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4146]) ).
thf(4315,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4146]) ).
thf(4316,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4147]) ).
thf(4317,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4148]) ).
thf(4318,plain,
! [SV492: $i,SV679: $i,SV199: $i] :
( ( ( ~ ( ~ ( in @ ( sK94_SY4093 @ SV199 @ SV679 @ SV492 ) @ SV492 )
| ( SV679
!= ( kpair @ ( sK39_SY3820 @ SV679 @ SV492 @ SV199 ) @ ( sK94_SY4093 @ SV199 @ SV679 @ SV492 ) ) ) ) )
= $true )
| ( ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4149]) ).
thf(4319,plain,
! [SV200: $i,SV493: $i,SV817: $i,SV951: $i] :
( ( ( in @ SV951 @ SV817 )
= $false )
| ( ( in @ SV951 @ ( binunion @ SV493 @ SV817 ) )
= $true )
| ( ( in @ SV951 @ SV200 )
= $false )
| ( ( in @ SV817 @ ( powerset @ SV200 ) )
= $false )
| ( ( in @ SV493 @ ( powerset @ SV200 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4150]) ).
thf(4320,plain,
! [SV496: $i,SV885: $o,SV203: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV203 ) )
= $true )
| ( SV885 = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4151]) ).
thf(4321,plain,
! [SV203: $i,SV885: $o,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 ) )
= $false )
| ( SV885 = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4152]) ).
thf(4322,plain,
! [SV496: $i,SV203: $i,SV683: $i,SV885: $o] :
( ( SV885 = $false )
| ( SV885 = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4152]) ).
thf(4323,plain,
! [SV885: $o,SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| SV885 )
= $false )
| ( SV885 = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4153]) ).
thf(4324,plain,
! [SV496: $i,SV885: $o,SV203: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV203 ) )
= $true )
| ( SV885 = $true )
| ( SV885 = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4154]) ).
thf(4325,plain,
! [SV203: $i,SV885: $o,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 ) )
= $false )
| ( SV885 = $true )
| ( SV885 = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4155]) ).
thf(4326,plain,
! [SV496: $i,SV203: $i,SV683: $i,SV885: $o] :
( ( SV885 = $false )
| ( SV885 = $true )
| ( SV885 = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4155]) ).
thf(4327,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV203 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4156]) ).
thf(4328,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4157]) ).
thf(4329,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4157]) ).
thf(4330,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4158]) ).
thf(4331,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV203 ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4159]) ).
thf(4332,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4160]) ).
thf(4333,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4160]) ).
thf(4334,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV203 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4161]) ).
thf(4335,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4162]) ).
thf(4336,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4162]) ).
thf(4337,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV203 )
| ~ ( in @ SV683 @ SV496 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4163]) ).
thf(4338,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV203 ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4164]) ).
thf(4339,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4165]) ).
thf(4340,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4165]) ).
thf(4341,plain,
! [SV500: $i > $o,SV207: $i,SV1011: $i] :
( ( ( in @ SV1011 @ SV207 )
= $false )
| ( ( ~ ( SV500 @ SV1011 ) )
= $true )
| ( ( in @ ( sK40_SY3540 @ SV500 @ SV207 ) @ SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4166]) ).
thf(4342,plain,
! [SV500: $i > $o,SV207: $i,SV1012: $i] :
( ( ( in @ SV1012 @ SV207 )
= $false )
| ( ( ~ ( SV500 @ SV1012 ) )
= $true )
| ( ( SV500 @ ( sK40_SY3540 @ SV500 @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4167]) ).
thf(4343,plain,
! [SV208: $i,SV818: $i,SV952: $o,SV501: $i,SV982: $i] :
( ( ( ~ ( ~ ( in @ SV982 @ SV501 )
| SV952 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV982 @ SV818 )
| SV952 )
| SV952 )
= $true )
| ( ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV982 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4168]) ).
thf(4344,plain,
! [SV208: $i,SV818: $i,SV501: $i,SV983: $i] :
( ( ( ~ ( ~ ( in @ SV983 @ SV501 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV983 @ SV818 )
| $true )
| $true )
= $true )
| ( ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV983 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4169]) ).
thf(4345,plain,
! [SV208: $i,SV818: $i,SV501: $i,SV984: $i] :
( ( ( ~ ( ~ ( in @ SV984 @ SV501 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV984 @ SV818 )
| $false )
| $false )
= $true )
| ( ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV984 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4170]) ).
thf(4346,plain,
! [SV209: $i,SV502: $i,SV889: $i > $o,SV689: $i,SV1013: $i] :
( ( ( in @ SV1013 @ SV689 )
= $false )
| ( ( SV889 @ SV1013 )
= $true )
| ( ( in @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ SV209 )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4171]) ).
thf(4347,plain,
! [SV502: $i,SV209: $i,SV889: $i > $o,SV689: $i,SV1038: $i] :
( ( ( ~ ( in @ SV1038 @ SV689 )
| ( SV889 @ SV1038 ) )
= $true )
| ( ( in @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) @ SV502 )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4172]) ).
thf(4348,plain,
! [SV209: $i,SV502: $i,SV689: $i,SV889: $i > $o] :
( ( ( in @ ( kpair @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) ) @ SV689 )
= $true )
| ( ( ! [SY4074: $i] :
( ~ ( in @ SY4074 @ SV689 )
| ( SV889 @ SY4074 ) ) )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4173]) ).
thf(4349,plain,
! [SV209: $i,SV502: $i,SV889: $i > $o,SV689: $i,SV1039: $i] :
( ( ( ~ ( in @ SV1039 @ SV689 )
| ( SV889 @ SV1039 ) )
= $true )
| ( ( SV889 @ ( kpair @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) ) )
= $false )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4174]) ).
thf(4350,plain,
! [SV216: $i,SV819: $i,SV508: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) ) )
= $true )
| ( ( ! [SY4155: $o] :
( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
| SY4155 )
| ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| SY4155 )
| SY4155 ) )
= $true )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4175]) ).
thf(4351,plain,
! [SV226: $i,SV1040: $i] :
( ( ~ ( in @ SV1040 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4178: $i] :
( ~ ( in @ SY4178 @ SV1040 )
| ( in @ SY4178 @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4176]) ).
thf(4352,plain,
! [SV226: $i,SV1041: $i] :
( ( ! [SY4179: $i] :
( ~ ~ ( ~ ( in @ SV1041 @ SV226 )
| ~ ( in @ SY4179 @ SV226 ) )
| ~ ! [SY4180: $i] :
( ~ ( in @ SY4180 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SV1041 @ SY4180 )
| ( in @ SY4179 @ SY4180 ) )
| ~ ( ~ ( in @ SY4179 @ SY4180 )
| ( in @ SV1041 @ SY4180 ) ) ) )
| ( SV1041 = SY4179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4177]) ).
thf(4353,plain,
! [SV1014: $i,SV226: $i,SV1002: $i] :
( ( ( ~ ( ~ ( in @ SV1002 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SV1014 @ ( sK2_SY2943 @ SV226 ) ) ) )
= $false )
| ( ( ! [SY4166: $i] :
( ~ ( in @ SY4166 @ SV1002 )
| ( in @ SY4166 @ SV1014 ) )
| ! [SY4167: $i] :
( ~ ( in @ SY4167 @ SV1014 )
| ( in @ SY4167 @ SV1002 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4178]) ).
thf(4354,plain,
! [SV955: $i,SV226: $i] :
( ( ( ~ ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
| ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 ) )
= $false )
| ( ( ~ ~ ! [SY4115: $i] :
~ ( in @ SY4115 @ SV955 ) )
= $true )
| ( ( ~ ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4179]) ).
thf(4355,plain,
! [SV229: $i,SV822: $i,SV519: $i,SV956: $i] :
( ( ( in @ SV956 @ SV519 )
= $false )
| ( ( in @ SV956 @ ( binunion @ SV519 @ SV822 ) )
= $true )
| ( ( in @ SV956 @ SV229 )
= $false )
| ( ( in @ SV822 @ ( powerset @ SV229 ) )
= $false )
| ( ( in @ SV519 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4180]) ).
thf(4356,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1003: $i] :
( ( ( ~ ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
| ~ ! [SY4159: $i] :
~ ~ ( ~ ( in @ SY4159 @ SV520 )
| ~ ( SV230 @ SY4159 @ SV1003 ) ) )
= $true )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4181]) ).
thf(4357,plain,
! [SV1003: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ~ ~ ! [SY4160: $i] :
~ ~ ( ~ ( in @ SY4160 @ SV520 )
| ~ ( SV230 @ SY4160 @ SV1003 ) )
| ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) ) )
= $true )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4182]) ).
thf(4358,plain,
! [SV957: $i,SV520: $i,SV230: $i > $i > $o] :
( ( ( ~ ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
| ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( ~ ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4183]) ).
thf(4359,plain,
! [SV233: $i,SV823: $i > $o,SV523: $i,SV1022: $i] :
( ( ( ~ ( in @ SV1022 @ SV523 ) )
= $true )
| ( ( SV823 @ SV1022 )
= $true )
| ( ( in @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) @ SV233 )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4186]) ).
thf(4360,plain,
! [SV233: $i,SV823: $i > $o,SV523: $i,SV1042: $i] :
( ( ( ~ ( in @ SV1042 @ SV523 )
| ( SV823 @ SV1042 ) )
= $true )
| ( ( in @ ( kpair @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) ) @ SV523 )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4187]) ).
thf(4361,plain,
! [SV233: $i,SV823: $i > $o,SV523: $i,SV1023: $i] :
( ( ( ~ ( in @ SV1023 @ SV523 ) )
= $true )
| ( ( SV823 @ SV1023 )
= $true )
| ( ( SV823 @ ( kpair @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) ) )
= $false )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4188]) ).
thf(4362,plain,
! [SV251: $i,SV538: $i,SV828: $i,SV960: $i] :
( ( ( ~ ~ ( in @ SV960 @ SV828 ) )
= $true )
| ( ( ~ ( in @ SV960 @ ( binunion @ SV538 @ SV828 ) ) )
= $true )
| ( ( in @ SV960 @ SV538 )
= $true )
| ( ( in @ SV960 @ SV251 )
= $false )
| ( ( in @ SV828 @ ( powerset @ SV251 ) )
= $false )
| ( ( in @ SV538 @ ( powerset @ SV251 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4190]) ).
thf(4363,plain,
! [SV549: $i,SV829: $i,SV260: $i] :
( ( ( ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4192]) ).
thf(4364,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( in @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) @ SV260 )
= $true )
| ( ( ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) )
| ( SV549 = SV829 ) )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4193]) ).
thf(4365,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV549 ) )
= $false )
| ( ( ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) )
| ( SV549 = SV829 ) )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4194]) ).
thf(4366,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV829 )
= $false )
| ( ( ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) )
| ( SV549 = SV829 ) )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4194]) ).
thf(4367,plain,
! [SV264: $i,SV830: $i,SV553: $i,SV1005: $i,SV961: $i] :
( ( ( ~ ( ( in @ ( kpair @ SV961 @ SV1005 ) @ SV553 )
| ( in @ ( kpair @ SV961 @ SV1005 ) @ SV830 ) ) )
= $true )
| ( ( in @ ( kpair @ SV961 @ SV1005 ) @ ( binunion @ SV553 @ SV830 ) )
= $true )
| ( ( in @ SV1005 @ SV264 )
= $false )
| ( ( in @ SV961 @ SV264 )
= $false )
| ( ( breln1 @ SV264 @ SV830 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4195]) ).
thf(4368,plain,
! [SV271: $i,SV833: $i > $o,SV559: $i,SV1024: $i] :
( ( ( ~ ( in @ SV1024 @ SV559 ) )
= $true )
| ( ( SV833 @ SV1024 )
= $true )
| ( ( in @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) @ SV271 )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4197]) ).
thf(4369,plain,
! [SV271: $i,SV833: $i > $o,SV559: $i,SV1043: $i] :
( ( ( ~ ( in @ SV1043 @ SV559 )
| ( SV833 @ SV1043 ) )
= $true )
| ( ( in @ ( kpair @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) ) @ SV559 )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4198]) ).
thf(4370,plain,
! [SV271: $i,SV833: $i > $o,SV559: $i,SV1025: $i] :
( ( ( ~ ( in @ SV1025 @ SV559 ) )
= $true )
| ( ( SV833 @ SV1025 )
= $true )
| ( ( SV833 @ ( kpair @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) ) )
= $false )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4199]) ).
thf(4371,plain,
! [SV563: $i > $o,SV275: $i,SV989: $i] :
( ( ( in @ SV989 @ SV275 )
= $false )
| ( ( ~ ( SV563 @ SV989 ) )
= $true )
| ( ( in @ ( sK16_SY3653 @ SV563 @ SV275 ) @ SV275 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4200]) ).
thf(4372,plain,
! [SV563: $i > $o,SV275: $i,SV990: $i] :
( ( ( in @ SV990 @ SV275 )
= $false )
| ( ( ~ ( SV563 @ SV990 ) )
= $true )
| ( ( SV563 @ ( sK16_SY3653 @ SV563 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4201]) ).
thf(4373,plain,
! [SV836: $i,SV568: $i,SV280: $i,SV1007: $i,SV963: $i] :
( ( ( ~ ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) ) )
= $true )
| ( ( ! [SY4161: $o] :
( ~ ! [SY4162: $i] :
( ~ ( in @ SY4162 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SY4162 ) @ SV568 )
| ~ ( in @ ( kpair @ SY4162 @ SV1007 ) @ SV836 )
| SY4161 )
| SY4161 ) )
= $true )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4202]) ).
thf(4374,plain,
! [SV837: $i,SV1044: $i,SV288: $i > $o] :
( ( ( ! [SY4181: $i] :
( ~ ( SV288 @ SV1044 )
| ~ ( SV288 @ SY4181 )
| ( SV1044 = SY4181 ) ) )
= $true )
| ( ( SV288 @ SV837 )
= $false )
| ( ( SV288 @ ( sK83_SY4034 @ SV837 @ SV288 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4203]) ).
thf(4375,plain,
! [SV837: $i,SV1045: $i,SV1026: $i,SV288: $i > $o] :
( ( ( ~ ( SV288 @ SV1026 )
| ~ ( SV288 @ SV1045 )
| ( SV1026 = SV1045 ) )
= $true )
| ( ( SV288 @ SV837 )
= $false )
| ( ( SV837
= ( sK83_SY4034 @ SV837 @ SV288 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4204]) ).
thf(4376,plain,
! [SV575: $i > $o,SV289: $i,SV1015: $i] :
( ( ( in @ SV1015 @ SV289 )
= $false )
| ( ( ~ ( SV575 @ SV1015 ) )
= $true )
| ( ( in @ ( sK43_SY3670 @ SV575 @ SV289 ) @ SV289 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4205]) ).
thf(4377,plain,
! [SV575: $i > $o,SV289: $i,SV1016: $i] :
( ( ( in @ SV1016 @ SV289 )
= $false )
| ( ( ~ ( SV575 @ SV1016 ) )
= $true )
| ( ( SV575 @ ( sK43_SY3670 @ SV575 @ SV289 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4206]) ).
thf(4378,plain,
! [SV298: $i,SV757: $o,SV583: $i,SV733: $i] :
( ( ( in @ SV733 @ SV583 )
= $true )
| ( SV757 = $true )
| ( ( in @ SV733 @ SV298 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4207]) ).
thf(4379,plain,
! [SV298: $i,SV583: $i,SV733: $i] :
( ( ( in @ SV733 @ SV583 )
= $true )
| ( $true = $true )
| ( ( in @ SV733 @ SV298 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4210]) ).
thf(4380,plain,
! [SV298: $i,SV583: $i,SV733: $i] :
( ( ( in @ SV733 @ SV583 )
= $true )
| ( $false = $true )
| ( ( in @ SV733 @ SV298 )
= $true )
| ( ( in @ SV733 @ ( binunion @ SV298 @ SV583 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4213]) ).
thf(4381,plain,
! [SV584: $i,SV840: $i,SV299: $i] :
( ( ( ! [SY4036: $i] :
( ~ ( in @ SY4036 @ SV299 )
| ~ ( in @ SY4036 @ SV840 )
| ( in @ SY4036 @ SV584 ) ) )
= $false )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV299 )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4216]) ).
thf(4382,plain,
! [SV584: $i,SV840: $i,SV299: $i] :
( ( ( ~ ! [SY4036: $i] :
( ~ ( in @ SY4036 @ SV299 )
| ~ ( in @ SY4036 @ SV840 )
| ( in @ SY4036 @ SV584 ) ) )
= $true )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV584 )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4217]) ).
thf(4383,plain,
! [SV584: $i,SV840: $i,SV299: $i] :
( ( ( ! [SY4036: $i] :
( ~ ( in @ SY4036 @ SV299 )
| ~ ( in @ SY4036 @ SV840 )
| ( in @ SY4036 @ SV584 ) ) )
= $false )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV840 )
= $false )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4218]) ).
thf(4384,plain,
! [SV300: $i,SV841: $i,SV585: $i,SV1008: $i,SV964: $i] :
( ( ( ~ ( in @ ( kpair @ SV964 @ SV1008 ) @ SV585 ) )
= $true )
| ( ( in @ ( kpair @ SV964 @ SV1008 ) @ ( binunion @ SV585 @ SV841 ) )
= $true )
| ( ( in @ SV1008 @ SV300 )
= $false )
| ( ( in @ SV964 @ SV300 )
= $false )
| ( ( breln1 @ SV300 @ SV841 )
= $false )
| ( ( breln1 @ SV300 @ SV585 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4219]) ).
thf(4385,plain,
! [SV734: $i,SV911: $i,SV586: $i,SV301: $i,SV1046: $i] :
( ( ( ~ ( in @ SV1046 @ SV301 )
| ! [SY4182: $i] :
( ~ ( in @ SY4182 @ SV586 )
| ~ ( in @ ( kpair @ SV1046 @ SY4182 ) @ SV911 )
| ( in @ ( kpair @ SV1046 @ SY4182 ) @ SV734 ) ) )
= $true )
| ( ( in @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) @ SV301 )
= $true )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4220]) ).
thf(4386,plain,
! [SV734: $i,SV911: $i,SV586: $i,SV301: $i,SV1027: $i] :
( ( ( ~ ( in @ SV1027 @ SV301 ) )
= $true )
| ( ( ! [SY4170: $i] :
( ~ ( in @ SY4170 @ SV586 )
| ~ ( in @ ( kpair @ SV1027 @ SY4170 ) @ SV911 )
| ( in @ ( kpair @ SV1027 @ SY4170 ) @ SV734 ) ) )
= $true )
| ( ( ( ap @ SV301 @ SV586 @ SV734 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) )
= ( ap @ SV301 @ SV586 @ SV911 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) ) )
= $false )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4221]) ).
thf(4387,plain,
! [SV592: $i,SV846: $i,SV309: $i,SV968: $i] :
( ( ( in @ SV968 @ ( setminus @ SV309 @ SV846 ) )
= $false )
| ( ( in @ SV968 @ ( setminus @ SV309 @ ( binunion @ SV592 @ SV846 ) ) )
= $true )
| ( ( in @ SV968 @ ( setminus @ SV309 @ SV592 ) )
= $false )
| ( ( in @ SV968 @ SV309 )
= $false )
| ( ( in @ SV846 @ ( powerset @ SV309 ) )
= $false )
| ( ( in @ SV592 @ ( powerset @ SV309 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4223]) ).
thf(4388,plain,
! [SV848: $i,SV316: $i > $o] :
( ( ( ! [SY3190: $i] :
~ ! [SY3191: $i] :
~ ( ~ ( ~ ( SV316 @ SY3191 )
| ( SY3191 = SY3190 ) )
| ~ ( ( SY3191 != SY3190 )
| ( SV316 @ SY3191 ) ) ) )
= $false )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV316 @ ( sK85_SY4045 @ SV848 @ SV316 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4225]) ).
thf(4389,plain,
! [SV848: $i,SV316: $i > $o] :
( ( ( ~ ! [SY4183: $i] :
~ ( ~ ( ~ ( SV316 @ SY4183 )
| ( SY4183
= ( sK104_SY3190 @ SV848 @ SV316 ) ) )
| ~ ( ( SY4183
!= ( sK104_SY3190 @ SV848 @ SV316 ) )
| ( SV316 @ SY4183 ) ) ) )
= $false )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV848
= ( sK85_SY4045 @ SV848 @ SV316 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4226]) ).
thf(4390,plain,
! [SV317: $i,SV1009: $i,SV849: $i,SV970: $i,SV599: $i] :
( ( ( ~ ( subset @ SV599 @ SV970 ) )
= $true )
| ( ( ~ ( subset @ SV849 @ SV1009 )
| ( subset @ ( binintersect @ SV599 @ SV849 ) @ ( binintersect @ SV970 @ SV1009 ) ) )
= $true )
| ( ( in @ SV1009 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV970 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV849 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4227]) ).
thf(4391,plain,
! [SV318: $i,SV850: $i,SV600: $i,SV971: $i] :
( ( ( in @ SV971 @ ( binintersect @ SV600 @ SV850 ) )
= $false )
| ( ( in @ SV971 @ SV850 )
= $true )
| ( ( in @ SV971 @ SV318 )
= $false )
| ( ( in @ SV850 @ ( powerset @ SV318 ) )
= $false )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4228]) ).
thf(4392,plain,
! [SV319: $i,SV601: $i,SV914: $i > $o,SV738: $i,SV1017: $i] :
( ( ( in @ SV1017 @ SV738 )
= $false )
| ( ( SV914 @ SV1017 )
= $true )
| ( ( in @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ SV319 )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4229]) ).
thf(4393,plain,
! [SV601: $i,SV319: $i,SV914: $i > $o,SV738: $i,SV1047: $i] :
( ( ( ~ ( in @ SV1047 @ SV738 )
| ( SV914 @ SV1047 ) )
= $true )
| ( ( in @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) @ SV601 )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4230]) ).
thf(4394,plain,
! [SV319: $i,SV601: $i,SV738: $i,SV914: $i > $o] :
( ( ( in @ ( kpair @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) ) @ SV738 )
= $true )
| ( ( ! [SY4092: $i] :
( ~ ( in @ SY4092 @ SV738 )
| ( SV914 @ SY4092 ) ) )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4231]) ).
thf(4395,plain,
! [SV319: $i,SV601: $i,SV914: $i > $o,SV738: $i,SV1048: $i] :
( ( ( ~ ( in @ SV1048 @ SV738 )
| ( SV914 @ SV1048 ) )
= $true )
| ( ( SV914 @ ( kpair @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) ) )
= $false )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4232]) ).
thf(4396,plain,
! [SV322: $i,SV851: $i] :
( ( ( ! [SY4130: $i] :
~ ~ ( ~ ( in @ SY4130 @ ( sK51_SY3211 @ SV851 @ SV322 ) )
| ~ ( in @ SY4130 @ SV322 ) ) )
= $true )
| ( ( in @ SV851 @ SV322 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4233]) ).
thf(4397,plain,
! [SV325: $i,SV852: $i,SV972: $i,SV606: $i] :
( ( ( subset @ SV606 @ SV972 )
= $false )
| ( ( subset @ SV606 @ ( binintersect @ SV852 @ SV972 ) )
= $true )
| ( ( subset @ SV606 @ SV852 )
= $false )
| ( ( in @ SV972 @ ( powerset @ SV325 ) )
= $false )
| ( ( in @ SV852 @ ( powerset @ SV325 ) )
= $false )
| ( ( in @ SV606 @ ( powerset @ SV325 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4234]) ).
thf(4398,plain,
! [SV759: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ ( sK105_SY2411 @ SV759 @ SV40 ) ) )
= $false )
| ( ( SV40 @ SV759 )
= $false )
| ( ( SV40 @ ( sK72_SY3941 @ SV759 @ SV40 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4235]) ).
thf(4399,plain,
! [SV759: $i,SV40: $i > $o] :
( ( ( SV40 @ ( sK95_SY2411 @ SV759 @ SV40 ) )
= $true )
| ( ( SV40 @ SV759 )
= $false )
| ( ( SV759
= ( sK72_SY3941 @ SV759 @ SV40 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4236]) ).
thf(4400,plain,
! [SV353: $i > $o,SV44: $i,SV991: $i] :
( ( ( in @ SV991 @ SV44 )
= $false )
| ( ( ~ ( SV353 @ SV991 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( in @ ( sK9_SY3238 @ SV353 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4237]) ).
thf(4401,plain,
! [SV353: $i > $o,SV44: $i,SV1018: $i] :
( ( ( ~ ( in @ SV1018 @ SV44 )
| ~ ( SV353 @ SV1018 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( in @ ( sK36_SY3943 @ SV353 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4238]) ).
thf(4402,plain,
! [SV353: $i > $o,SV44: $i,SV1028: $i] :
( ( ( ~ ( ~ ( in @ SV1028 @ SV44 )
| ~ ( SV353 @ SV1028 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( SV353 @ ( sK9_SY3238 @ SV353 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4239]) ).
thf(4403,plain,
! [SV353: $i > $o,SV44: $i,SV1049: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1049 @ SV44 )
| ~ ( SV353 @ SV1049 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( SV353 @ ( sK36_SY3943 @ SV353 @ SV44 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4240]) ).
thf(4404,plain,
! [SV353: $i > $o,SV44: $i,SV1029: $i] :
( ( ( ~ ( ~ ( in @ SV1029 @ SV44 )
| ~ ( SV353 @ SV1029 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( ( sK9_SY3238 @ SV353 @ SV44 )
= ( sK36_SY3943 @ SV353 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4241]) ).
thf(4405,plain,
! [SV52: $i,SV923: $i,SV762: $i,SV361: $i,SV992: $i] :
( ( ( in @ SV992 @ ( binintersect @ SV361 @ SV762 ) )
= $false )
| ( ( in @ SV992 @ ( binunion @ SV762 @ SV923 ) )
= $true )
| ( ( in @ SV992 @ SV52 )
= $false )
| ( ( in @ SV923 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV762 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4242]) ).
thf(4406,plain,
! [SV765: $i,SV1050: $i,SV1030: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV1030 )
| ~ ( SV58 @ SV1050 )
| ( SV1030 = SV1050 ) )
= $true )
| ( ( SV58 @ SV765 )
= $false )
| ( ( SV58 @ ( sK75_SY3949 @ SV765 @ SV58 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4244]) ).
thf(4407,plain,
! [SV765: $i,SV1031: $i,SV1019: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV1019 ) )
= $true )
| ( ( ~ ( SV58 @ SV1031 )
| ( SV1019 = SV1031 ) )
= $true )
| ( ( SV58 @ SV765 )
= $false )
| ( ( SV765
= ( sK75_SY3949 @ SV765 @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4245]) ).
thf(4408,plain,
! [SV59: $i > $o,SV766: $i] :
( ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( ~ ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4246]) ).
thf(4409,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4247]) ).
thf(4410,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4248]) ).
thf(4411,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ~ ( ~ ( SV59 @ ( sK106_SY2468 @ SV766 @ SV59 ) )
| ~ ! [SY4184: $i] :
( ~ ( SV59 @ SY4184 )
| ( ( sK106_SY2468 @ SV766 @ SV59 )
= SY4184 ) ) ) )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4249]) ).
thf(4412,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ~ ~ ( ~ ( SV60 @ ( sK107_SY2472 @ SV767 @ SV60 ) )
| ~ ! [SY4185: $i] :
( ~ ( SV60 @ SY4185 )
| ( ( sK107_SY2472 @ SV767 @ SV60 )
= SY4185 ) ) ) )
= $false )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV60 @ ( sK76_SY3951 @ SV767 @ SV60 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4250]) ).
thf(4413,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ~ ( ~ ( SV60 @ ( sK96_SY2472 @ SV767 @ SV60 ) )
| ~ ! [SY4172: $i] :
( ~ ( SV60 @ SY4172 )
| ( ( sK96_SY2472 @ SV767 @ SV60 )
= SY4172 ) ) ) )
= $true )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV767
= ( sK76_SY3951 @ SV767 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4251]) ).
thf(4414,plain,
! [SV61: $i,SV858: $i,SV367: $i > $o] :
( ( ( SV367 @ ( sK59_SY3268 @ SV858 @ SV367 @ SV61 ) )
= $false )
| ( ( SV367 @ SV858 )
= $true )
| ( ( in @ SV858 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4253]) ).
thf(4415,plain,
! [SV76: $i,SV987: $i,SV380: $i > $i,SV622: $i] :
( ( ( SV622
= ( SV380 @ SV987 ) )
= $false )
| ( ( in @ SV987 @ SV76 )
= $false )
| ( ( in @ SV622
@ ( image1 @ SV76
@ ^ [SY3290: $i] : ( SV380 @ SY3290 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4260]) ).
thf(4416,plain,
! [SV773: $i,SV382: $i,SV78: $i,SV994: $i,SV927: $i] :
( ( ( in @ ( kpair @ SV927 @ SV994 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
= $false )
| ( ( ~ ! [SY4151: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY4151 @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ SY4151 ) @ SV382 ) )
| ~ ( in @ ( kpair @ SY4151 @ SV994 ) @ SV773 ) ) )
= $true )
| ( ( in @ SV994 @ SV78 )
= $false )
| ( ( in @ SV927 @ SV78 )
= $false )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4261]) ).
thf(4417,plain,
! [SV82: $i,SV774: $i,SV386: $i,SV995: $i,SV928: $i] :
( ( ( in @ ( kpair @ SV928 @ SV995 ) @ ( binunion @ SV386 @ SV774 ) )
= $false )
| ( ( ( in @ ( kpair @ SV928 @ SV995 ) @ SV386 )
| ( in @ ( kpair @ SV928 @ SV995 ) @ SV774 ) )
= $true )
| ( ( in @ SV995 @ SV82 )
= $false )
| ( ( in @ SV928 @ SV82 )
= $false )
| ( ( breln1 @ SV82 @ SV774 )
= $false )
| ( ( breln1 @ SV82 @ SV386 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4262]) ).
thf(4418,plain,
! [SV86: $i,SV776: $i,SV389: $i,SV929: $i] :
( ( ( in @ SV929 @ SV389 )
= $false )
| ( ( in @ SV929 @ SV776 )
= $false )
| ( ( subset @ SV389 @ ( setminus @ SV86 @ SV776 ) )
= $false )
| ( ( in @ SV929 @ SV86 )
= $false )
| ( ( in @ SV776 @ ( powerset @ SV86 ) )
= $false )
| ( ( in @ SV389 @ ( powerset @ SV86 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4263]) ).
thf(4419,plain,
! [SV87: $i,SV390: $i,SV777: $i,SV930: $i] :
( ( ( in @ SV930 @ SV777 )
= $true )
| ( ( ~ ( in @ SV930 @ SV390 ) )
= $true )
| ( ( subset @ SV390 @ SV777 )
= $false )
| ( ( in @ SV930 @ SV87 )
= $false )
| ( ( in @ SV777 @ ( powerset @ SV87 ) )
= $false )
| ( ( in @ SV390 @ ( powerset @ SV87 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4264]) ).
thf(4420,plain,
! [SV90: $i,SV931: $i,SV779: $i,SV393: $i,SV996: $i] :
( ( ( in @ SV996 @ ( binintersect @ SV393 @ SV779 ) )
= $false )
| ( ( in @ SV996 @ ( binintersect @ ( binunion @ SV393 @ SV931 ) @ ( binunion @ SV779 @ SV931 ) ) )
= $true )
| ( ( in @ SV996 @ SV90 )
= $false )
| ( ( in @ SV931 @ ( powerset @ SV90 ) )
= $false )
| ( ( in @ SV779 @ ( powerset @ SV90 ) )
= $false )
| ( ( in @ SV393 @ ( powerset @ SV90 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4265]) ).
thf(4421,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ( ~ ( SV100 @ ( sK97_SY2565 @ SV781 @ SV100 ) )
| ~ ! [SY4173: $i] :
( ~ ( SV100 @ SY4173 )
| ( ( sK97_SY2565 @ SV781 @ SV100 )
= SY4173 ) ) ) )
= $true )
| ( ( SV100 @ ( sK53_SY2563 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4266]) ).
thf(4422,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ~ ( ~ ( SV100 @ ( sK108_SY2565 @ SV781 @ SV100 ) )
| ~ ! [SY4186: $i] :
( ~ ( SV100 @ SY4186 )
| ( ( sK108_SY2565 @ SV781 @ SV100 )
= SY4186 ) ) ) )
= $false )
| ( ( SV100 @ ( sK61_SY4131 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4267]) ).
thf(4423,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ( ~ ( SV100 @ ( sK98_SY2565 @ SV781 @ SV100 ) )
| ~ ! [SY4174: $i] :
( ~ ( SV100 @ SY4174 )
| ( ( sK98_SY2565 @ SV781 @ SV100 )
= SY4174 ) ) ) )
= $true )
| ( ( ( sK53_SY2563 @ SV781 @ SV100 )
= ( sK61_SY4131 @ SV781 @ SV100 ) )
= $false )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4268]) ).
thf(4424,plain,
! [SV104: $i,SV404: $i > $o,SV862: $i] :
( ( ( ~ ( in @ ( sK99_SY3324 @ SV862 @ SV404 @ SV104 ) @ SV104 ) )
= $false )
| ( ( in @ SV862 @ SV104 )
= $false )
| ( ( SV404 @ SV862 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4269]) ).
thf(4425,plain,
! [SV104: $i,SV862: $i,SV404: $i > $o] :
( ( ( SV404 @ ( sK99_SY3324 @ SV862 @ SV404 @ SV104 ) )
= $false )
| ( ( in @ SV862 @ SV104 )
= $false )
| ( ( SV404 @ SV862 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4269]) ).
thf(4426,plain,
! [SV106: $i,SV1032: $i] :
( ( ( ~ ( in @ SV1032 @ omega ) )
= $true )
| ( ( in @ SV1032 @ SV106 )
= $true )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( in @ ( sK44_SY2577 @ SV106 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4270]) ).
thf(4427,plain,
! [SV106: $i,SV1033: $i] :
( ( ( ~ ( in @ SV1033 @ omega ) )
= $true )
| ( ( in @ SV1033 @ SV106 )
= $true )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( in @ ( sK44_SY2577 @ SV106 ) @ SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4271]) ).
thf(4428,plain,
! [SV122: $i,SV420: $i,SV865: $i > $o,SV788: $i > $o] :
( ( ( ~ ( ~ ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) )
| ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
| ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4274]) ).
thf(4429,plain,
! [SV125: $i,SV423: $i,SV790: $i,SV997: $i,SV937: $i] :
( ( ( in @ ( kpair @ SV937 @ SV997 ) @ SV790 )
= $false )
| ( ( in @ ( kpair @ SV937 @ SV997 ) @ ( binunion @ SV423 @ SV790 ) )
= $true )
| ( ( in @ SV997 @ SV125 )
= $false )
| ( ( in @ SV937 @ SV125 )
= $false )
| ( ( breln1 @ SV125 @ SV790 )
= $false )
| ( ( breln1 @ SV125 @ SV423 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4276]) ).
thf(4430,plain,
! [SV792: $i,SV998: $i,SV428: $i,SV939: $i,SV131: $i,SV1034: $i] :
( ( ( ~ ( in @ SV1034 @ SV131 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV939 @ SV1034 ) @ SV428 )
| ~ ( in @ ( kpair @ SV1034 @ SV998 ) @ SV792 )
| ( in @ ( kpair @ SV939 @ SV998 ) @ ( breln1compset @ SV131 @ SV428 @ SV792 ) ) )
= $true )
| ( ( in @ SV998 @ SV131 )
= $false )
| ( ( in @ SV939 @ SV131 )
= $false )
| ( ( breln1 @ SV131 @ SV792 )
= $false )
| ( ( breln1 @ SV131 @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4277]) ).
thf(4431,plain,
! [SV135: $i,SV432: $i,SV794: $i] :
( ( ( in @ ( kpair @ ( sK64_SY3983 @ SV794 @ SV432 @ SV135 ) @ ( sK87_SY4149 @ SV432 @ SV794 @ SV135 ) ) @ SV432 )
= $true )
| ( ( subset @ SV432 @ SV794 )
= $true )
| ( ( breln1 @ SV135 @ SV794 )
= $false )
| ( ( breln1 @ SV135 @ SV432 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4279]) ).
thf(4432,plain,
! [SV650: $i,SV870: $i,SV436: $i,SV140: $i] :
( ( ( ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SV140 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4281]) ).
thf(4433,plain,
! [SV436: $i,SV870: $i,SV650: $i,SV140: $i] :
( ( ( in @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) @ SV436 )
= $true )
| ( ( ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) )
| ( SV650 = SV870 ) )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4282]) ).
thf(4434,plain,
! [SV140: $i,SV436: $i,SV650: $i,SV870: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV650 ) )
= $false )
| ( ( ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) )
| ( SV650 = SV870 ) )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4283]) ).
thf(4435,plain,
! [SV140: $i,SV436: $i,SV650: $i,SV870: $i] :
( ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV870 )
= $false )
| ( ( ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) )
| ( SV650 = SV870 ) )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4283]) ).
thf(4436,plain,
! [SV144: $i,SV440: $i,SV975: $i,SV654: $i > $i] :
( ( ( ~ ( in @ ( sK100_SY4134 @ SV654 @ SV975 @ SV440 @ SV144 ) @ SV144 ) )
= $false )
| ( ( surjective @ SV440 @ SV144 @ SV975 )
= $true )
| ( ( in @ SV975 @ ( funcSet @ SV440 @ SV144 ) )
= $false )
| ( ( in @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) @ SV144 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4284]) ).
thf(4437,plain,
! [SV654: $i > $i,SV975: $i,SV144: $i,SV440: $i] :
( ( ( ( ap @ SV440 @ SV144 @ SV975 @ ( SV654 @ ( sK100_SY4134 @ SV654 @ SV975 @ SV440 @ SV144 ) ) )
= ( sK100_SY4134 @ SV654 @ SV975 @ SV440 @ SV144 ) )
= $false )
| ( ( surjective @ SV440 @ SV144 @ SV975 )
= $true )
| ( ( in @ SV975 @ ( funcSet @ SV440 @ SV144 ) )
= $false )
| ( ( in @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) @ SV144 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4284]) ).
thf(4438,plain,
! [SV144: $i,SV440: $i,SV941: $i,SV654: $i > $i] :
( ( ( in @ ( sK91_SY4108 @ SV654 @ SV941 @ SV440 @ SV144 ) @ SV144 )
= $true )
| ( ( surjective @ SV440 @ SV144 @ SV941 )
= $true )
| ( ( in @ SV941 @ ( funcSet @ SV440 @ SV144 ) )
= $false )
| ( ( in @ ( SV654 @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) ) @ SV440 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4285]) ).
thf(4439,plain,
! [SV442: $i > $o,SV146: $i,SV999: $i] :
( ( ( in @ SV999 @ SV146 )
= $false )
| ( ( ~ ( SV442 @ SV999 ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( in @ ( sK11_SY3407 @ SV442 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4287]) ).
thf(4440,plain,
! [SV442: $i > $o,SV146: $i,SV1020: $i] :
( ( ( ~ ( in @ SV1020 @ SV146 )
| ~ ( SV442 @ SV1020 ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( in @ ( sK38_SY3987 @ SV442 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4288]) ).
thf(4441,plain,
! [SV442: $i > $o,SV146: $i,SV1035: $i] :
( ( ( ~ ( ~ ( in @ SV1035 @ SV146 )
| ~ ( SV442 @ SV1035 ) ) )
= $false )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( SV442 @ ( sK11_SY3407 @ SV442 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4289]) ).
thf(4442,plain,
! [SV442: $i > $o,SV146: $i,SV1051: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1051 @ SV146 )
| ~ ( SV442 @ SV1051 ) ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( SV442 @ ( sK38_SY3987 @ SV442 @ SV146 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4290]) ).
thf(4443,plain,
! [SV442: $i > $o,SV146: $i,SV1036: $i] :
( ( ( ~ ( ~ ( in @ SV1036 @ SV146 )
| ~ ( SV442 @ SV1036 ) ) )
= $false )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( ( sK11_SY3407 @ SV442 @ SV146 )
= ( sK38_SY3987 @ SV442 @ SV146 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4291]) ).
thf(4444,plain,
! [SV148: $i,SV943: $i,SV799: $i,SV444: $i,SV1000: $i] :
( ( ( in @ SV1000 @ ( binintersect @ SV444 @ SV799 ) )
= $false )
| ( ( in @ SV1000 @ ( binunion @ SV444 @ SV943 ) )
= $true )
| ( ( in @ SV1000 @ SV148 )
= $false )
| ( ( in @ SV943 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV799 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV444 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4292]) ).
thf(4445,plain,
! [SV448: $i > $o,SV1010: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ SV1010 ) )
= $true )
| ( ( ~ ! [SY4163: $i] :
( ~ ( SV152 @ SY4163 )
| ( SV1010 = SY4163 ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4293]) ).
thf(4446,plain,
! [SV152: $i > $o,SV448: $i > $o] :
( ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) )
| ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4294]) ).
thf(4447,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4295]) ).
thf(4448,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4296]) ).
thf(4449,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4297]) ).
thf(4450,plain,
! [SV464: $i,SV877: $i,SV666: $i,SV168: $i] :
( ( ( in @ ( sK92_SY4154 @ SV168 @ SV666 @ SV877 @ SV464 ) @ SV464 )
= $true )
| ( ( subset @ SV666 @ SV877 )
= $true )
| ( ( breln @ SV168 @ SV464 @ SV877 )
= $false )
| ( ( breln @ SV168 @ SV464 @ SV666 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4298]) ).
thf(4451,plain,
! [SV168: $i,SV464: $i,SV666: $i,SV877: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK79_SY4066 @ SV877 @ SV666 @ SV464 @ SV168 ) @ ( sK92_SY4154 @ SV168 @ SV666 @ SV877 @ SV464 ) ) @ SV666 ) )
= $false )
| ( ( subset @ SV666 @ SV877 )
= $true )
| ( ( breln @ SV168 @ SV464 @ SV877 )
= $false )
| ( ( breln @ SV168 @ SV464 @ SV666 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4299]) ).
thf(4452,plain,
! [SV168: $i,SV464: $i,SV666: $i,SV877: $i] :
( ( ( in @ ( kpair @ ( sK79_SY4066 @ SV877 @ SV666 @ SV464 @ SV168 ) @ ( sK92_SY4154 @ SV168 @ SV666 @ SV877 @ SV464 ) ) @ SV877 )
= $false )
| ( ( subset @ SV666 @ SV877 )
= $true )
| ( ( breln @ SV168 @ SV464 @ SV877 )
= $false )
| ( ( breln @ SV168 @ SV464 @ SV666 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4299]) ).
thf(4453,plain,
! [SV470: $i > $i,SV976: $i,SV175: $i] :
( ( ( ! [SY4135: $i] :
~ ~ ( ~ ( in @ SY4135 @ SV175 )
| ( SV976
!= ( SV470 @ SY4135 ) ) ) )
= $false )
| ( ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4300]) ).
thf(4454,plain,
! [SV470: $i > $i,SV976: $i,SV175: $i] :
( ( ( ! [SY4136: $i] :
~ ~ ( ~ ( in @ SY4136 @ SV175 )
| ( SV976
!= ( SV470 @ SY4136 ) ) ) )
= $true )
| ( ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4301]) ).
thf(4455,plain,
! [SV977: $i,SV175: $i,SV470: $i > $i] :
( ( ( ~ ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
| ~ ! [SY4164: $i] :
~ ~ ( ~ ( in @ SY4164 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4164 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) )
| ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 ) ) )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4302]) ).
thf(4456,plain,
! [SV978: $i,SV670: $i > $i > $o,SV475: $i,SV180: $i,SV1037: $i] :
( ( ( ~ ( in @ SV1037 @ SV180 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY4175: $i] :
~ ( ~ ( SV670 @ SV1037 @ SY4175 )
| ~ ! [SY4176: $i] :
( ~ ( in @ SY4176 @ SV475 )
| ~ ( SV670 @ SV1037 @ SY4176 )
| ( in @ ( kpair @ SY4175 @ SY4176 ) @ SV978 ) ) ) ) )
= $true )
| ( ( reflwellordering @ SV475 @ SV978 )
= $false )
| ( ( in @ SV978 @ ( breln1Set @ SV475 ) )
= $false )
| ( ( in @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV180 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4303]) ).
thf(4457,plain,
! [SV979: $i,SV670: $i > $i > $o,SV180: $i,SV475: $i,SV1052: $i] :
( ( ( ~ ( in @ SV1052 @ ( breln1Set @ SV475 ) )
| ~ ( reflwellordering @ SV475 @ SV1052 )
| ! [SY4187: $i] :
( ~ ( in @ SY4187 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY4188: $i] :
~ ( ~ ( SV670 @ SY4187 @ SY4188 )
| ~ ! [SY4189: $i] :
( ~ ( in @ SY4189 @ SV475 )
| ~ ( SV670 @ SY4187 @ SY4189 )
| ( in @ ( kpair @ SY4188 @ SY4189 ) @ SV1052 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV979 @ SV475 )
= $false )
| ( ( SV670 @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV979 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4304]) ).
thf(4458,plain,
! [SV189: $i,SV879: $i,SV484: $i > $o] :
( ( ( SV484 @ ( sK65_SY3497 @ SV879 @ SV484 @ SV189 ) )
= $false )
| ( ( SV484 @ SV879 )
= $true )
| ( ( in @ SV879 @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4307]) ).
thf(4459,plain,
! [SV193: $i,SV881: $i,SV488: $i > $i] :
( ( ( ~ ( in @ ( sK93_SY4070 @ SV488 @ SV881 @ SV193 ) @ SV193 )
| ( SV881
!= ( SV488 @ ( sK93_SY4070 @ SV488 @ SV881 @ SV193 ) ) ) )
= $false )
| ( ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4308]) ).
thf(4460,plain,
! [SV488: $i > $i,SV881: $i,SV193: $i,SV1021: $i] :
( ( ( ~ ( in @ SV1021 @ SV193 )
| ( SV881
!= ( SV488 @ SV1021 ) ) )
= $true )
| ( ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4309]) ).
thf(4461,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ~ ~ ( ~ ( SV196 @ ( sK109_SY2855 @ SV816 @ SV196 ) )
| ~ ! [SY4190: $i] :
( ~ ( SV196 @ SY4190 )
| ( ( sK109_SY2855 @ SV816 @ SV196 )
= SY4190 ) ) ) )
= $false )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV196 @ ( sK80_SY4002 @ SV816 @ SV196 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4310]) ).
thf(4462,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ~ ( ~ ( SV196 @ ( sK101_SY2855 @ SV816 @ SV196 ) )
| ~ ! [SY4177: $i] :
( ~ ( SV196 @ SY4177 )
| ( ( sK101_SY2855 @ SV816 @ SV196 )
= SY4177 ) ) ) )
= $true )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV816
= ( sK80_SY4002 @ SV816 @ SV196 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4311]) ).
thf(4463,plain,
! [SV491: $i > $o,SV1053: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ SV1053 )
| ~ ! [SY4191: $i] :
( ~ ( SV197 @ SY4191 )
| ( SV1053 = SY4191 ) ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4312]) ).
thf(4464,plain,
! [SV197: $i > $o,SV1054: $i,SV491: $i > $o] :
( ( ( ~ ~ ( ~ ( SV491 @ SV1054 )
| ~ ! [SY4192: $i] :
( ~ ( SV491 @ SY4192 )
| ( SV1054 = SY4192 ) ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4313]) ).
thf(4465,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4314]) ).
thf(4466,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4315]) ).
thf(4467,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4316]) ).
thf(4468,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4317]) ).
thf(4469,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4317]) ).
thf(4470,plain,
! [SV492: $i,SV679: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK94_SY4093 @ SV199 @ SV679 @ SV492 ) @ SV492 )
| ( SV679
!= ( kpair @ ( sK39_SY3820 @ SV679 @ SV492 @ SV199 ) @ ( sK94_SY4093 @ SV199 @ SV679 @ SV492 ) ) ) )
= $false )
| ( ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4318]) ).
thf(4471,plain,
! [SV496: $i,SV885: $o,SV203: $i,SV683: $i] :
( ( ( in @ SV683 @ SV203 )
= $false )
| ( SV885 = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4320]) ).
thf(4472,plain,
! [SV203: $i,SV885: $o,SV496: $i,SV683: $i] :
( ( ( in @ SV683 @ SV496 )
= $true )
| ( SV885 = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4321]) ).
thf(4473,plain,
! [SV496: $i,SV885: $o,SV203: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV203 ) )
= $false )
| ( SV885 = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4323]) ).
thf(4474,plain,
! [SV203: $i,SV885: $o,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 )
| SV885 )
= $false )
| ( SV885 = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4323]) ).
thf(4475,plain,
! [SV496: $i,SV885: $o,SV203: $i,SV683: $i] :
( ( ( in @ SV683 @ SV203 )
= $false )
| ( SV885 = $true )
| ( SV885 = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4324]) ).
thf(4476,plain,
! [SV203: $i,SV885: $o,SV496: $i,SV683: $i] :
( ( ( in @ SV683 @ SV496 )
= $true )
| ( SV885 = $true )
| ( SV885 = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4325]) ).
thf(4477,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( in @ SV683 @ SV203 )
= $false )
| ( $true = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4327]) ).
thf(4478,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( in @ SV683 @ SV496 )
= $true )
| ( $true = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4328]) ).
thf(4479,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV203 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4330]) ).
thf(4480,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4330]) ).
thf(4481,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( in @ SV683 @ SV203 )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4331]) ).
thf(4482,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( in @ SV683 @ SV496 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4332]) ).
thf(4483,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( in @ SV683 @ SV203 )
= $false )
| ( $false = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4334]) ).
thf(4484,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( in @ SV683 @ SV496 )
= $true )
| ( $false = $true )
| ( ( in @ SV683 @ SV203 )
= $true )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4335]) ).
thf(4485,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ~ ( in @ SV683 @ SV203 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4337]) ).
thf(4486,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4337]) ).
thf(4487,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( in @ SV683 @ SV203 )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4338]) ).
thf(4488,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( in @ SV683 @ SV496 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4339]) ).
thf(4489,plain,
! [SV207: $i,SV1011: $i,SV500: $i > $o] :
( ( ( SV500 @ SV1011 )
= $false )
| ( ( in @ SV1011 @ SV207 )
= $false )
| ( ( in @ ( sK40_SY3540 @ SV500 @ SV207 ) @ SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4341]) ).
thf(4490,plain,
! [SV207: $i,SV1012: $i,SV500: $i > $o] :
( ( ( SV500 @ SV1012 )
= $false )
| ( ( in @ SV1012 @ SV207 )
= $false )
| ( ( SV500 @ ( sK40_SY3540 @ SV500 @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4342]) ).
thf(4491,plain,
! [SV208: $i,SV818: $i,SV952: $o,SV501: $i,SV982: $i] :
( ( ( ~ ( in @ SV982 @ SV501 )
| SV952 )
= $false )
| ( ( ~ ( ~ ( in @ SV982 @ SV818 )
| SV952 )
| SV952 )
= $true )
| ( ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV982 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4343]) ).
thf(4492,plain,
! [SV208: $i,SV818: $i,SV501: $i,SV983: $i] :
( ( ( ~ ( in @ SV983 @ SV501 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV983 @ SV818 )
| $true )
| $true )
= $true )
| ( ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV983 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4344]) ).
thf(4493,plain,
! [SV208: $i,SV818: $i,SV501: $i,SV984: $i] :
( ( ( ~ ( in @ SV984 @ SV501 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV984 @ SV818 )
| $false )
| $false )
= $true )
| ( ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV984 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4345]) ).
thf(4494,plain,
! [SV502: $i,SV209: $i,SV889: $i > $o,SV689: $i,SV1038: $i] :
( ( ( ~ ( in @ SV1038 @ SV689 ) )
= $true )
| ( ( SV889 @ SV1038 )
= $true )
| ( ( in @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) @ SV502 )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4347]) ).
thf(4495,plain,
! [SV209: $i,SV502: $i,SV889: $i > $o,SV689: $i,SV1055: $i] :
( ( ( ~ ( in @ SV1055 @ SV689 )
| ( SV889 @ SV1055 ) )
= $true )
| ( ( in @ ( kpair @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) ) @ SV689 )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4348]) ).
thf(4496,plain,
! [SV209: $i,SV502: $i,SV889: $i > $o,SV689: $i,SV1039: $i] :
( ( ( ~ ( in @ SV1039 @ SV689 ) )
= $true )
| ( ( SV889 @ SV1039 )
= $true )
| ( ( SV889 @ ( kpair @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) ) )
= $false )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4349]) ).
thf(4497,plain,
! [SV216: $i,SV819: $i,SV508: $i,SV1001: $i,SV953: $i] :
( ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( ! [SY4155: $o] :
( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
| SY4155 )
| ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| SY4155 )
| SY4155 ) )
= $true )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4350]) ).
thf(4498,plain,
! [SV226: $i,SV1040: $i] :
( ( ( ~ ( in @ SV1040 @ ( sK2_SY2943 @ SV226 ) ) )
= $true )
| ( ( ! [SY4178: $i] :
( ~ ( in @ SY4178 @ SV1040 )
| ( in @ SY4178 @ SV226 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4351]) ).
thf(4499,plain,
! [SV1056: $i,SV226: $i,SV1041: $i] :
( ( ~ ~ ( ~ ( in @ SV1041 @ SV226 )
| ~ ( in @ SV1056 @ SV226 ) )
| ~ ! [SY4193: $i] :
( ~ ( in @ SY4193 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SV1041 @ SY4193 )
| ( in @ SV1056 @ SY4193 ) )
| ~ ( ~ ( in @ SV1056 @ SY4193 )
| ( in @ SV1041 @ SY4193 ) ) ) )
| ( SV1041 = SV1056 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4352]) ).
thf(4500,plain,
! [SV1014: $i,SV226: $i,SV1002: $i] :
( ( ( ~ ( in @ SV1002 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SV1014 @ ( sK2_SY2943 @ SV226 ) ) )
= $true )
| ( ( ! [SY4166: $i] :
( ~ ( in @ SY4166 @ SV1002 )
| ( in @ SY4166 @ SV1014 ) )
| ! [SY4167: $i] :
( ~ ( in @ SY4167 @ SV1014 )
| ( in @ SY4167 @ SV1002 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4353]) ).
thf(4501,plain,
! [SV955: $i,SV226: $i] :
( ( ( ~ ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 ) )
= $false )
| ( ( ~ ~ ! [SY4115: $i] :
~ ( in @ SY4115 @ SV955 ) )
= $true )
| ( ( ~ ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4354]) ).
thf(4502,plain,
! [SV955: $i,SV226: $i] :
( ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( ~ ~ ! [SY4115: $i] :
~ ( in @ SY4115 @ SV955 ) )
= $true )
| ( ( ~ ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4354]) ).
thf(4503,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1003: $i] :
( ( ( ~ ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) ) )
= $true )
| ( ( ~ ! [SY4159: $i] :
~ ~ ( ~ ( in @ SY4159 @ SV520 )
| ~ ( SV230 @ SY4159 @ SV1003 ) ) )
= $true )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4356]) ).
thf(4504,plain,
! [SV1003: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ~ ~ ! [SY4160: $i] :
~ ~ ( ~ ( in @ SY4160 @ SV520 )
| ~ ( SV230 @ SY4160 @ SV1003 ) ) )
= $true )
| ( ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
= $true )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4357]) ).
thf(4505,plain,
! [SV957: $i,SV520: $i,SV230: $i > $i > $o] :
( ( ( ~ ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( ~ ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4358]) ).
thf(4506,plain,
! [SV230: $i > $i > $o,SV520: $i,SV957: $i] :
( ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( ~ ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4358]) ).
thf(4507,plain,
! [SV233: $i,SV823: $i > $o,SV523: $i,SV1022: $i] :
( ( ( in @ SV1022 @ SV523 )
= $false )
| ( ( SV823 @ SV1022 )
= $true )
| ( ( in @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) @ SV233 )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4359]) ).
thf(4508,plain,
! [SV233: $i,SV823: $i > $o,SV523: $i,SV1042: $i] :
( ( ( ~ ( in @ SV1042 @ SV523 ) )
= $true )
| ( ( SV823 @ SV1042 )
= $true )
| ( ( in @ ( kpair @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) ) @ SV523 )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4360]) ).
thf(4509,plain,
! [SV233: $i,SV823: $i > $o,SV523: $i,SV1023: $i] :
( ( ( in @ SV1023 @ SV523 )
= $false )
| ( ( SV823 @ SV1023 )
= $true )
| ( ( SV823 @ ( kpair @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) ) )
= $false )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4361]) ).
thf(4510,plain,
! [SV251: $i,SV538: $i,SV828: $i,SV960: $i] :
( ( ( ~ ( in @ SV960 @ SV828 ) )
= $false )
| ( ( ~ ( in @ SV960 @ ( binunion @ SV538 @ SV828 ) ) )
= $true )
| ( ( in @ SV960 @ SV538 )
= $true )
| ( ( in @ SV960 @ SV251 )
= $false )
| ( ( in @ SV828 @ ( powerset @ SV251 ) )
= $false )
| ( ( in @ SV538 @ ( powerset @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4362]) ).
thf(4511,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( ~ ( in @ ( sK110_SY4022 @ SV549 @ SV829 @ SV260 ) @ SV260 )
| ! [SY4194: $i] :
( ~ ( in @ SY4194 @ SV260 )
| ~ ( in @ ( kpair @ ( sK110_SY4022 @ SV549 @ SV829 @ SV260 ) @ SY4194 ) @ SV829 )
| ( in @ ( kpair @ ( sK110_SY4022 @ SV549 @ SV829 @ SV260 ) @ SY4194 ) @ SV549 ) ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4363]) ).
thf(4512,plain,
! [SV549: $i,SV829: $i,SV260: $i] :
( ( ( ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) ) )
= $true )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4364]) ).
thf(4513,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV549 )
= $true )
| ( ( ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) )
| ( SV549 = SV829 ) )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4365]) ).
thf(4514,plain,
! [SV549: $i,SV829: $i,SV260: $i] :
( ( ( ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) ) )
= $true )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4366]) ).
thf(4515,plain,
! [SV264: $i,SV830: $i,SV553: $i,SV1005: $i,SV961: $i] :
( ( ( ( in @ ( kpair @ SV961 @ SV1005 ) @ SV553 )
| ( in @ ( kpair @ SV961 @ SV1005 ) @ SV830 ) )
= $false )
| ( ( in @ ( kpair @ SV961 @ SV1005 ) @ ( binunion @ SV553 @ SV830 ) )
= $true )
| ( ( in @ SV1005 @ SV264 )
= $false )
| ( ( in @ SV961 @ SV264 )
= $false )
| ( ( breln1 @ SV264 @ SV830 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4367]) ).
thf(4516,plain,
! [SV271: $i,SV833: $i > $o,SV559: $i,SV1024: $i] :
( ( ( in @ SV1024 @ SV559 )
= $false )
| ( ( SV833 @ SV1024 )
= $true )
| ( ( in @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) @ SV271 )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4368]) ).
thf(4517,plain,
! [SV271: $i,SV833: $i > $o,SV559: $i,SV1043: $i] :
( ( ( ~ ( in @ SV1043 @ SV559 ) )
= $true )
| ( ( SV833 @ SV1043 )
= $true )
| ( ( in @ ( kpair @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) ) @ SV559 )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4369]) ).
thf(4518,plain,
! [SV271: $i,SV833: $i > $o,SV559: $i,SV1025: $i] :
( ( ( in @ SV1025 @ SV559 )
= $false )
| ( ( SV833 @ SV1025 )
= $true )
| ( ( SV833 @ ( kpair @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) ) )
= $false )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4370]) ).
thf(4519,plain,
! [SV275: $i,SV989: $i,SV563: $i > $o] :
( ( ( SV563 @ SV989 )
= $false )
| ( ( in @ SV989 @ SV275 )
= $false )
| ( ( in @ ( sK16_SY3653 @ SV563 @ SV275 ) @ SV275 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4371]) ).
thf(4520,plain,
! [SV275: $i,SV990: $i,SV563: $i > $o] :
( ( ( SV563 @ SV990 )
= $false )
| ( ( in @ SV990 @ SV275 )
= $false )
| ( ( SV563 @ ( sK16_SY3653 @ SV563 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4372]) ).
thf(4521,plain,
! [SV836: $i,SV568: $i,SV280: $i,SV1007: $i,SV963: $i] :
( ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( ! [SY4161: $o] :
( ~ ! [SY4162: $i] :
( ~ ( in @ SY4162 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SY4162 ) @ SV568 )
| ~ ( in @ ( kpair @ SY4162 @ SV1007 ) @ SV836 )
| SY4161 )
| SY4161 ) )
= $true )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4373]) ).
thf(4522,plain,
! [SV837: $i,SV1057: $i,SV1044: $i,SV288: $i > $o] :
( ( ( ~ ( SV288 @ SV1044 )
| ~ ( SV288 @ SV1057 )
| ( SV1044 = SV1057 ) )
= $true )
| ( ( SV288 @ SV837 )
= $false )
| ( ( SV288 @ ( sK83_SY4034 @ SV837 @ SV288 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4374]) ).
thf(4523,plain,
! [SV837: $i,SV1045: $i,SV1026: $i,SV288: $i > $o] :
( ( ( ~ ( SV288 @ SV1026 ) )
= $true )
| ( ( ~ ( SV288 @ SV1045 )
| ( SV1026 = SV1045 ) )
= $true )
| ( ( SV288 @ SV837 )
= $false )
| ( ( SV837
= ( sK83_SY4034 @ SV837 @ SV288 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4375]) ).
thf(4524,plain,
! [SV289: $i,SV1015: $i,SV575: $i > $o] :
( ( ( SV575 @ SV1015 )
= $false )
| ( ( in @ SV1015 @ SV289 )
= $false )
| ( ( in @ ( sK43_SY3670 @ SV575 @ SV289 ) @ SV289 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4376]) ).
thf(4525,plain,
! [SV289: $i,SV1016: $i,SV575: $i > $o] :
( ( ( SV575 @ SV1016 )
= $false )
| ( ( in @ SV1016 @ SV289 )
= $false )
| ( ( SV575 @ ( sK43_SY3670 @ SV575 @ SV289 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4377]) ).
thf(4526,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( ~ ( in @ ( sK111_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV299 )
| ~ ( in @ ( sK111_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV840 )
| ( in @ ( sK111_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV584 ) )
= $false )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV299 )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4381]) ).
thf(4527,plain,
! [SV584: $i,SV840: $i,SV299: $i] :
( ( ( ! [SY4036: $i] :
( ~ ( in @ SY4036 @ SV299 )
| ~ ( in @ SY4036 @ SV840 )
| ( in @ SY4036 @ SV584 ) ) )
= $false )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV584 )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4382]) ).
thf(4528,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( ~ ( in @ ( sK112_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV299 )
| ~ ( in @ ( sK112_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV840 )
| ( in @ ( sK112_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV584 ) )
= $false )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV840 )
= $false )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4383]) ).
thf(4529,plain,
! [SV300: $i,SV841: $i,SV585: $i,SV1008: $i,SV964: $i] :
( ( ( in @ ( kpair @ SV964 @ SV1008 ) @ SV585 )
= $false )
| ( ( in @ ( kpair @ SV964 @ SV1008 ) @ ( binunion @ SV585 @ SV841 ) )
= $true )
| ( ( in @ SV1008 @ SV300 )
= $false )
| ( ( in @ SV964 @ SV300 )
= $false )
| ( ( breln1 @ SV300 @ SV841 )
= $false )
| ( ( breln1 @ SV300 @ SV585 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4384]) ).
thf(4530,plain,
! [SV734: $i,SV911: $i,SV586: $i,SV301: $i,SV1046: $i] :
( ( ( ~ ( in @ SV1046 @ SV301 ) )
= $true )
| ( ( ! [SY4182: $i] :
( ~ ( in @ SY4182 @ SV586 )
| ~ ( in @ ( kpair @ SV1046 @ SY4182 ) @ SV911 )
| ( in @ ( kpair @ SV1046 @ SY4182 ) @ SV734 ) ) )
= $true )
| ( ( in @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) @ SV301 )
= $true )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4385]) ).
thf(4531,plain,
! [SV734: $i,SV911: $i,SV586: $i,SV301: $i,SV1027: $i] :
( ( ( in @ SV1027 @ SV301 )
= $false )
| ( ( ! [SY4170: $i] :
( ~ ( in @ SY4170 @ SV586 )
| ~ ( in @ ( kpair @ SV1027 @ SY4170 ) @ SV911 )
| ( in @ ( kpair @ SV1027 @ SY4170 ) @ SV734 ) ) )
= $true )
| ( ( ( ap @ SV301 @ SV586 @ SV734 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) )
= ( ap @ SV301 @ SV586 @ SV911 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) ) )
= $false )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4386]) ).
thf(4532,plain,
! [SV848: $i,SV316: $i > $o] :
( ( ( ~ ! [SY4195: $i] :
~ ( ~ ( ~ ( SV316 @ SY4195 )
| ( SY4195
= ( sK113_SY3190 @ SV848 @ SV316 ) ) )
| ~ ( ( SY4195
!= ( sK113_SY3190 @ SV848 @ SV316 ) )
| ( SV316 @ SY4195 ) ) ) )
= $false )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV316 @ ( sK85_SY4045 @ SV848 @ SV316 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4388]) ).
thf(4533,plain,
! [SV848: $i,SV316: $i > $o] :
( ( ( ! [SY4183: $i] :
~ ( ~ ( ~ ( SV316 @ SY4183 )
| ( SY4183
= ( sK104_SY3190 @ SV848 @ SV316 ) ) )
| ~ ( ( SY4183
!= ( sK104_SY3190 @ SV848 @ SV316 ) )
| ( SV316 @ SY4183 ) ) ) )
= $true )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV848
= ( sK85_SY4045 @ SV848 @ SV316 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4389]) ).
thf(4534,plain,
! [SV317: $i,SV1009: $i,SV849: $i,SV970: $i,SV599: $i] :
( ( ( subset @ SV599 @ SV970 )
= $false )
| ( ( ~ ( subset @ SV849 @ SV1009 )
| ( subset @ ( binintersect @ SV599 @ SV849 ) @ ( binintersect @ SV970 @ SV1009 ) ) )
= $true )
| ( ( in @ SV1009 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV970 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV849 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4390]) ).
thf(4535,plain,
! [SV601: $i,SV319: $i,SV914: $i > $o,SV738: $i,SV1047: $i] :
( ( ( ~ ( in @ SV1047 @ SV738 ) )
= $true )
| ( ( SV914 @ SV1047 )
= $true )
| ( ( in @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) @ SV601 )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4393]) ).
thf(4536,plain,
! [SV319: $i,SV601: $i,SV914: $i > $o,SV738: $i,SV1058: $i] :
( ( ( ~ ( in @ SV1058 @ SV738 )
| ( SV914 @ SV1058 ) )
= $true )
| ( ( in @ ( kpair @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) ) @ SV738 )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4394]) ).
thf(4537,plain,
! [SV319: $i,SV601: $i,SV914: $i > $o,SV738: $i,SV1048: $i] :
( ( ( ~ ( in @ SV1048 @ SV738 ) )
= $true )
| ( ( SV914 @ SV1048 )
= $true )
| ( ( SV914 @ ( kpair @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) ) )
= $false )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4395]) ).
thf(4538,plain,
! [SV322: $i,SV851: $i,SV1059: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1059 @ ( sK51_SY3211 @ SV851 @ SV322 ) )
| ~ ( in @ SV1059 @ SV322 ) ) )
= $true )
| ( ( in @ SV851 @ SV322 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4396]) ).
thf(4539,plain,
! [SV759: $i,SV40: $i > $o] :
( ( ( SV40 @ ( sK105_SY2411 @ SV759 @ SV40 ) )
= $true )
| ( ( SV40 @ SV759 )
= $false )
| ( ( SV40 @ ( sK72_SY3941 @ SV759 @ SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4398]) ).
thf(4540,plain,
! [SV44: $i,SV991: $i,SV353: $i > $o] :
( ( ( SV353 @ SV991 )
= $false )
| ( ( in @ SV991 @ SV44 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( in @ ( sK9_SY3238 @ SV353 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4400]) ).
thf(4541,plain,
! [SV353: $i > $o,SV44: $i,SV1018: $i] :
( ( ( ~ ( in @ SV1018 @ SV44 ) )
= $true )
| ( ( ~ ( SV353 @ SV1018 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( in @ ( sK36_SY3943 @ SV353 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4401]) ).
thf(4542,plain,
! [SV353: $i > $o,SV44: $i,SV1028: $i] :
( ( ( ~ ( in @ SV1028 @ SV44 )
| ~ ( SV353 @ SV1028 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( SV353 @ ( sK9_SY3238 @ SV353 @ SV44 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4402]) ).
thf(4543,plain,
! [SV353: $i > $o,SV44: $i,SV1049: $i] :
( ( ( ~ ( ~ ( in @ SV1049 @ SV44 )
| ~ ( SV353 @ SV1049 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( SV353 @ ( sK36_SY3943 @ SV353 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4403]) ).
thf(4544,plain,
! [SV353: $i > $o,SV44: $i,SV1029: $i] :
( ( ( ~ ( in @ SV1029 @ SV44 )
| ~ ( SV353 @ SV1029 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( ( sK9_SY3238 @ SV353 @ SV44 )
= ( sK36_SY3943 @ SV353 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4404]) ).
thf(4545,plain,
! [SV765: $i,SV1050: $i,SV1030: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV1030 ) )
= $true )
| ( ( ~ ( SV58 @ SV1050 )
| ( SV1030 = SV1050 ) )
= $true )
| ( ( SV58 @ SV765 )
= $false )
| ( ( SV58 @ ( sK75_SY3949 @ SV765 @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4406]) ).
thf(4546,plain,
! [SV765: $i,SV1031: $i,SV1019: $i,SV58: $i > $o] :
( ( ( SV58 @ SV1019 )
= $false )
| ( ( ~ ( SV58 @ SV1031 )
| ( SV1019 = SV1031 ) )
= $true )
| ( ( SV58 @ SV765 )
= $false )
| ( ( SV765
= ( sK75_SY3949 @ SV765 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4407]) ).
thf(4547,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ! [SY2468: $i] :
~ ~ ( ~ ( SV59 @ SY2468 )
| ~ ! [SY2469: $i] :
( ~ ( SV59 @ SY2469 )
| ( SY2468 = SY2469 ) ) ) )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4408]) ).
thf(4548,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ~ ( ~ ( SV59 @ ( sK114_SY2468 @ SV766 @ SV59 ) )
| ~ ! [SY4196: $i] :
( ~ ( SV59 @ SY4196 )
| ( ( sK114_SY2468 @ SV766 @ SV59 )
= SY4196 ) ) ) )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4409]) ).
thf(4549,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ~ ( ~ ( SV59 @ ( sK115_SY2468 @ SV766 @ SV59 ) )
| ~ ! [SY4197: $i] :
( ~ ( SV59 @ SY4197 )
| ( ( sK115_SY2468 @ SV766 @ SV59 )
= SY4197 ) ) ) )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4410]) ).
thf(4550,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ( ~ ( SV59 @ ( sK106_SY2468 @ SV766 @ SV59 ) )
| ~ ! [SY4184: $i] :
( ~ ( SV59 @ SY4184 )
| ( ( sK106_SY2468 @ SV766 @ SV59 )
= SY4184 ) ) ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4411]) ).
thf(4551,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ~ ( ~ ( SV60 @ ( sK107_SY2472 @ SV767 @ SV60 ) )
| ~ ! [SY4185: $i] :
( ~ ( SV60 @ SY4185 )
| ( ( sK107_SY2472 @ SV767 @ SV60 )
= SY4185 ) ) ) )
= $true )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV60 @ ( sK76_SY3951 @ SV767 @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4412]) ).
thf(4552,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ~ ( SV60 @ ( sK96_SY2472 @ SV767 @ SV60 ) )
| ~ ! [SY4172: $i] :
( ~ ( SV60 @ SY4172 )
| ( ( sK96_SY2472 @ SV767 @ SV60 )
= SY4172 ) ) )
= $false )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV767
= ( sK76_SY3951 @ SV767 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4413]) ).
thf(4553,plain,
! [SV773: $i,SV994: $i,SV382: $i,SV927: $i,SV78: $i] :
( ( ( ! [SY4151: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY4151 @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ SY4151 ) @ SV382 ) )
| ~ ( in @ ( kpair @ SY4151 @ SV994 ) @ SV773 ) ) )
= $false )
| ( ( in @ ( kpair @ SV927 @ SV994 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
= $false )
| ( ( in @ SV994 @ SV78 )
= $false )
| ( ( in @ SV927 @ SV78 )
= $false )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4416]) ).
thf(4554,plain,
! [SV82: $i,SV774: $i,SV386: $i,SV995: $i,SV928: $i] :
( ( ( in @ ( kpair @ SV928 @ SV995 ) @ SV386 )
= $true )
| ( ( in @ ( kpair @ SV928 @ SV995 ) @ SV774 )
= $true )
| ( ( in @ ( kpair @ SV928 @ SV995 ) @ ( binunion @ SV386 @ SV774 ) )
= $false )
| ( ( in @ SV995 @ SV82 )
= $false )
| ( ( in @ SV928 @ SV82 )
= $false )
| ( ( breln1 @ SV82 @ SV774 )
= $false )
| ( ( breln1 @ SV82 @ SV386 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4417]) ).
thf(4555,plain,
! [SV87: $i,SV777: $i,SV390: $i,SV930: $i] :
( ( ( in @ SV930 @ SV390 )
= $false )
| ( ( in @ SV930 @ SV777 )
= $true )
| ( ( subset @ SV390 @ SV777 )
= $false )
| ( ( in @ SV930 @ SV87 )
= $false )
| ( ( in @ SV777 @ ( powerset @ SV87 ) )
= $false )
| ( ( in @ SV390 @ ( powerset @ SV87 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4419]) ).
thf(4556,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK97_SY2565 @ SV781 @ SV100 ) )
| ~ ! [SY4173: $i] :
( ~ ( SV100 @ SY4173 )
| ( ( sK97_SY2565 @ SV781 @ SV100 )
= SY4173 ) ) )
= $false )
| ( ( SV100 @ ( sK53_SY2563 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4421]) ).
thf(4557,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ( ~ ( SV100 @ ( sK108_SY2565 @ SV781 @ SV100 ) )
| ~ ! [SY4186: $i] :
( ~ ( SV100 @ SY4186 )
| ( ( sK108_SY2565 @ SV781 @ SV100 )
= SY4186 ) ) ) )
= $true )
| ( ( SV100 @ ( sK61_SY4131 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4422]) ).
thf(4558,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK98_SY2565 @ SV781 @ SV100 ) )
| ~ ! [SY4174: $i] :
( ~ ( SV100 @ SY4174 )
| ( ( sK98_SY2565 @ SV781 @ SV100 )
= SY4174 ) ) )
= $false )
| ( ( ( sK53_SY2563 @ SV781 @ SV100 )
= ( sK61_SY4131 @ SV781 @ SV100 ) )
= $false )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4423]) ).
thf(4559,plain,
! [SV104: $i,SV404: $i > $o,SV862: $i] :
( ( ( in @ ( sK99_SY3324 @ SV862 @ SV404 @ SV104 ) @ SV104 )
= $true )
| ( ( in @ SV862 @ SV104 )
= $false )
| ( ( SV404 @ SV862 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4424]) ).
thf(4560,plain,
! [SV106: $i,SV1032: $i] :
( ( ( in @ SV1032 @ omega )
= $false )
| ( ( in @ SV1032 @ SV106 )
= $true )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( in @ ( sK44_SY2577 @ SV106 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4426]) ).
thf(4561,plain,
! [SV106: $i,SV1033: $i] :
( ( ( in @ SV1033 @ omega )
= $false )
| ( ( in @ SV1033 @ SV106 )
= $true )
| ( ( in @ emptyset @ SV106 )
= $false )
| ( ( in @ ( sK44_SY2577 @ SV106 ) @ SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4427]) ).
thf(4562,plain,
! [SV122: $i,SV420: $i,SV865: $i > $o,SV788: $i > $o] :
( ( ( ~ ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) )
| ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) ) )
= $false )
| ( ( ~ ( ~ ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
| ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4428]) ).
thf(4563,plain,
! [SV792: $i,SV998: $i,SV428: $i,SV939: $i,SV131: $i,SV1034: $i] :
( ( ( in @ SV1034 @ SV131 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV939 @ SV1034 ) @ SV428 )
| ~ ( in @ ( kpair @ SV1034 @ SV998 ) @ SV792 )
| ( in @ ( kpair @ SV939 @ SV998 ) @ ( breln1compset @ SV131 @ SV428 @ SV792 ) ) )
= $true )
| ( ( in @ SV998 @ SV131 )
= $false )
| ( ( in @ SV939 @ SV131 )
= $false )
| ( ( breln1 @ SV131 @ SV792 )
= $false )
| ( ( breln1 @ SV131 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4430]) ).
thf(4564,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( ~ ( in @ ( sK116_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SV140 )
| ! [SY4198: $i] :
( ~ ( in @ SY4198 @ SV436 )
| ~ ( in @ ( kpair @ ( sK116_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SY4198 ) @ SV870 )
| ( in @ ( kpair @ ( sK116_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SY4198 ) @ SV650 ) ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SV140 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4432]) ).
thf(4565,plain,
! [SV650: $i,SV870: $i,SV436: $i,SV140: $i] :
( ( ( ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) ) )
= $true )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) @ SV436 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4433]) ).
thf(4566,plain,
! [SV140: $i,SV436: $i,SV650: $i,SV870: $i] :
( ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV650 )
= $true )
| ( ( ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) )
| ( SV650 = SV870 ) )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4434]) ).
thf(4567,plain,
! [SV650: $i,SV870: $i,SV436: $i,SV140: $i] :
( ( ( ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) ) )
= $true )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4435]) ).
thf(4568,plain,
! [SV144: $i,SV440: $i,SV975: $i,SV654: $i > $i] :
( ( ( in @ ( sK100_SY4134 @ SV654 @ SV975 @ SV440 @ SV144 ) @ SV144 )
= $true )
| ( ( surjective @ SV440 @ SV144 @ SV975 )
= $true )
| ( ( in @ SV975 @ ( funcSet @ SV440 @ SV144 ) )
= $false )
| ( ( in @ ( sK26_SY3786 @ SV440 @ SV654 @ SV144 ) @ SV144 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4436]) ).
thf(4569,plain,
! [SV146: $i,SV999: $i,SV442: $i > $o] :
( ( ( SV442 @ SV999 )
= $false )
| ( ( in @ SV999 @ SV146 )
= $false )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( in @ ( sK11_SY3407 @ SV442 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4439]) ).
thf(4570,plain,
! [SV442: $i > $o,SV146: $i,SV1020: $i] :
( ( ( ~ ( in @ SV1020 @ SV146 ) )
= $true )
| ( ( ~ ( SV442 @ SV1020 ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( in @ ( sK38_SY3987 @ SV442 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4440]) ).
thf(4571,plain,
! [SV442: $i > $o,SV146: $i,SV1035: $i] :
( ( ( ~ ( in @ SV1035 @ SV146 )
| ~ ( SV442 @ SV1035 ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( SV442 @ ( sK11_SY3407 @ SV442 @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4441]) ).
thf(4572,plain,
! [SV442: $i > $o,SV146: $i,SV1051: $i] :
( ( ( ~ ( ~ ( in @ SV1051 @ SV146 )
| ~ ( SV442 @ SV1051 ) ) )
= $false )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( SV442 @ ( sK38_SY3987 @ SV442 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4442]) ).
thf(4573,plain,
! [SV442: $i > $o,SV146: $i,SV1036: $i] :
( ( ( ~ ( in @ SV1036 @ SV146 )
| ~ ( SV442 @ SV1036 ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( ( sK11_SY3407 @ SV442 @ SV146 )
= ( sK38_SY3987 @ SV442 @ SV146 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4443]) ).
thf(4574,plain,
! [SV448: $i > $o,SV1010: $i,SV152: $i > $o] :
( ( ( SV152 @ SV1010 )
= $false )
| ( ( ~ ! [SY4163: $i] :
( ~ ( SV152 @ SY4163 )
| ( SV1010 = SY4163 ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4445]) ).
thf(4575,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4446]) ).
thf(4576,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4447]) ).
thf(4577,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4448]) ).
thf(4578,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4449]) ).
thf(4579,plain,
! [SV168: $i,SV464: $i,SV666: $i,SV877: $i] :
( ( ( in @ ( kpair @ ( sK79_SY4066 @ SV877 @ SV666 @ SV464 @ SV168 ) @ ( sK92_SY4154 @ SV168 @ SV666 @ SV877 @ SV464 ) ) @ SV666 )
= $true )
| ( ( subset @ SV666 @ SV877 )
= $true )
| ( ( breln @ SV168 @ SV464 @ SV877 )
= $false )
| ( ( breln @ SV168 @ SV464 @ SV666 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4451]) ).
thf(4580,plain,
! [SV175: $i,SV976: $i,SV470: $i > $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK117_SY4135 @ SV470 @ SV976 @ SV175 ) @ SV175 )
| ( SV976
!= ( SV470 @ ( sK117_SY4135 @ SV470 @ SV976 @ SV175 ) ) ) ) )
= $false )
| ( ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4453]) ).
thf(4581,plain,
! [SV470: $i > $i,SV976: $i,SV175: $i,SV1060: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1060 @ SV175 )
| ( SV976
!= ( SV470 @ SV1060 ) ) ) )
= $true )
| ( ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4454]) ).
thf(4582,plain,
! [SV977: $i,SV175: $i,SV470: $i > $i] :
( ( ( ~ ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) )
| ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 ) ) )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4455]) ).
thf(4583,plain,
! [SV977: $i,SV470: $i > $i,SV175: $i] :
( ( ( ~ ! [SY4164: $i] :
~ ~ ( ~ ( in @ SY4164 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4164 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) )
| ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 ) ) )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4455]) ).
thf(4584,plain,
! [SV978: $i,SV670: $i > $i > $o,SV475: $i,SV180: $i,SV1037: $i] :
( ( ( in @ SV1037 @ SV180 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY4175: $i] :
~ ( ~ ( SV670 @ SV1037 @ SY4175 )
| ~ ! [SY4176: $i] :
( ~ ( in @ SY4176 @ SV475 )
| ~ ( SV670 @ SV1037 @ SY4176 )
| ( in @ ( kpair @ SY4175 @ SY4176 ) @ SV978 ) ) ) ) )
= $true )
| ( ( reflwellordering @ SV475 @ SV978 )
= $false )
| ( ( in @ SV978 @ ( breln1Set @ SV475 ) )
= $false )
| ( ( in @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4456]) ).
thf(4585,plain,
! [SV979: $i,SV670: $i > $i > $o,SV180: $i,SV475: $i,SV1052: $i] :
( ( ( ~ ( in @ SV1052 @ ( breln1Set @ SV475 ) ) )
= $true )
| ( ( ~ ( reflwellordering @ SV475 @ SV1052 )
| ! [SY4187: $i] :
( ~ ( in @ SY4187 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY4188: $i] :
~ ( ~ ( SV670 @ SY4187 @ SY4188 )
| ~ ! [SY4189: $i] :
( ~ ( in @ SY4189 @ SV475 )
| ~ ( SV670 @ SY4187 @ SY4189 )
| ( in @ ( kpair @ SY4188 @ SY4189 ) @ SV1052 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV979 @ SV475 )
= $false )
| ( ( SV670 @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV979 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4457]) ).
thf(4586,plain,
! [SV193: $i,SV881: $i,SV488: $i > $i] :
( ( ( ~ ( in @ ( sK93_SY4070 @ SV488 @ SV881 @ SV193 ) @ SV193 ) )
= $false )
| ( ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4459]) ).
thf(4587,plain,
! [SV193: $i,SV488: $i > $i,SV881: $i] :
( ( ( SV881
!= ( SV488 @ ( sK93_SY4070 @ SV488 @ SV881 @ SV193 ) ) )
= $false )
| ( ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4459]) ).
thf(4588,plain,
! [SV488: $i > $i,SV881: $i,SV193: $i,SV1021: $i] :
( ( ( ~ ( in @ SV1021 @ SV193 ) )
= $true )
| ( ( SV881
!= ( SV488 @ SV1021 ) )
= $true )
| ( ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4460]) ).
thf(4589,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ~ ( ~ ( SV196 @ ( sK109_SY2855 @ SV816 @ SV196 ) )
| ~ ! [SY4190: $i] :
( ~ ( SV196 @ SY4190 )
| ( ( sK109_SY2855 @ SV816 @ SV196 )
= SY4190 ) ) ) )
= $true )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV196 @ ( sK80_SY4002 @ SV816 @ SV196 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4461]) ).
thf(4590,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ ( sK101_SY2855 @ SV816 @ SV196 ) )
| ~ ! [SY4177: $i] :
( ~ ( SV196 @ SY4177 )
| ( ( sK101_SY2855 @ SV816 @ SV196 )
= SY4177 ) ) )
= $false )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV816
= ( sK80_SY4002 @ SV816 @ SV196 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4462]) ).
thf(4591,plain,
! [SV491: $i > $o,SV1053: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ SV1053 )
| ~ ! [SY4191: $i] :
( ~ ( SV197 @ SY4191 )
| ( SV1053 = SY4191 ) ) ) )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4463]) ).
thf(4592,plain,
! [SV197: $i > $o,SV1054: $i,SV491: $i > $o] :
( ( ( ~ ( ~ ( SV491 @ SV1054 )
| ~ ! [SY4192: $i] :
( ~ ( SV491 @ SY4192 )
| ( SV1054 = SY4192 ) ) ) )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4464]) ).
thf(4593,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
| ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4465]) ).
thf(4594,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4466]) ).
thf(4595,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4466]) ).
thf(4596,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4467]) ).
thf(4597,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4467]) ).
thf(4598,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4468]) ).
thf(4599,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4469]) ).
thf(4600,plain,
! [SV492: $i,SV679: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK94_SY4093 @ SV199 @ SV679 @ SV492 ) @ SV492 ) )
= $false )
| ( ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4470]) ).
thf(4601,plain,
! [SV199: $i,SV492: $i,SV679: $i] :
( ( ( SV679
!= ( kpair @ ( sK39_SY3820 @ SV679 @ SV492 @ SV199 ) @ ( sK94_SY4093 @ SV199 @ SV679 @ SV492 ) ) )
= $false )
| ( ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4470]) ).
thf(4602,plain,
! [SV496: $i,SV885: $o,SV203: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV203 ) )
= $true )
| ( SV885 = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4473]) ).
thf(4603,plain,
! [SV203: $i,SV885: $o,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 ) )
= $false )
| ( SV885 = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4474]) ).
thf(4604,plain,
! [SV203: $i,SV496: $i,SV683: $i,SV885: $o] :
( ( SV885 = $false )
| ( SV885 = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4474]) ).
thf(4605,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV203 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4479]) ).
thf(4606,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4480]) ).
thf(4607,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4480]) ).
thf(4608,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV203 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4485]) ).
thf(4609,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV496 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4486]) ).
thf(4610,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4486]) ).
thf(4611,plain,
! [SV208: $i,SV952: $o,SV818: $i,SV501: $i,SV982: $i] :
( ( ( ~ ( in @ SV982 @ SV501 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV982 @ SV818 )
| SV952 )
| SV952 )
= $true )
| ( ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV982 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4491]) ).
thf(4612,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV982: $i,SV952: $o] :
( ( SV952 = $false )
| ( ( ~ ( ~ ( in @ SV982 @ SV818 )
| SV952 )
| SV952 )
= $true )
| ( ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV982 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4491]) ).
thf(4613,plain,
! [SV208: $i,SV818: $i,SV501: $i,SV983: $i] :
( ( ( ~ ( in @ SV983 @ SV501 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV983 @ SV818 )
| $true )
| $true )
= $true )
| ( ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV983 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4492]) ).
thf(4614,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV983: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV983 @ SV818 )
| $true )
| $true )
= $true )
| ( ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV983 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4492]) ).
thf(4615,plain,
! [SV208: $i,SV818: $i,SV501: $i,SV984: $i] :
( ( ( ~ ( in @ SV984 @ SV501 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV984 @ SV818 )
| $false )
| $false )
= $true )
| ( ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV984 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4493]) ).
thf(4616,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV984: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV984 @ SV818 )
| $false )
| $false )
= $true )
| ( ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV984 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4493]) ).
thf(4617,plain,
! [SV502: $i,SV209: $i,SV889: $i > $o,SV689: $i,SV1038: $i] :
( ( ( in @ SV1038 @ SV689 )
= $false )
| ( ( SV889 @ SV1038 )
= $true )
| ( ( in @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) @ SV502 )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4494]) ).
thf(4618,plain,
! [SV209: $i,SV502: $i,SV889: $i > $o,SV689: $i,SV1055: $i] :
( ( ( ~ ( in @ SV1055 @ SV689 ) )
= $true )
| ( ( SV889 @ SV1055 )
= $true )
| ( ( in @ ( kpair @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) ) @ SV689 )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4495]) ).
thf(4619,plain,
! [SV209: $i,SV502: $i,SV889: $i > $o,SV689: $i,SV1039: $i] :
( ( ( in @ SV1039 @ SV689 )
= $false )
| ( ( SV889 @ SV1039 )
= $true )
| ( ( SV889 @ ( kpair @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) ) )
= $false )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4496]) ).
thf(4620,plain,
! [SV216: $i,SV819: $i,SV1061: $o,SV508: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
| SV1061 )
| ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| SV1061 )
| SV1061 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[4497]) ).
thf(4621,plain,
! [SV216: $i,SV819: $i,SV508: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
| $true )
| ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $true )
| $true )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[4497]) ).
thf(4622,plain,
! [SV216: $i,SV819: $i,SV508: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
| $false )
| ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $false )
| $false )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[4497]) ).
thf(4623,plain,
! [SV226: $i,SV1040: $i] :
( ( ( in @ SV1040 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( ! [SY4178: $i] :
( ~ ( in @ SY4178 @ SV1040 )
| ( in @ SY4178 @ SV226 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4498]) ).
thf(4624,plain,
! [SV1056: $i,SV226: $i,SV1041: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1041 @ SV226 )
| ~ ( in @ SV1056 @ SV226 ) ) )
= $true )
| ( ( ~ ! [SY4193: $i] :
( ~ ( in @ SY4193 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SV1041 @ SY4193 )
| ( in @ SV1056 @ SY4193 ) )
| ~ ( ~ ( in @ SV1056 @ SY4193 )
| ( in @ SV1041 @ SY4193 ) ) ) )
| ( SV1041 = SV1056 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4499]) ).
thf(4625,plain,
! [SV1014: $i,SV226: $i,SV1002: $i] :
( ( ( ~ ( in @ SV1002 @ ( sK2_SY2943 @ SV226 ) ) )
= $true )
| ( ( ~ ( in @ SV1014 @ ( sK2_SY2943 @ SV226 ) ) )
= $true )
| ( ( ! [SY4166: $i] :
( ~ ( in @ SY4166 @ SV1002 )
| ( in @ SY4166 @ SV1014 ) )
| ! [SY4167: $i] :
( ~ ( in @ SY4167 @ SV1014 )
| ( in @ SY4167 @ SV1002 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4500]) ).
thf(4626,plain,
! [SV955: $i,SV226: $i] :
( ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( ~ ~ ! [SY4115: $i] :
~ ( in @ SY4115 @ SV955 ) )
= $true )
| ( ( ~ ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4501]) ).
thf(4627,plain,
! [SV226: $i,SV955: $i] :
( ( ( ~ ! [SY4115: $i] :
~ ( in @ SY4115 @ SV955 ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( ~ ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4502]) ).
thf(4628,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1003: $i] :
( ( ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
= $false )
| ( ( ~ ! [SY4159: $i] :
~ ~ ( ~ ( in @ SY4159 @ SV520 )
| ~ ( SV230 @ SY4159 @ SV1003 ) ) )
= $true )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4503]) ).
thf(4629,plain,
! [SV1003: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ~ ! [SY4160: $i] :
~ ~ ( ~ ( in @ SY4160 @ SV520 )
| ~ ( SV230 @ SY4160 @ SV1003 ) ) )
= $false )
| ( ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
= $true )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4504]) ).
thf(4630,plain,
! [SV957: $i,SV520: $i,SV230: $i > $i > $o] :
( ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( ~ ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4505]) ).
thf(4631,plain,
! [SV957: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4506]) ).
thf(4632,plain,
! [SV233: $i,SV823: $i > $o,SV523: $i,SV1042: $i] :
( ( ( in @ SV1042 @ SV523 )
= $false )
| ( ( SV823 @ SV1042 )
= $true )
| ( ( in @ ( kpair @ ( sK49_SY4014 @ SV823 @ SV523 @ SV233 ) @ ( sK66_SY4122 @ SV523 @ SV823 @ SV233 ) ) @ SV523 )
= $true )
| ( ( breln1 @ SV233 @ SV523 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4508]) ).
thf(4633,plain,
! [SV251: $i,SV538: $i,SV828: $i,SV960: $i] :
( ( ( in @ SV960 @ SV828 )
= $true )
| ( ( ~ ( in @ SV960 @ ( binunion @ SV538 @ SV828 ) ) )
= $true )
| ( ( in @ SV960 @ SV538 )
= $true )
| ( ( in @ SV960 @ SV251 )
= $false )
| ( ( in @ SV828 @ ( powerset @ SV251 ) )
= $false )
| ( ( in @ SV538 @ ( powerset @ SV251 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4510]) ).
thf(4634,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( ~ ( in @ ( sK110_SY4022 @ SV549 @ SV829 @ SV260 ) @ SV260 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4511]) ).
thf(4635,plain,
! [SV829: $i,SV549: $i,SV260: $i] :
( ( ( ! [SY4194: $i] :
( ~ ( in @ SY4194 @ SV260 )
| ~ ( in @ ( kpair @ ( sK110_SY4022 @ SV549 @ SV829 @ SV260 ) @ SY4194 ) @ SV829 )
| ( in @ ( kpair @ ( sK110_SY4022 @ SV549 @ SV829 @ SV260 ) @ SY4194 ) @ SV549 ) ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4511]) ).
thf(4636,plain,
! [SV549: $i,SV829: $i,SV260: $i] :
( ( ( ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4512]) ).
thf(4637,plain,
! [SV549: $i,SV829: $i,SV260: $i] :
( ( ( ~ ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) ) )
= $true )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV549 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4513]) ).
thf(4638,plain,
! [SV549: $i,SV829: $i,SV260: $i] :
( ( ( ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4514]) ).
thf(4639,plain,
! [SV264: $i,SV830: $i,SV553: $i,SV1005: $i,SV961: $i] :
( ( ( in @ ( kpair @ SV961 @ SV1005 ) @ SV553 )
= $false )
| ( ( in @ ( kpair @ SV961 @ SV1005 ) @ ( binunion @ SV553 @ SV830 ) )
= $true )
| ( ( in @ SV1005 @ SV264 )
= $false )
| ( ( in @ SV961 @ SV264 )
= $false )
| ( ( breln1 @ SV264 @ SV830 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4515]) ).
thf(4640,plain,
! [SV264: $i,SV553: $i,SV830: $i,SV1005: $i,SV961: $i] :
( ( ( in @ ( kpair @ SV961 @ SV1005 ) @ SV830 )
= $false )
| ( ( in @ ( kpair @ SV961 @ SV1005 ) @ ( binunion @ SV553 @ SV830 ) )
= $true )
| ( ( in @ SV1005 @ SV264 )
= $false )
| ( ( in @ SV961 @ SV264 )
= $false )
| ( ( breln1 @ SV264 @ SV830 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4515]) ).
thf(4641,plain,
! [SV271: $i,SV833: $i > $o,SV559: $i,SV1043: $i] :
( ( ( in @ SV1043 @ SV559 )
= $false )
| ( ( SV833 @ SV1043 )
= $true )
| ( ( in @ ( kpair @ ( sK50_SY4026 @ SV833 @ SV559 @ SV271 ) @ ( sK68_SY4124 @ SV559 @ SV833 @ SV271 ) ) @ SV559 )
= $true )
| ( ( breln1 @ SV271 @ SV559 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4517]) ).
thf(4642,plain,
! [SV1062: $o,SV836: $i,SV1007: $i,SV568: $i,SV963: $i,SV280: $i] :
( ( ( ~ ! [SY4199: $i] :
( ~ ( in @ SY4199 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SY4199 ) @ SV568 )
| ~ ( in @ ( kpair @ SY4199 @ SV1007 ) @ SV836 )
| SV1062 )
| SV1062 )
= $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[4521]) ).
thf(4643,plain,
! [SV836: $i,SV1007: $i,SV568: $i,SV963: $i,SV280: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SX0 ) @ SV568 )
| ~ ( in @ ( kpair @ SX0 @ SV1007 ) @ SV836 )
| $true )
| $true )
= $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[4521]) ).
thf(4644,plain,
! [SV836: $i,SV1007: $i,SV568: $i,SV963: $i,SV280: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SX0 ) @ SV568 )
| ~ ( in @ ( kpair @ SX0 @ SV1007 ) @ SV836 )
| $false )
| $false )
= $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[4521]) ).
thf(4645,plain,
! [SV837: $i,SV1057: $i,SV1044: $i,SV288: $i > $o] :
( ( ( ~ ( SV288 @ SV1044 ) )
= $true )
| ( ( ~ ( SV288 @ SV1057 )
| ( SV1044 = SV1057 ) )
= $true )
| ( ( SV288 @ SV837 )
= $false )
| ( ( SV288 @ ( sK83_SY4034 @ SV837 @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4522]) ).
thf(4646,plain,
! [SV837: $i,SV1045: $i,SV1026: $i,SV288: $i > $o] :
( ( ( SV288 @ SV1026 )
= $false )
| ( ( ~ ( SV288 @ SV1045 )
| ( SV1026 = SV1045 ) )
= $true )
| ( ( SV288 @ SV837 )
= $false )
| ( ( SV837
= ( sK83_SY4034 @ SV837 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4523]) ).
thf(4647,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( ~ ( in @ ( sK111_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV299 ) )
= $false )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV299 )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4526]) ).
thf(4648,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( ~ ( in @ ( sK111_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV840 )
| ( in @ ( sK111_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV584 ) )
= $false )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV299 )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4526]) ).
thf(4649,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( ~ ( in @ ( sK118_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV299 )
| ~ ( in @ ( sK118_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV840 )
| ( in @ ( sK118_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV584 ) )
= $false )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV584 )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4527]) ).
thf(4650,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( ~ ( in @ ( sK112_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV299 ) )
= $false )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV840 )
= $false )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4528]) ).
thf(4651,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( ~ ( in @ ( sK112_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV840 )
| ( in @ ( sK112_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV584 ) )
= $false )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV840 )
= $false )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4528]) ).
thf(4652,plain,
! [SV734: $i,SV911: $i,SV586: $i,SV301: $i,SV1046: $i] :
( ( ( in @ SV1046 @ SV301 )
= $false )
| ( ( ! [SY4182: $i] :
( ~ ( in @ SY4182 @ SV586 )
| ~ ( in @ ( kpair @ SV1046 @ SY4182 ) @ SV911 )
| ( in @ ( kpair @ SV1046 @ SY4182 ) @ SV734 ) ) )
= $true )
| ( ( in @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) @ SV301 )
= $true )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4530]) ).
thf(4653,plain,
! [SV301: $i,SV734: $i,SV911: $i,SV1027: $i,SV586: $i,SV1063: $i] :
( ( ( ~ ( in @ SV1063 @ SV586 )
| ~ ( in @ ( kpair @ SV1027 @ SV1063 ) @ SV911 )
| ( in @ ( kpair @ SV1027 @ SV1063 ) @ SV734 ) )
= $true )
| ( ( in @ SV1027 @ SV301 )
= $false )
| ( ( ( ap @ SV301 @ SV586 @ SV734 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) )
= ( ap @ SV301 @ SV586 @ SV911 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) ) )
= $false )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4531]) ).
thf(4654,plain,
! [SV848: $i,SV316: $i > $o] :
( ( ( ! [SY4195: $i] :
~ ( ~ ( ~ ( SV316 @ SY4195 )
| ( SY4195
= ( sK113_SY3190 @ SV848 @ SV316 ) ) )
| ~ ( ( SY4195
!= ( sK113_SY3190 @ SV848 @ SV316 ) )
| ( SV316 @ SY4195 ) ) ) )
= $true )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV316 @ ( sK85_SY4045 @ SV848 @ SV316 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4532]) ).
thf(4655,plain,
! [SV848: $i,SV1064: $i,SV316: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV316 @ SV1064 )
| ( SV1064
= ( sK104_SY3190 @ SV848 @ SV316 ) ) )
| ~ ( ( SV1064
!= ( sK104_SY3190 @ SV848 @ SV316 ) )
| ( SV316 @ SV1064 ) ) ) )
= $true )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV848
= ( sK85_SY4045 @ SV848 @ SV316 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4533]) ).
thf(4656,plain,
! [SV317: $i,SV970: $i,SV599: $i,SV1009: $i,SV849: $i] :
( ( ( ~ ( subset @ SV849 @ SV1009 ) )
= $true )
| ( ( subset @ ( binintersect @ SV599 @ SV849 ) @ ( binintersect @ SV970 @ SV1009 ) )
= $true )
| ( ( subset @ SV599 @ SV970 )
= $false )
| ( ( in @ SV1009 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV970 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV849 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4534]) ).
thf(4657,plain,
! [SV601: $i,SV319: $i,SV914: $i > $o,SV738: $i,SV1047: $i] :
( ( ( in @ SV1047 @ SV738 )
= $false )
| ( ( SV914 @ SV1047 )
= $true )
| ( ( in @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) @ SV601 )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4535]) ).
thf(4658,plain,
! [SV319: $i,SV601: $i,SV914: $i > $o,SV738: $i,SV1058: $i] :
( ( ( ~ ( in @ SV1058 @ SV738 ) )
= $true )
| ( ( SV914 @ SV1058 )
= $true )
| ( ( in @ ( kpair @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) ) @ SV738 )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4536]) ).
thf(4659,plain,
! [SV319: $i,SV601: $i,SV914: $i > $o,SV738: $i,SV1048: $i] :
( ( ( in @ SV1048 @ SV738 )
= $false )
| ( ( SV914 @ SV1048 )
= $true )
| ( ( SV914 @ ( kpair @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) ) )
= $false )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4537]) ).
thf(4660,plain,
! [SV322: $i,SV851: $i,SV1059: $i] :
( ( ( ~ ( ~ ( in @ SV1059 @ ( sK51_SY3211 @ SV851 @ SV322 ) )
| ~ ( in @ SV1059 @ SV322 ) ) )
= $false )
| ( ( in @ SV851 @ SV322 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4538]) ).
thf(4661,plain,
! [SV353: $i > $o,SV44: $i,SV1018: $i] :
( ( ( in @ SV1018 @ SV44 )
= $false )
| ( ( ~ ( SV353 @ SV1018 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( in @ ( sK36_SY3943 @ SV353 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4541]) ).
thf(4662,plain,
! [SV353: $i > $o,SV44: $i,SV1028: $i] :
( ( ( ~ ( in @ SV1028 @ SV44 ) )
= $true )
| ( ( ~ ( SV353 @ SV1028 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( SV353 @ ( sK9_SY3238 @ SV353 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4542]) ).
thf(4663,plain,
! [SV353: $i > $o,SV44: $i,SV1049: $i] :
( ( ( ~ ( in @ SV1049 @ SV44 )
| ~ ( SV353 @ SV1049 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( SV353 @ ( sK36_SY3943 @ SV353 @ SV44 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4543]) ).
thf(4664,plain,
! [SV353: $i > $o,SV44: $i,SV1029: $i] :
( ( ( ~ ( in @ SV1029 @ SV44 ) )
= $true )
| ( ( ~ ( SV353 @ SV1029 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( ( sK9_SY3238 @ SV353 @ SV44 )
= ( sK36_SY3943 @ SV353 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4544]) ).
thf(4665,plain,
! [SV765: $i,SV1050: $i,SV1030: $i,SV58: $i > $o] :
( ( ( SV58 @ SV1030 )
= $false )
| ( ( ~ ( SV58 @ SV1050 )
| ( SV1030 = SV1050 ) )
= $true )
| ( ( SV58 @ SV765 )
= $false )
| ( ( SV58 @ ( sK75_SY3949 @ SV765 @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4545]) ).
thf(4666,plain,
! [SV765: $i,SV1019: $i,SV1031: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV1031 ) )
= $true )
| ( ( SV1019 = SV1031 )
= $true )
| ( ( SV58 @ SV1019 )
= $false )
| ( ( SV58 @ SV765 )
= $false )
| ( ( SV765
= ( sK75_SY3949 @ SV765 @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4546]) ).
thf(4667,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ~ ( ~ ( SV59 @ ( sK119_SY2468 @ SV766 @ SV59 ) )
| ~ ! [SY4200: $i] :
( ~ ( SV59 @ SY4200 )
| ( ( sK119_SY2468 @ SV766 @ SV59 )
= SY4200 ) ) ) )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4547]) ).
thf(4668,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ( ~ ( SV59 @ ( sK114_SY2468 @ SV766 @ SV59 ) )
| ~ ! [SY4196: $i] :
( ~ ( SV59 @ SY4196 )
| ( ( sK114_SY2468 @ SV766 @ SV59 )
= SY4196 ) ) ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4548]) ).
thf(4669,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ( ~ ( SV59 @ ( sK115_SY2468 @ SV766 @ SV59 ) )
| ~ ! [SY4197: $i] :
( ~ ( SV59 @ SY4197 )
| ( ( sK115_SY2468 @ SV766 @ SV59 )
= SY4197 ) ) ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4549]) ).
thf(4670,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ ( sK106_SY2468 @ SV766 @ SV59 ) )
| ~ ! [SY4184: $i] :
( ~ ( SV59 @ SY4184 )
| ( ( sK106_SY2468 @ SV766 @ SV59 )
= SY4184 ) ) )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4550]) ).
thf(4671,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ~ ( SV60 @ ( sK107_SY2472 @ SV767 @ SV60 ) )
| ~ ! [SY4185: $i] :
( ~ ( SV60 @ SY4185 )
| ( ( sK107_SY2472 @ SV767 @ SV60 )
= SY4185 ) ) )
= $false )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV60 @ ( sK76_SY3951 @ SV767 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4551]) ).
thf(4672,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ~ ( SV60 @ ( sK96_SY2472 @ SV767 @ SV60 ) ) )
= $false )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV767
= ( sK76_SY3951 @ SV767 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4552]) ).
thf(4673,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ~ ! [SY4172: $i] :
( ~ ( SV60 @ SY4172 )
| ( ( sK96_SY2472 @ SV767 @ SV60 )
= SY4172 ) ) )
= $false )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV767
= ( sK76_SY3951 @ SV767 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4552]) ).
thf(4674,plain,
! [SV78: $i,SV927: $i,SV382: $i,SV994: $i,SV773: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) ) @ SV382 ) )
| ~ ( in @ ( kpair @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) @ SV994 ) @ SV773 ) ) )
= $false )
| ( ( in @ ( kpair @ SV927 @ SV994 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
= $false )
| ( ( in @ SV994 @ SV78 )
= $false )
| ( ( in @ SV927 @ SV78 )
= $false )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4553]) ).
thf(4675,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK97_SY2565 @ SV781 @ SV100 ) ) )
= $false )
| ( ( SV100 @ ( sK53_SY2563 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4556]) ).
thf(4676,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ! [SY4173: $i] :
( ~ ( SV100 @ SY4173 )
| ( ( sK97_SY2565 @ SV781 @ SV100 )
= SY4173 ) ) )
= $false )
| ( ( SV100 @ ( sK53_SY2563 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4556]) ).
thf(4677,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK108_SY2565 @ SV781 @ SV100 ) )
| ~ ! [SY4186: $i] :
( ~ ( SV100 @ SY4186 )
| ( ( sK108_SY2565 @ SV781 @ SV100 )
= SY4186 ) ) )
= $false )
| ( ( SV100 @ ( sK61_SY4131 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4557]) ).
thf(4678,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK98_SY2565 @ SV781 @ SV100 ) ) )
= $false )
| ( ( ( sK53_SY2563 @ SV781 @ SV100 )
= ( sK61_SY4131 @ SV781 @ SV100 ) )
= $false )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4558]) ).
thf(4679,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ! [SY4174: $i] :
( ~ ( SV100 @ SY4174 )
| ( ( sK98_SY2565 @ SV781 @ SV100 )
= SY4174 ) ) )
= $false )
| ( ( ( sK53_SY2563 @ SV781 @ SV100 )
= ( sK61_SY4131 @ SV781 @ SV100 ) )
= $false )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4558]) ).
thf(4680,plain,
! [SV122: $i,SV420: $i,SV865: $i > $o,SV788: $i > $o] :
( ( ( ~ ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) ) )
= $false )
| ( ( ~ ( ~ ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
| ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4562]) ).
thf(4681,plain,
! [SV420: $i,SV788: $i > $o,SV122: $i,SV865: $i > $o] :
( ( ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
= $false )
| ( ( ~ ( ~ ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
| ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4562]) ).
thf(4682,plain,
! [SV131: $i,SV792: $i,SV998: $i,SV428: $i,SV1034: $i,SV939: $i] :
( ( ( ~ ( in @ ( kpair @ SV939 @ SV1034 ) @ SV428 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV1034 @ SV998 ) @ SV792 )
| ( in @ ( kpair @ SV939 @ SV998 ) @ ( breln1compset @ SV131 @ SV428 @ SV792 ) ) )
= $true )
| ( ( in @ SV1034 @ SV131 )
= $false )
| ( ( in @ SV998 @ SV131 )
= $false )
| ( ( in @ SV939 @ SV131 )
= $false )
| ( ( breln1 @ SV131 @ SV792 )
= $false )
| ( ( breln1 @ SV131 @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4563]) ).
thf(4683,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( ~ ( in @ ( sK116_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SV140 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SV140 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4564]) ).
thf(4684,plain,
! [SV140: $i,SV870: $i,SV650: $i,SV436: $i] :
( ( ( ! [SY4198: $i] :
( ~ ( in @ SY4198 @ SV436 )
| ~ ( in @ ( kpair @ ( sK116_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SY4198 ) @ SV870 )
| ( in @ ( kpair @ ( sK116_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SY4198 ) @ SV650 ) ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SV140 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4564]) ).
thf(4685,plain,
! [SV650: $i,SV870: $i,SV436: $i,SV140: $i] :
( ( ( ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) @ SV436 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4565]) ).
thf(4686,plain,
! [SV650: $i,SV870: $i,SV436: $i,SV140: $i] :
( ( ( ~ ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) ) )
= $true )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV650 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4566]) ).
thf(4687,plain,
! [SV650: $i,SV870: $i,SV436: $i,SV140: $i] :
( ( ( ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4567]) ).
thf(4688,plain,
! [SV442: $i > $o,SV146: $i,SV1020: $i] :
( ( ( in @ SV1020 @ SV146 )
= $false )
| ( ( ~ ( SV442 @ SV1020 ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( in @ ( sK38_SY3987 @ SV442 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4570]) ).
thf(4689,plain,
! [SV442: $i > $o,SV146: $i,SV1035: $i] :
( ( ( ~ ( in @ SV1035 @ SV146 ) )
= $true )
| ( ( ~ ( SV442 @ SV1035 ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( SV442 @ ( sK11_SY3407 @ SV442 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4571]) ).
thf(4690,plain,
! [SV442: $i > $o,SV146: $i,SV1051: $i] :
( ( ( ~ ( in @ SV1051 @ SV146 )
| ~ ( SV442 @ SV1051 ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( SV442 @ ( sK38_SY3987 @ SV442 @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4572]) ).
thf(4691,plain,
! [SV442: $i > $o,SV146: $i,SV1036: $i] :
( ( ( ~ ( in @ SV1036 @ SV146 ) )
= $true )
| ( ( ~ ( SV442 @ SV1036 ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( ( sK11_SY3407 @ SV442 @ SV146 )
= ( sK38_SY3987 @ SV442 @ SV146 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4573]) ).
thf(4692,plain,
! [SV448: $i > $o,SV1010: $i,SV152: $i > $o] :
( ( ( ! [SY4163: $i] :
( ~ ( SV152 @ SY4163 )
| ( SV1010 = SY4163 ) ) )
= $false )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4574]) ).
thf(4693,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4575]) ).
thf(4694,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4576]) ).
thf(4695,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4577]) ).
thf(4696,plain,
! [SV448: $i > $o,SV1065: $i,SV152: $i > $o] :
( ( ( ~ ~ ( ~ ( SV152 @ SV1065 )
| ~ ! [SY4201: $i] :
( ~ ( SV152 @ SY4201 )
| ( SV1065 = SY4201 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4578]) ).
thf(4697,plain,
! [SV175: $i,SV976: $i,SV470: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK117_SY4135 @ SV470 @ SV976 @ SV175 ) @ SV175 )
| ( SV976
!= ( SV470 @ ( sK117_SY4135 @ SV470 @ SV976 @ SV175 ) ) ) ) )
= $true )
| ( ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4580]) ).
thf(4698,plain,
! [SV470: $i > $i,SV976: $i,SV175: $i,SV1060: $i] :
( ( ( ~ ( ~ ( in @ SV1060 @ SV175 )
| ( SV976
!= ( SV470 @ SV1060 ) ) ) )
= $false )
| ( ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4581]) ).
thf(4699,plain,
! [SV977: $i,SV175: $i,SV470: $i > $i] :
( ( ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
= $true )
| ( ( ~ ( ~ ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) )
| ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 ) ) )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4582]) ).
thf(4700,plain,
! [SV977: $i,SV470: $i > $i,SV175: $i] :
( ( ( ! [SY4164: $i] :
~ ~ ( ~ ( in @ SY4164 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4164 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) )
| ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 ) ) )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4583]) ).
thf(4701,plain,
! [SV979: $i,SV670: $i > $i > $o,SV180: $i,SV475: $i,SV1052: $i] :
( ( ( in @ SV1052 @ ( breln1Set @ SV475 ) )
= $false )
| ( ( ~ ( reflwellordering @ SV475 @ SV1052 )
| ! [SY4187: $i] :
( ~ ( in @ SY4187 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY4188: $i] :
~ ( ~ ( SV670 @ SY4187 @ SY4188 )
| ~ ! [SY4189: $i] :
( ~ ( in @ SY4189 @ SV475 )
| ~ ( SV670 @ SY4187 @ SY4189 )
| ( in @ ( kpair @ SY4188 @ SY4189 ) @ SV1052 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV979 @ SV475 )
= $false )
| ( ( SV670 @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV979 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4585]) ).
thf(4702,plain,
! [SV193: $i,SV881: $i,SV488: $i > $i] :
( ( ( in @ ( sK93_SY4070 @ SV488 @ SV881 @ SV193 ) @ SV193 )
= $true )
| ( ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4586]) ).
thf(4703,plain,
! [SV193: $i,SV488: $i > $i,SV881: $i] :
( ( ( SV881
= ( SV488 @ ( sK93_SY4070 @ SV488 @ SV881 @ SV193 ) ) )
= $true )
| ( ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4587]) ).
thf(4704,plain,
! [SV488: $i > $i,SV881: $i,SV193: $i,SV1021: $i] :
( ( ( in @ SV1021 @ SV193 )
= $false )
| ( ( SV881
!= ( SV488 @ SV1021 ) )
= $true )
| ( ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4588]) ).
thf(4705,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ ( sK109_SY2855 @ SV816 @ SV196 ) )
| ~ ! [SY4190: $i] :
( ~ ( SV196 @ SY4190 )
| ( ( sK109_SY2855 @ SV816 @ SV196 )
= SY4190 ) ) )
= $false )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV196 @ ( sK80_SY4002 @ SV816 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4589]) ).
thf(4706,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ ( sK101_SY2855 @ SV816 @ SV196 ) ) )
= $false )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV816
= ( sK80_SY4002 @ SV816 @ SV196 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4590]) ).
thf(4707,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ~ ! [SY4177: $i] :
( ~ ( SV196 @ SY4177 )
| ( ( sK101_SY2855 @ SV816 @ SV196 )
= SY4177 ) ) )
= $false )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV816
= ( sK80_SY4002 @ SV816 @ SV196 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4590]) ).
thf(4708,plain,
! [SV491: $i > $o,SV1053: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1053 )
| ~ ! [SY4191: $i] :
( ~ ( SV197 @ SY4191 )
| ( SV1053 = SY4191 ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4591]) ).
thf(4709,plain,
! [SV197: $i > $o,SV1054: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1054 )
| ~ ! [SY4192: $i] :
( ~ ( SV491 @ SY4192 )
| ( SV1054 = SY4192 ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4592]) ).
thf(4710,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4593]) ).
thf(4711,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4593]) ).
thf(4712,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4594]) ).
thf(4713,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4595]) ).
thf(4714,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4596]) ).
thf(4715,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4597]) ).
thf(4716,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4598]) ).
thf(4717,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4599]) ).
thf(4718,plain,
! [SV492: $i,SV679: $i,SV199: $i] :
( ( ( in @ ( sK94_SY4093 @ SV199 @ SV679 @ SV492 ) @ SV492 )
= $true )
| ( ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4600]) ).
thf(4719,plain,
! [SV199: $i,SV492: $i,SV679: $i] :
( ( ( SV679
= ( kpair @ ( sK39_SY3820 @ SV679 @ SV492 @ SV199 ) @ ( sK94_SY4093 @ SV199 @ SV679 @ SV492 ) ) )
= $true )
| ( ( in @ SV679 @ ( cartprod @ SV199 @ SV492 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4601]) ).
thf(4720,plain,
! [SV496: $i,SV885: $o,SV203: $i,SV683: $i] :
( ( ( in @ SV683 @ SV203 )
= $false )
| ( SV885 = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4602]) ).
thf(4721,plain,
! [SV203: $i,SV885: $o,SV496: $i,SV683: $i] :
( ( ( in @ SV683 @ SV496 )
= $true )
| ( SV885 = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4603]) ).
thf(4722,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( in @ SV683 @ SV203 )
= $false )
| ( $true = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4605]) ).
thf(4723,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( in @ SV683 @ SV496 )
= $true )
| ( $true = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4606]) ).
thf(4724,plain,
! [SV496: $i,SV203: $i,SV683: $i] :
( ( ( in @ SV683 @ SV203 )
= $false )
| ( $false = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4608]) ).
thf(4725,plain,
! [SV203: $i,SV496: $i,SV683: $i] :
( ( ( in @ SV683 @ SV496 )
= $true )
| ( $false = $true )
| ( ( in @ SV683 @ SV496 )
= $false )
| ( ( in @ SV683 @ ( symdiff @ SV203 @ SV496 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4609]) ).
thf(4726,plain,
! [SV208: $i,SV952: $o,SV818: $i,SV501: $i,SV982: $i] :
( ( ( in @ SV982 @ SV501 )
= $true )
| ( ( ~ ( ~ ( in @ SV982 @ SV818 )
| SV952 )
| SV952 )
= $true )
| ( ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV982 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4611]) ).
thf(4727,plain,
! [SV208: $i,SV501: $i,SV952: $o,SV818: $i,SV982: $i] :
( ( ( ~ ( ~ ( in @ SV982 @ SV818 )
| SV952 ) )
= $true )
| ( SV952 = $true )
| ( SV952 = $false )
| ( ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV982 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4612]) ).
thf(4728,plain,
! [SV208: $i,SV818: $i,SV501: $i,SV983: $i] :
( ( ( in @ SV983 @ SV501 )
= $true )
| ( ( ~ ( ~ ( in @ SV983 @ SV818 )
| $true )
| $true )
= $true )
| ( ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV983 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4613]) ).
thf(4729,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV983: $i] :
( ( ( ~ ( ~ ( in @ SV983 @ SV818 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV983 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4614]) ).
thf(4730,plain,
! [SV208: $i,SV818: $i,SV501: $i,SV984: $i] :
( ( ( in @ SV984 @ SV501 )
= $true )
| ( ( ~ ( ~ ( in @ SV984 @ SV818 )
| $false )
| $false )
= $true )
| ( ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV984 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4615]) ).
thf(4731,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV984: $i] :
( ( ( ~ ( ~ ( in @ SV984 @ SV818 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV984 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4616]) ).
thf(4732,plain,
! [SV209: $i,SV502: $i,SV889: $i > $o,SV689: $i,SV1055: $i] :
( ( ( in @ SV1055 @ SV689 )
= $false )
| ( ( SV889 @ SV1055 )
= $true )
| ( ( in @ ( kpair @ ( sK55_SY4072 @ SV889 @ SV689 @ SV502 @ SV209 ) @ ( sK81_SY4144 @ SV209 @ SV689 @ SV889 @ SV502 ) ) @ SV689 )
= $true )
| ( ( breln @ SV209 @ SV502 @ SV689 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4618]) ).
thf(4733,plain,
! [SV216: $i,SV819: $i,SV1061: $o,SV508: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
| SV1061 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| SV1061 )
| SV1061 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4620]) ).
thf(4734,plain,
! [SV216: $i,SV819: $i,SV508: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $true )
| $true )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4621]) ).
thf(4735,plain,
! [SV216: $i,SV819: $i,SV508: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $false )
| $false )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4622]) ).
thf(4736,plain,
! [SV226: $i,SV1040: $i,SV1066: $i] :
( ( ( ~ ( in @ SV1066 @ SV1040 )
| ( in @ SV1066 @ SV226 ) )
= $true )
| ( ( in @ SV1040 @ ( sK2_SY2943 @ SV226 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4623]) ).
thf(4737,plain,
! [SV1056: $i,SV226: $i,SV1041: $i] :
( ( ( ~ ( ~ ( in @ SV1041 @ SV226 )
| ~ ( in @ SV1056 @ SV226 ) ) )
= $false )
| ( ( ~ ! [SY4193: $i] :
( ~ ( in @ SY4193 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SV1041 @ SY4193 )
| ( in @ SV1056 @ SY4193 ) )
| ~ ( ~ ( in @ SV1056 @ SY4193 )
| ( in @ SV1041 @ SY4193 ) ) ) )
| ( SV1041 = SV1056 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4624]) ).
thf(4738,plain,
! [SV1014: $i,SV226: $i,SV1002: $i] :
( ( ( in @ SV1002 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( ~ ( in @ SV1014 @ ( sK2_SY2943 @ SV226 ) ) )
= $true )
| ( ( ! [SY4166: $i] :
( ~ ( in @ SY4166 @ SV1002 )
| ( in @ SY4166 @ SV1014 ) )
| ! [SY4167: $i] :
( ~ ( in @ SY4167 @ SV1014 )
| ( in @ SY4167 @ SV1002 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4625]) ).
thf(4739,plain,
! [SV226: $i,SV955: $i] :
( ( ( ~ ! [SY4115: $i] :
~ ( in @ SY4115 @ SV955 ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( ~ ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4626]) ).
thf(4740,plain,
! [SV226: $i,SV955: $i] :
( ( ( ! [SY4115: $i] :
~ ( in @ SY4115 @ SV955 ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( ~ ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4627]) ).
thf(4741,plain,
! [SV1003: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ! [SY4159: $i] :
~ ~ ( ~ ( in @ SY4159 @ SV520 )
| ~ ( SV230 @ SY4159 @ SV1003 ) ) )
= $false )
| ( ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
= $false )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4628]) ).
thf(4742,plain,
! [SV1003: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ! [SY4160: $i] :
~ ~ ( ~ ( in @ SY4160 @ SV520 )
| ~ ( SV230 @ SY4160 @ SV1003 ) ) )
= $true )
| ( ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
= $true )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4629]) ).
thf(4743,plain,
! [SV957: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ! [SY3585: $i] :
~ ! [SY3586: $i] :
~ ( ~ ( ~ ( in @ SY3586 @ SY3585 )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY3586 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY3586 ) )
| ( in @ SY3586 @ SY3585 ) ) ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4630]) ).
thf(4744,plain,
! [SV520: $i,SV230: $i > $i > $o,SV957: $i] :
( ( ( ~ ! [SY4202: $i] :
~ ( ~ ( ~ ( in @ SY4202 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY4202 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY4202 ) )
| ( in @ SY4202 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) ) ) ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4631]) ).
thf(4745,plain,
! [SV251: $i,SV828: $i,SV538: $i,SV960: $i] :
( ( ( in @ SV960 @ ( binunion @ SV538 @ SV828 ) )
= $false )
| ( ( in @ SV960 @ SV828 )
= $true )
| ( ( in @ SV960 @ SV538 )
= $true )
| ( ( in @ SV960 @ SV251 )
= $false )
| ( ( in @ SV828 @ ( powerset @ SV251 ) )
= $false )
| ( ( in @ SV538 @ ( powerset @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4633]) ).
thf(4746,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( in @ ( sK110_SY4022 @ SV549 @ SV829 @ SV260 ) @ SV260 )
= $true )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4634]) ).
thf(4747,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK122_SY4194 @ SV829 @ SV549 @ SV260 ) @ SV260 )
| ~ ( in @ ( kpair @ ( sK110_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK122_SY4194 @ SV829 @ SV549 @ SV260 ) ) @ SV829 )
| ( in @ ( kpair @ ( sK110_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK122_SY4194 @ SV829 @ SV549 @ SV260 ) ) @ SV549 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4635]) ).
thf(4748,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( ~ ( in @ ( sK123_SY4022 @ SV549 @ SV829 @ SV260 ) @ SV260 )
| ! [SY4205: $i] :
( ~ ( in @ SY4205 @ SV260 )
| ~ ( in @ ( kpair @ ( sK123_SY4022 @ SV549 @ SV829 @ SV260 ) @ SY4205 ) @ SV829 )
| ( in @ ( kpair @ ( sK123_SY4022 @ SV549 @ SV829 @ SV260 ) @ SY4205 ) @ SV549 ) ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4636]) ).
thf(4749,plain,
! [SV549: $i,SV829: $i,SV260: $i] :
( ( ( ! [SY4022: $i] :
( ~ ( in @ SY4022 @ SV260 )
| ! [SY4023: $i] :
( ~ ( in @ SY4023 @ SV260 )
| ~ ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV829 )
| ( in @ ( kpair @ SY4022 @ SY4023 ) @ SV549 ) ) ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV549 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4637]) ).
thf(4750,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( ~ ( in @ ( sK124_SY4022 @ SV549 @ SV829 @ SV260 ) @ SV260 )
| ! [SY4206: $i] :
( ~ ( in @ SY4206 @ SV260 )
| ~ ( in @ ( kpair @ ( sK124_SY4022 @ SV549 @ SV829 @ SV260 ) @ SY4206 ) @ SV829 )
| ( in @ ( kpair @ ( sK124_SY4022 @ SV549 @ SV829 @ SV260 ) @ SY4206 ) @ SV549 ) ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4638]) ).
thf(4751,plain,
! [SV1062: $o,SV836: $i,SV1007: $i,SV568: $i,SV963: $i,SV280: $i] :
( ( ( ~ ! [SY4199: $i] :
( ~ ( in @ SY4199 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SY4199 ) @ SV568 )
| ~ ( in @ ( kpair @ SY4199 @ SV1007 ) @ SV836 )
| SV1062 ) )
= $true )
| ( SV1062 = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4642]) ).
thf(4752,plain,
! [SV836: $i,SV1007: $i,SV568: $i,SV963: $i,SV280: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SX0 ) @ SV568 )
| ~ ( in @ ( kpair @ SX0 @ SV1007 ) @ SV836 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4643]) ).
thf(4753,plain,
! [SV836: $i,SV1007: $i,SV568: $i,SV963: $i,SV280: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SX0 ) @ SV568 )
| ~ ( in @ ( kpair @ SX0 @ SV1007 ) @ SV836 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4644]) ).
thf(4754,plain,
! [SV837: $i,SV1057: $i,SV1044: $i,SV288: $i > $o] :
( ( ( SV288 @ SV1044 )
= $false )
| ( ( ~ ( SV288 @ SV1057 )
| ( SV1044 = SV1057 ) )
= $true )
| ( ( SV288 @ SV837 )
= $false )
| ( ( SV288 @ ( sK83_SY4034 @ SV837 @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4645]) ).
thf(4755,plain,
! [SV837: $i,SV1026: $i,SV1045: $i,SV288: $i > $o] :
( ( ( ~ ( SV288 @ SV1045 ) )
= $true )
| ( ( SV1026 = SV1045 )
= $true )
| ( ( SV288 @ SV1026 )
= $false )
| ( ( SV288 @ SV837 )
= $false )
| ( ( SV837
= ( sK83_SY4034 @ SV837 @ SV288 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4646]) ).
thf(4756,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( in @ ( sK111_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV299 )
= $true )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV299 )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4647]) ).
thf(4757,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( ~ ( in @ ( sK111_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV840 ) )
= $false )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV299 )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4648]) ).
thf(4758,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( in @ ( sK111_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV584 )
= $false )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV299 )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4648]) ).
thf(4759,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( ~ ( in @ ( sK118_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV299 ) )
= $false )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV584 )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4649]) ).
thf(4760,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( ~ ( in @ ( sK118_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV840 )
| ( in @ ( sK118_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV584 ) )
= $false )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV584 )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4649]) ).
thf(4761,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( in @ ( sK112_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV299 )
= $true )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV840 )
= $false )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4650]) ).
thf(4762,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( ~ ( in @ ( sK112_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV840 ) )
= $false )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV840 )
= $false )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4651]) ).
thf(4763,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( in @ ( sK112_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV584 )
= $false )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV840 )
= $false )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4651]) ).
thf(4764,plain,
! [SV301: $i,SV734: $i,SV911: $i,SV1046: $i,SV586: $i,SV1067: $i] :
( ( ( ~ ( in @ SV1067 @ SV586 )
| ~ ( in @ ( kpair @ SV1046 @ SV1067 ) @ SV911 )
| ( in @ ( kpair @ SV1046 @ SV1067 ) @ SV734 ) )
= $true )
| ( ( in @ SV1046 @ SV301 )
= $false )
| ( ( in @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) @ SV301 )
= $true )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4652]) ).
thf(4765,plain,
! [SV301: $i,SV734: $i,SV911: $i,SV1027: $i,SV586: $i,SV1063: $i] :
( ( ( ~ ( in @ SV1063 @ SV586 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV1027 @ SV1063 ) @ SV911 )
| ( in @ ( kpair @ SV1027 @ SV1063 ) @ SV734 ) )
= $true )
| ( ( in @ SV1027 @ SV301 )
= $false )
| ( ( ( ap @ SV301 @ SV586 @ SV734 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) )
= ( ap @ SV301 @ SV586 @ SV911 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) ) )
= $false )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4653]) ).
thf(4766,plain,
! [SV848: $i,SV1068: $i,SV316: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV316 @ SV1068 )
| ( SV1068
= ( sK113_SY3190 @ SV848 @ SV316 ) ) )
| ~ ( ( SV1068
!= ( sK113_SY3190 @ SV848 @ SV316 ) )
| ( SV316 @ SV1068 ) ) ) )
= $true )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV316 @ ( sK85_SY4045 @ SV848 @ SV316 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4654]) ).
thf(4767,plain,
! [SV848: $i,SV1064: $i,SV316: $i > $o] :
( ( ( ~ ( ~ ( SV316 @ SV1064 )
| ( SV1064
= ( sK104_SY3190 @ SV848 @ SV316 ) ) )
| ~ ( ( SV1064
!= ( sK104_SY3190 @ SV848 @ SV316 ) )
| ( SV316 @ SV1064 ) ) )
= $false )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV848
= ( sK85_SY4045 @ SV848 @ SV316 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4655]) ).
thf(4768,plain,
! [SV317: $i,SV970: $i,SV599: $i,SV1009: $i,SV849: $i] :
( ( ( subset @ SV849 @ SV1009 )
= $false )
| ( ( subset @ ( binintersect @ SV599 @ SV849 ) @ ( binintersect @ SV970 @ SV1009 ) )
= $true )
| ( ( subset @ SV599 @ SV970 )
= $false )
| ( ( in @ SV1009 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV970 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV849 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4656]) ).
thf(4769,plain,
! [SV319: $i,SV601: $i,SV914: $i > $o,SV738: $i,SV1058: $i] :
( ( ( in @ SV1058 @ SV738 )
= $false )
| ( ( SV914 @ SV1058 )
= $true )
| ( ( in @ ( kpair @ ( sK58_SY4090 @ SV914 @ SV738 @ SV601 @ SV319 ) @ ( sK86_SY4148 @ SV319 @ SV738 @ SV914 @ SV601 ) ) @ SV738 )
= $true )
| ( ( breln @ SV319 @ SV601 @ SV738 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4658]) ).
thf(4770,plain,
! [SV322: $i,SV851: $i,SV1059: $i] :
( ( ( ~ ( in @ SV1059 @ ( sK51_SY3211 @ SV851 @ SV322 ) )
| ~ ( in @ SV1059 @ SV322 ) )
= $true )
| ( ( in @ SV851 @ SV322 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4660]) ).
thf(4771,plain,
! [SV44: $i,SV1018: $i,SV353: $i > $o] :
( ( ( SV353 @ SV1018 )
= $false )
| ( ( in @ SV1018 @ SV44 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( in @ ( sK36_SY3943 @ SV353 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4661]) ).
thf(4772,plain,
! [SV353: $i > $o,SV44: $i,SV1028: $i] :
( ( ( in @ SV1028 @ SV44 )
= $false )
| ( ( ~ ( SV353 @ SV1028 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( SV353 @ ( sK9_SY3238 @ SV353 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4662]) ).
thf(4773,plain,
! [SV353: $i > $o,SV44: $i,SV1049: $i] :
( ( ( ~ ( in @ SV1049 @ SV44 ) )
= $true )
| ( ( ~ ( SV353 @ SV1049 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( SV353 @ ( sK36_SY3943 @ SV353 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4663]) ).
thf(4774,plain,
! [SV353: $i > $o,SV44: $i,SV1029: $i] :
( ( ( in @ SV1029 @ SV44 )
= $false )
| ( ( ~ ( SV353 @ SV1029 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( ( sK9_SY3238 @ SV353 @ SV44 )
= ( sK36_SY3943 @ SV353 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4664]) ).
thf(4775,plain,
! [SV765: $i,SV1030: $i,SV1050: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV1050 ) )
= $true )
| ( ( SV1030 = SV1050 )
= $true )
| ( ( SV58 @ SV1030 )
= $false )
| ( ( SV58 @ SV765 )
= $false )
| ( ( SV58 @ ( sK75_SY3949 @ SV765 @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4665]) ).
thf(4776,plain,
! [SV765: $i,SV1019: $i,SV1031: $i,SV58: $i > $o] :
( ( ( SV58 @ SV1031 )
= $false )
| ( ( SV1019 = SV1031 )
= $true )
| ( ( SV58 @ SV1019 )
= $false )
| ( ( SV58 @ SV765 )
= $false )
| ( ( SV765
= ( sK75_SY3949 @ SV765 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4666]) ).
thf(4777,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ( ~ ( SV59 @ ( sK119_SY2468 @ SV766 @ SV59 ) )
| ~ ! [SY4200: $i] :
( ~ ( SV59 @ SY4200 )
| ( ( sK119_SY2468 @ SV766 @ SV59 )
= SY4200 ) ) ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4667]) ).
thf(4778,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ ( sK114_SY2468 @ SV766 @ SV59 ) )
| ~ ! [SY4196: $i] :
( ~ ( SV59 @ SY4196 )
| ( ( sK114_SY2468 @ SV766 @ SV59 )
= SY4196 ) ) )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4668]) ).
thf(4779,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ ( sK115_SY2468 @ SV766 @ SV59 ) )
| ~ ! [SY4197: $i] :
( ~ ( SV59 @ SY4197 )
| ( ( sK115_SY2468 @ SV766 @ SV59 )
= SY4197 ) ) )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4669]) ).
thf(4780,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ ( sK106_SY2468 @ SV766 @ SV59 ) ) )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4670]) ).
thf(4781,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ! [SY4184: $i] :
( ~ ( SV59 @ SY4184 )
| ( ( sK106_SY2468 @ SV766 @ SV59 )
= SY4184 ) ) )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4670]) ).
thf(4782,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ~ ( SV60 @ ( sK107_SY2472 @ SV767 @ SV60 ) ) )
= $false )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV60 @ ( sK76_SY3951 @ SV767 @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4671]) ).
thf(4783,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ~ ! [SY4185: $i] :
( ~ ( SV60 @ SY4185 )
| ( ( sK107_SY2472 @ SV767 @ SV60 )
= SY4185 ) ) )
= $false )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV60 @ ( sK76_SY3951 @ SV767 @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4671]) ).
thf(4784,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( SV60 @ ( sK96_SY2472 @ SV767 @ SV60 ) )
= $true )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV767
= ( sK76_SY3951 @ SV767 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4672]) ).
thf(4785,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ! [SY4172: $i] :
( ~ ( SV60 @ SY4172 )
| ( ( sK96_SY2472 @ SV767 @ SV60 )
= SY4172 ) ) )
= $true )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV767
= ( sK76_SY3951 @ SV767 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4673]) ).
thf(4786,plain,
! [SV78: $i,SV927: $i,SV382: $i,SV994: $i,SV773: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) ) @ SV382 ) )
| ~ ( in @ ( kpair @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) @ SV994 ) @ SV773 ) ) )
= $true )
| ( ( in @ ( kpair @ SV927 @ SV994 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
= $false )
| ( ( in @ SV994 @ SV78 )
= $false )
| ( ( in @ SV927 @ SV78 )
= $false )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4674]) ).
thf(4787,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( SV100 @ ( sK97_SY2565 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ ( sK53_SY2563 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4675]) ).
thf(4788,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ! [SY4173: $i] :
( ~ ( SV100 @ SY4173 )
| ( ( sK97_SY2565 @ SV781 @ SV100 )
= SY4173 ) ) )
= $true )
| ( ( SV100 @ ( sK53_SY2563 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4676]) ).
thf(4789,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK108_SY2565 @ SV781 @ SV100 ) ) )
= $false )
| ( ( SV100 @ ( sK61_SY4131 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4677]) ).
thf(4790,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ~ ! [SY4186: $i] :
( ~ ( SV100 @ SY4186 )
| ( ( sK108_SY2565 @ SV781 @ SV100 )
= SY4186 ) ) )
= $false )
| ( ( SV100 @ ( sK61_SY4131 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4677]) ).
thf(4791,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( SV100 @ ( sK98_SY2565 @ SV781 @ SV100 ) )
= $true )
| ( ( ( sK53_SY2563 @ SV781 @ SV100 )
= ( sK61_SY4131 @ SV781 @ SV100 ) )
= $false )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4678]) ).
thf(4792,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ! [SY4174: $i] :
( ~ ( SV100 @ SY4174 )
| ( ( sK98_SY2565 @ SV781 @ SV100 )
= SY4174 ) ) )
= $true )
| ( ( ( sK53_SY2563 @ SV781 @ SV100 )
= ( sK61_SY4131 @ SV781 @ SV100 ) )
= $false )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4679]) ).
thf(4793,plain,
! [SV122: $i,SV420: $i,SV865: $i > $o,SV788: $i > $o] :
( ( ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) )
= $true )
| ( ( ~ ( ~ ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
| ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4680]) ).
thf(4794,plain,
! [SV420: $i,SV788: $i > $o,SV122: $i,SV865: $i > $o] :
( ( ( ~ ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
| ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) ) )
= $false )
| ( ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
= $false )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4681]) ).
thf(4795,plain,
! [SV131: $i,SV792: $i,SV998: $i,SV428: $i,SV1034: $i,SV939: $i] :
( ( ( in @ ( kpair @ SV939 @ SV1034 ) @ SV428 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV1034 @ SV998 ) @ SV792 )
| ( in @ ( kpair @ SV939 @ SV998 ) @ ( breln1compset @ SV131 @ SV428 @ SV792 ) ) )
= $true )
| ( ( in @ SV1034 @ SV131 )
= $false )
| ( ( in @ SV998 @ SV131 )
= $false )
| ( ( in @ SV939 @ SV131 )
= $false )
| ( ( breln1 @ SV131 @ SV792 )
= $false )
| ( ( breln1 @ SV131 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4682]) ).
thf(4796,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( in @ ( sK116_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SV140 )
= $true )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SV140 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4683]) ).
thf(4797,plain,
! [SV436: $i,SV650: $i,SV870: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK125_SY4198 @ SV140 @ SV870 @ SV650 @ SV436 ) @ SV436 )
| ~ ( in @ ( kpair @ ( sK116_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK125_SY4198 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV870 )
| ( in @ ( kpair @ ( sK116_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK125_SY4198 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV650 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SV140 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4684]) ).
thf(4798,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( ~ ( in @ ( sK126_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SV140 )
| ! [SY4207: $i] :
( ~ ( in @ SY4207 @ SV436 )
| ~ ( in @ ( kpair @ ( sK126_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SY4207 ) @ SV870 )
| ( in @ ( kpair @ ( sK126_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SY4207 ) @ SV650 ) ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) @ SV436 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4685]) ).
thf(4799,plain,
! [SV650: $i,SV870: $i,SV436: $i,SV140: $i] :
( ( ( ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV140 )
| ! [SY4062: $i] :
( ~ ( in @ SY4062 @ SV436 )
| ~ ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV870 )
| ( in @ ( kpair @ SY4061 @ SY4062 ) @ SV650 ) ) ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV650 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4686]) ).
thf(4800,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( ~ ( in @ ( sK127_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SV140 )
| ! [SY4208: $i] :
( ~ ( in @ SY4208 @ SV436 )
| ~ ( in @ ( kpair @ ( sK127_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SY4208 ) @ SV870 )
| ( in @ ( kpair @ ( sK127_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SY4208 ) @ SV650 ) ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4687]) ).
thf(4801,plain,
! [SV146: $i,SV1020: $i,SV442: $i > $o] :
( ( ( SV442 @ SV1020 )
= $false )
| ( ( in @ SV1020 @ SV146 )
= $false )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( in @ ( sK38_SY3987 @ SV442 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4688]) ).
thf(4802,plain,
! [SV442: $i > $o,SV146: $i,SV1035: $i] :
( ( ( in @ SV1035 @ SV146 )
= $false )
| ( ( ~ ( SV442 @ SV1035 ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( SV442 @ ( sK11_SY3407 @ SV442 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4689]) ).
thf(4803,plain,
! [SV442: $i > $o,SV146: $i,SV1051: $i] :
( ( ( ~ ( in @ SV1051 @ SV146 ) )
= $true )
| ( ( ~ ( SV442 @ SV1051 ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( SV442 @ ( sK38_SY3987 @ SV442 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4690]) ).
thf(4804,plain,
! [SV442: $i > $o,SV146: $i,SV1036: $i] :
( ( ( in @ SV1036 @ SV146 )
= $false )
| ( ( ~ ( SV442 @ SV1036 ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( ( sK11_SY3407 @ SV442 @ SV146 )
= ( sK38_SY3987 @ SV442 @ SV146 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4691]) ).
thf(4805,plain,
! [SV1010: $i,SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
| ( SV1010
= ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) ) )
= $false )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4692]) ).
thf(4806,plain,
! [SV448: $i > $o,SV152: $i > $o] :
( ( ( ! [SY2727: $i] :
~ ~ ( ~ ( SV152 @ SY2727 )
| ~ ! [SY2728: $i] :
( ~ ( SV152 @ SY2728 )
| ( SY2727 = SY2728 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4693]) ).
thf(4807,plain,
! [SV448: $i > $o,SV1069: $i,SV152: $i > $o] :
( ( ( ~ ~ ( ~ ( SV152 @ SV1069 )
| ~ ! [SY4209: $i] :
( ~ ( SV152 @ SY4209 )
| ( SV1069 = SY4209 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4694]) ).
thf(4808,plain,
! [SV448: $i > $o,SV1070: $i,SV152: $i > $o] :
( ( ( ~ ~ ( ~ ( SV152 @ SV1070 )
| ~ ! [SY4210: $i] :
( ~ ( SV152 @ SY4210 )
| ( SV1070 = SY4210 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4695]) ).
thf(4809,plain,
! [SV448: $i > $o,SV1065: $i,SV152: $i > $o] :
( ( ( ~ ( ~ ( SV152 @ SV1065 )
| ~ ! [SY4201: $i] :
( ~ ( SV152 @ SY4201 )
| ( SV1065 = SY4201 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4696]) ).
thf(4810,plain,
! [SV175: $i,SV976: $i,SV470: $i > $i] :
( ( ( ~ ( in @ ( sK117_SY4135 @ SV470 @ SV976 @ SV175 ) @ SV175 )
| ( SV976
!= ( SV470 @ ( sK117_SY4135 @ SV470 @ SV976 @ SV175 ) ) ) )
= $false )
| ( ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4697]) ).
thf(4811,plain,
! [SV470: $i > $i,SV976: $i,SV175: $i,SV1060: $i] :
( ( ( ~ ( in @ SV1060 @ SV175 )
| ( SV976
!= ( SV470 @ SV1060 ) ) )
= $true )
| ( ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4698]) ).
thf(4812,plain,
! [SV977: $i,SV470: $i > $i,SV175: $i] :
( ( ( ~ ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) )
| ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 ) )
= $false )
| ( ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4699]) ).
thf(4813,plain,
! [SV977: $i,SV470: $i > $i,SV175: $i,SV1071: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1071 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SV1071 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) )
| ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 ) ) )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4700]) ).
thf(4814,plain,
! [SV979: $i,SV670: $i > $i > $o,SV180: $i,SV1052: $i,SV475: $i] :
( ( ( ~ ( reflwellordering @ SV475 @ SV1052 ) )
= $true )
| ( ( ! [SY4187: $i] :
( ~ ( in @ SY4187 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY4188: $i] :
~ ( ~ ( SV670 @ SY4187 @ SY4188 )
| ~ ! [SY4189: $i] :
( ~ ( in @ SY4189 @ SV475 )
| ~ ( SV670 @ SY4187 @ SY4189 )
| ( in @ ( kpair @ SY4188 @ SY4189 ) @ SV1052 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV1052 @ ( breln1Set @ SV475 ) )
= $false )
| ( ( in @ SV979 @ SV475 )
= $false )
| ( ( SV670 @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV979 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4701]) ).
thf(4815,plain,
! [SV193: $i,SV1021: $i,SV488: $i > $i,SV881: $i] :
( ( ( SV881
= ( SV488 @ SV1021 ) )
= $false )
| ( ( in @ SV1021 @ SV193 )
= $false )
| ( ( in @ SV881 @ ( sK4_SY3504 @ SV488 @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4704]) ).
thf(4816,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ ( sK109_SY2855 @ SV816 @ SV196 ) ) )
= $false )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV196 @ ( sK80_SY4002 @ SV816 @ SV196 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4705]) ).
thf(4817,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ~ ! [SY4190: $i] :
( ~ ( SV196 @ SY4190 )
| ( ( sK109_SY2855 @ SV816 @ SV196 )
= SY4190 ) ) )
= $false )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV196 @ ( sK80_SY4002 @ SV816 @ SV196 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4705]) ).
thf(4818,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( SV196 @ ( sK101_SY2855 @ SV816 @ SV196 ) )
= $true )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV816
= ( sK80_SY4002 @ SV816 @ SV196 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4706]) ).
thf(4819,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ! [SY4177: $i] :
( ~ ( SV196 @ SY4177 )
| ( ( sK101_SY2855 @ SV816 @ SV196 )
= SY4177 ) ) )
= $true )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV816
= ( sK80_SY4002 @ SV816 @ SV196 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4707]) ).
thf(4820,plain,
! [SV491: $i > $o,SV1053: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1053 ) )
= $true )
| ( ( ~ ! [SY4191: $i] :
( ~ ( SV197 @ SY4191 )
| ( SV1053 = SY4191 ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4708]) ).
thf(4821,plain,
! [SV197: $i > $o,SV1054: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1054 ) )
= $true )
| ( ( ~ ! [SY4192: $i] :
( ~ ( SV491 @ SY4192 )
| ( SV1054 = SY4192 ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4709]) ).
thf(4822,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) )
| ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4710]) ).
thf(4823,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) )
| ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4711]) ).
thf(4824,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4712]) ).
thf(4825,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4713]) ).
thf(4826,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4714]) ).
thf(4827,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4715]) ).
thf(4828,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) ) )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4716]) ).
thf(4829,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) ) )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4717]) ).
thf(4830,plain,
! [SV208: $i,SV501: $i,SV952: $o,SV818: $i,SV982: $i] :
( ( ( ~ ( ~ ( in @ SV982 @ SV818 )
| SV952 ) )
= $true )
| ( SV952 = $true )
| ( ( in @ SV982 @ SV501 )
= $true )
| ( ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV982 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4726]) ).
thf(4831,plain,
! [SV208: $i,SV501: $i,SV952: $o,SV818: $i,SV982: $i] :
( ( ( ~ ( in @ SV982 @ SV818 )
| SV952 )
= $false )
| ( SV952 = $true )
| ( SV952 = $false )
| ( ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV982 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4727]) ).
thf(4832,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV983: $i] :
( ( ( ~ ( ~ ( in @ SV983 @ SV818 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV983 @ SV501 )
= $true )
| ( ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV983 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4728]) ).
thf(4833,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV983: $i] :
( ( ( ~ ( in @ SV983 @ SV818 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV983 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4729]) ).
thf(4834,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV984: $i] :
( ( ( ~ ( ~ ( in @ SV984 @ SV818 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV984 @ SV501 )
= $true )
| ( ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV984 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4730]) ).
thf(4835,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV984: $i] :
( ( ( ~ ( in @ SV984 @ SV818 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV984 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4731]) ).
thf(4836,plain,
! [SV216: $i,SV819: $i,SV1061: $o,SV508: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
| SV1061 )
= $false )
| ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| SV1061 )
| SV1061 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4733]) ).
thf(4837,plain,
! [SV216: $i,SV819: $i,SV508: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $true )
| $true )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4734]) ).
thf(4838,plain,
! [SV216: $i,SV819: $i,SV508: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $false )
| $false )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4735]) ).
thf(4839,plain,
! [SV226: $i,SV1040: $i,SV1066: $i] :
( ( ( ~ ( in @ SV1066 @ SV1040 ) )
= $true )
| ( ( in @ SV1066 @ SV226 )
= $true )
| ( ( in @ SV1040 @ ( sK2_SY2943 @ SV226 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4736]) ).
thf(4840,plain,
! [SV1056: $i,SV226: $i,SV1041: $i] :
( ( ( ~ ( in @ SV1041 @ SV226 )
| ~ ( in @ SV1056 @ SV226 ) )
= $true )
| ( ( ~ ! [SY4193: $i] :
( ~ ( in @ SY4193 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SV1041 @ SY4193 )
| ( in @ SV1056 @ SY4193 ) )
| ~ ( ~ ( in @ SV1056 @ SY4193 )
| ( in @ SV1041 @ SY4193 ) ) ) )
| ( SV1041 = SV1056 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4737]) ).
thf(4841,plain,
! [SV1002: $i,SV226: $i,SV1014: $i] :
( ( ( in @ SV1014 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( in @ SV1002 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( ! [SY4166: $i] :
( ~ ( in @ SY4166 @ SV1002 )
| ( in @ SY4166 @ SV1014 ) )
| ! [SY4167: $i] :
( ~ ( in @ SY4167 @ SV1014 )
| ( in @ SY4167 @ SV1002 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4738]) ).
thf(4842,plain,
! [SV226: $i,SV955: $i] :
( ( ( ! [SY4115: $i] :
~ ( in @ SY4115 @ SV955 ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( ~ ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4739]) ).
thf(4843,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( ~ ( in @ SV1072 @ SV955 ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( ~ ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4740]) ).
thf(4844,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1003: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK129_SY4159 @ SV1003 @ SV230 @ SV520 ) @ SV520 )
| ~ ( SV230 @ ( sK129_SY4159 @ SV1003 @ SV230 @ SV520 ) @ SV1003 ) ) )
= $false )
| ( ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
= $false )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4741]) ).
thf(4845,plain,
! [SV1003: $i,SV230: $i > $i > $o,SV520: $i,SV1073: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1073 @ SV520 )
| ~ ( SV230 @ SV1073 @ SV1003 ) ) )
= $true )
| ( ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
= $true )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4742]) ).
thf(4846,plain,
! [SV520: $i,SV230: $i > $i > $o,SV957: $i] :
( ( ( ~ ! [SY4211: $i] :
~ ( ~ ( ~ ( in @ SY4211 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY4211 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY4211 ) )
| ( in @ SY4211 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) ) ) ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4743]) ).
thf(4847,plain,
! [SV520: $i,SV230: $i > $i > $o,SV957: $i] :
( ( ( ! [SY4202: $i] :
~ ( ~ ( ~ ( in @ SY4202 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY4202 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY4202 ) )
| ( in @ SY4202 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) ) ) ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4744]) ).
thf(4848,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK122_SY4194 @ SV829 @ SV549 @ SV260 ) @ SV260 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4747]) ).
thf(4849,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK110_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK122_SY4194 @ SV829 @ SV549 @ SV260 ) ) @ SV829 )
| ( in @ ( kpair @ ( sK110_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK122_SY4194 @ SV829 @ SV549 @ SV260 ) ) @ SV549 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4747]) ).
thf(4850,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( ~ ( in @ ( sK123_SY4022 @ SV549 @ SV829 @ SV260 ) @ SV260 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4748]) ).
thf(4851,plain,
! [SV829: $i,SV549: $i,SV260: $i] :
( ( ( ! [SY4205: $i] :
( ~ ( in @ SY4205 @ SV260 )
| ~ ( in @ ( kpair @ ( sK123_SY4022 @ SV549 @ SV829 @ SV260 ) @ SY4205 ) @ SV829 )
| ( in @ ( kpair @ ( sK123_SY4022 @ SV549 @ SV829 @ SV260 ) @ SY4205 ) @ SV549 ) ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4748]) ).
thf(4852,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( ~ ( in @ ( sK131_SY4022 @ SV549 @ SV829 @ SV260 ) @ SV260 )
| ! [SY4214: $i] :
( ~ ( in @ SY4214 @ SV260 )
| ~ ( in @ ( kpair @ ( sK131_SY4022 @ SV549 @ SV829 @ SV260 ) @ SY4214 ) @ SV829 )
| ( in @ ( kpair @ ( sK131_SY4022 @ SV549 @ SV829 @ SV260 ) @ SY4214 ) @ SV549 ) ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV549 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4749]) ).
thf(4853,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( ~ ( in @ ( sK124_SY4022 @ SV549 @ SV829 @ SV260 ) @ SV260 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4750]) ).
thf(4854,plain,
! [SV829: $i,SV549: $i,SV260: $i] :
( ( ( ! [SY4206: $i] :
( ~ ( in @ SY4206 @ SV260 )
| ~ ( in @ ( kpair @ ( sK124_SY4022 @ SV549 @ SV829 @ SV260 ) @ SY4206 ) @ SV829 )
| ( in @ ( kpair @ ( sK124_SY4022 @ SV549 @ SV829 @ SV260 ) @ SY4206 ) @ SV549 ) ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4750]) ).
thf(4855,plain,
! [SV1062: $o,SV836: $i,SV1007: $i,SV568: $i,SV963: $i,SV280: $i] :
( ( ( ! [SY4199: $i] :
( ~ ( in @ SY4199 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SY4199 ) @ SV568 )
| ~ ( in @ ( kpair @ SY4199 @ SV1007 ) @ SV836 )
| SV1062 ) )
= $false )
| ( SV1062 = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4751]) ).
thf(4856,plain,
! [SV836: $i,SV1007: $i,SV568: $i,SV963: $i,SV280: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SX0 ) @ SV568 )
| ~ ( in @ ( kpair @ SX0 @ SV1007 ) @ SV836 )
| $true ) )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4752]) ).
thf(4857,plain,
! [SV836: $i,SV1007: $i,SV568: $i,SV963: $i,SV280: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ SX0 ) @ SV568 )
| ~ ( in @ ( kpair @ SX0 @ SV1007 ) @ SV836 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4753]) ).
thf(4858,plain,
! [SV837: $i,SV1044: $i,SV1057: $i,SV288: $i > $o] :
( ( ( ~ ( SV288 @ SV1057 ) )
= $true )
| ( ( SV1044 = SV1057 )
= $true )
| ( ( SV288 @ SV1044 )
= $false )
| ( ( SV288 @ SV837 )
= $false )
| ( ( SV288 @ ( sK83_SY4034 @ SV837 @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4754]) ).
thf(4859,plain,
! [SV837: $i,SV1026: $i,SV1045: $i,SV288: $i > $o] :
( ( ( SV288 @ SV1045 )
= $false )
| ( ( SV1026 = SV1045 )
= $true )
| ( ( SV288 @ SV1026 )
= $false )
| ( ( SV288 @ SV837 )
= $false )
| ( ( SV837
= ( sK83_SY4034 @ SV837 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4755]) ).
thf(4860,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( in @ ( sK111_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV840 )
= $true )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV299 )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4757]) ).
thf(4861,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( in @ ( sK118_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV299 )
= $true )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV584 )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4759]) ).
thf(4862,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( ~ ( in @ ( sK118_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV840 ) )
= $false )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV584 )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4760]) ).
thf(4863,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( in @ ( sK118_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV584 )
= $false )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV584 )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4760]) ).
thf(4864,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( in @ ( sK112_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV840 )
= $true )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV840 )
= $false )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4762]) ).
thf(4865,plain,
! [SV301: $i,SV734: $i,SV911: $i,SV1046: $i,SV586: $i,SV1067: $i] :
( ( ( ~ ( in @ SV1067 @ SV586 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV1046 @ SV1067 ) @ SV911 )
| ( in @ ( kpair @ SV1046 @ SV1067 ) @ SV734 ) )
= $true )
| ( ( in @ SV1046 @ SV301 )
= $false )
| ( ( in @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) @ SV301 )
= $true )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4764]) ).
thf(4866,plain,
! [SV301: $i,SV734: $i,SV911: $i,SV1027: $i,SV586: $i,SV1063: $i] :
( ( ( in @ SV1063 @ SV586 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV1027 @ SV1063 ) @ SV911 )
| ( in @ ( kpair @ SV1027 @ SV1063 ) @ SV734 ) )
= $true )
| ( ( in @ SV1027 @ SV301 )
= $false )
| ( ( ( ap @ SV301 @ SV586 @ SV734 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) )
= ( ap @ SV301 @ SV586 @ SV911 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) ) )
= $false )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4765]) ).
thf(4867,plain,
! [SV848: $i,SV1068: $i,SV316: $i > $o] :
( ( ( ~ ( ~ ( SV316 @ SV1068 )
| ( SV1068
= ( sK113_SY3190 @ SV848 @ SV316 ) ) )
| ~ ( ( SV1068
!= ( sK113_SY3190 @ SV848 @ SV316 ) )
| ( SV316 @ SV1068 ) ) )
= $false )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV316 @ ( sK85_SY4045 @ SV848 @ SV316 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4766]) ).
thf(4868,plain,
! [SV848: $i,SV1064: $i,SV316: $i > $o] :
( ( ( ~ ( ~ ( SV316 @ SV1064 )
| ( SV1064
= ( sK104_SY3190 @ SV848 @ SV316 ) ) ) )
= $false )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV848
= ( sK85_SY4045 @ SV848 @ SV316 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4767]) ).
thf(4869,plain,
! [SV316: $i > $o,SV848: $i,SV1064: $i] :
( ( ( ~ ( ( SV1064
!= ( sK104_SY3190 @ SV848 @ SV316 ) )
| ( SV316 @ SV1064 ) ) )
= $false )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV848
= ( sK85_SY4045 @ SV848 @ SV316 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4767]) ).
thf(4870,plain,
! [SV322: $i,SV851: $i,SV1059: $i] :
( ( ( ~ ( in @ SV1059 @ ( sK51_SY3211 @ SV851 @ SV322 ) ) )
= $true )
| ( ( ~ ( in @ SV1059 @ SV322 ) )
= $true )
| ( ( in @ SV851 @ SV322 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4770]) ).
thf(4871,plain,
! [SV44: $i,SV1028: $i,SV353: $i > $o] :
( ( ( SV353 @ SV1028 )
= $false )
| ( ( in @ SV1028 @ SV44 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( SV353 @ ( sK9_SY3238 @ SV353 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4772]) ).
thf(4872,plain,
! [SV353: $i > $o,SV44: $i,SV1049: $i] :
( ( ( in @ SV1049 @ SV44 )
= $false )
| ( ( ~ ( SV353 @ SV1049 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( SV353 @ ( sK36_SY3943 @ SV353 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4773]) ).
thf(4873,plain,
! [SV44: $i,SV1029: $i,SV353: $i > $o] :
( ( ( SV353 @ SV1029 )
= $false )
| ( ( in @ SV1029 @ SV44 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( ( sK9_SY3238 @ SV353 @ SV44 )
= ( sK36_SY3943 @ SV353 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4774]) ).
thf(4874,plain,
! [SV765: $i,SV1030: $i,SV1050: $i,SV58: $i > $o] :
( ( ( SV58 @ SV1050 )
= $false )
| ( ( SV1030 = SV1050 )
= $true )
| ( ( SV58 @ SV1030 )
= $false )
| ( ( SV58 @ SV765 )
= $false )
| ( ( SV58 @ ( sK75_SY3949 @ SV765 @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4775]) ).
thf(4875,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ ( sK119_SY2468 @ SV766 @ SV59 ) )
| ~ ! [SY4200: $i] :
( ~ ( SV59 @ SY4200 )
| ( ( sK119_SY2468 @ SV766 @ SV59 )
= SY4200 ) ) )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4777]) ).
thf(4876,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ ( sK114_SY2468 @ SV766 @ SV59 ) ) )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4778]) ).
thf(4877,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ! [SY4196: $i] :
( ~ ( SV59 @ SY4196 )
| ( ( sK114_SY2468 @ SV766 @ SV59 )
= SY4196 ) ) )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4778]) ).
thf(4878,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ ( sK115_SY2468 @ SV766 @ SV59 ) ) )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4779]) ).
thf(4879,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ! [SY4197: $i] :
( ~ ( SV59 @ SY4197 )
| ( ( sK115_SY2468 @ SV766 @ SV59 )
= SY4197 ) ) )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4779]) ).
thf(4880,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( SV59 @ ( sK106_SY2468 @ SV766 @ SV59 ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4780]) ).
thf(4881,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ! [SY4184: $i] :
( ~ ( SV59 @ SY4184 )
| ( ( sK106_SY2468 @ SV766 @ SV59 )
= SY4184 ) ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4781]) ).
thf(4882,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( SV60 @ ( sK107_SY2472 @ SV767 @ SV60 ) )
= $true )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV60 @ ( sK76_SY3951 @ SV767 @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4782]) ).
thf(4883,plain,
! [SV767: $i,SV60: $i > $o] :
( ( ( ! [SY4185: $i] :
( ~ ( SV60 @ SY4185 )
| ( ( sK107_SY2472 @ SV767 @ SV60 )
= SY4185 ) ) )
= $true )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV60 @ ( sK76_SY3951 @ SV767 @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4783]) ).
thf(4884,plain,
! [SV767: $i,SV1074: $i,SV60: $i > $o] :
( ( ( ~ ( SV60 @ SV1074 )
| ( ( sK96_SY2472 @ SV767 @ SV60 )
= SV1074 ) )
= $true )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV767
= ( sK76_SY3951 @ SV767 @ SV60 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4785]) ).
thf(4885,plain,
! [SV78: $i,SV927: $i,SV382: $i,SV994: $i,SV773: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) ) @ SV382 ) )
| ~ ( in @ ( kpair @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) @ SV994 ) @ SV773 ) )
= $false )
| ( ( in @ ( kpair @ SV927 @ SV994 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
= $false )
| ( ( in @ SV994 @ SV78 )
= $false )
| ( ( in @ SV927 @ SV78 )
= $false )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4786]) ).
thf(4886,plain,
! [SV781: $i,SV1075: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV1075 )
| ( ( sK97_SY2565 @ SV781 @ SV100 )
= SV1075 ) )
= $true )
| ( ( SV100 @ ( sK53_SY2563 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4788]) ).
thf(4887,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( SV100 @ ( sK108_SY2565 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ ( sK61_SY4131 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4789]) ).
thf(4888,plain,
! [SV781: $i,SV100: $i > $o] :
( ( ( ! [SY4186: $i] :
( ~ ( SV100 @ SY4186 )
| ( ( sK108_SY2565 @ SV781 @ SV100 )
= SY4186 ) ) )
= $true )
| ( ( SV100 @ ( sK61_SY4131 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4790]) ).
thf(4889,plain,
! [SV781: $i,SV1076: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV1076 )
| ( ( sK98_SY2565 @ SV781 @ SV100 )
= SV1076 ) )
= $true )
| ( ( ( sK53_SY2563 @ SV781 @ SV100 )
= ( sK61_SY4131 @ SV781 @ SV100 ) )
= $false )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4792]) ).
thf(4890,plain,
! [SV420: $i,SV788: $i > $o,SV122: $i,SV865: $i > $o] :
( ( ( ~ ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
| ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) ) )
= $false )
| ( ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) )
= $true )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4793]) ).
thf(4891,plain,
! [SV420: $i,SV788: $i > $o,SV122: $i,SV865: $i > $o] :
( ( ( ~ ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) ) )
= $false )
| ( ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
= $false )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4794]) ).
thf(4892,plain,
! [SV122: $i,SV420: $i,SV865: $i > $o,SV788: $i > $o] :
( ( ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) )
= $false )
| ( ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
= $false )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4794]) ).
thf(4893,plain,
! [SV428: $i,SV131: $i,SV939: $i,SV792: $i,SV998: $i,SV1034: $i] :
( ( ( ~ ( in @ ( kpair @ SV1034 @ SV998 ) @ SV792 ) )
= $true )
| ( ( in @ ( kpair @ SV939 @ SV998 ) @ ( breln1compset @ SV131 @ SV428 @ SV792 ) )
= $true )
| ( ( in @ ( kpair @ SV939 @ SV1034 ) @ SV428 )
= $false )
| ( ( in @ SV1034 @ SV131 )
= $false )
| ( ( in @ SV998 @ SV131 )
= $false )
| ( ( in @ SV939 @ SV131 )
= $false )
| ( ( breln1 @ SV131 @ SV792 )
= $false )
| ( ( breln1 @ SV131 @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4795]) ).
thf(4894,plain,
! [SV436: $i,SV650: $i,SV870: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK125_SY4198 @ SV140 @ SV870 @ SV650 @ SV436 ) @ SV436 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SV140 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4797]) ).
thf(4895,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK116_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK125_SY4198 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV870 )
| ( in @ ( kpair @ ( sK116_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK125_SY4198 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV650 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SV140 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4797]) ).
thf(4896,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( ~ ( in @ ( sK126_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SV140 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) @ SV436 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4798]) ).
thf(4897,plain,
! [SV140: $i,SV870: $i,SV650: $i,SV436: $i] :
( ( ( ! [SY4207: $i] :
( ~ ( in @ SY4207 @ SV436 )
| ~ ( in @ ( kpair @ ( sK126_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SY4207 ) @ SV870 )
| ( in @ ( kpair @ ( sK126_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SY4207 ) @ SV650 ) ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) @ SV436 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4798]) ).
thf(4898,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( ~ ( in @ ( sK132_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SV140 )
| ! [SY4215: $i] :
( ~ ( in @ SY4215 @ SV436 )
| ~ ( in @ ( kpair @ ( sK132_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SY4215 ) @ SV870 )
| ( in @ ( kpair @ ( sK132_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SY4215 ) @ SV650 ) ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV650 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4799]) ).
thf(4899,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( ~ ( in @ ( sK127_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SV140 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4800]) ).
thf(4900,plain,
! [SV140: $i,SV870: $i,SV650: $i,SV436: $i] :
( ( ( ! [SY4208: $i] :
( ~ ( in @ SY4208 @ SV436 )
| ~ ( in @ ( kpair @ ( sK127_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SY4208 ) @ SV870 )
| ( in @ ( kpair @ ( sK127_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SY4208 ) @ SV650 ) ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4800]) ).
thf(4901,plain,
! [SV146: $i,SV1035: $i,SV442: $i > $o] :
( ( ( SV442 @ SV1035 )
= $false )
| ( ( in @ SV1035 @ SV146 )
= $false )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( SV442 @ ( sK11_SY3407 @ SV442 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4802]) ).
thf(4902,plain,
! [SV442: $i > $o,SV146: $i,SV1051: $i] :
( ( ( in @ SV1051 @ SV146 )
= $false )
| ( ( ~ ( SV442 @ SV1051 ) )
= $true )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( SV442 @ ( sK38_SY3987 @ SV442 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4803]) ).
thf(4903,plain,
! [SV146: $i,SV1036: $i,SV442: $i > $o] :
( ( ( SV442 @ SV1036 )
= $false )
| ( ( in @ SV1036 @ SV146 )
= $false )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( ( sK11_SY3407 @ SV442 @ SV146 )
= ( sK38_SY3987 @ SV442 @ SV146 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4804]) ).
thf(4904,plain,
! [SV1010: $i,SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) ) )
= $false )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4805]) ).
thf(4905,plain,
! [SV152: $i > $o,SV448: $i > $o,SV1010: $i] :
( ( ( SV1010
= ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $false )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4805]) ).
thf(4906,plain,
! [SV448: $i > $o,SV1077: $i,SV152: $i > $o] :
( ( ( ~ ~ ( ~ ( SV152 @ SV1077 )
| ~ ! [SY4216: $i] :
( ~ ( SV152 @ SY4216 )
| ( SV1077 = SY4216 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4806]) ).
thf(4907,plain,
! [SV448: $i > $o,SV1069: $i,SV152: $i > $o] :
( ( ( ~ ( ~ ( SV152 @ SV1069 )
| ~ ! [SY4209: $i] :
( ~ ( SV152 @ SY4209 )
| ( SV1069 = SY4209 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4807]) ).
thf(4908,plain,
! [SV448: $i > $o,SV1070: $i,SV152: $i > $o] :
( ( ( ~ ( ~ ( SV152 @ SV1070 )
| ~ ! [SY4210: $i] :
( ~ ( SV152 @ SY4210 )
| ( SV1070 = SY4210 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4808]) ).
thf(4909,plain,
! [SV448: $i > $o,SV1065: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ SV1065 )
| ~ ! [SY4201: $i] :
( ~ ( SV152 @ SY4201 )
| ( SV1065 = SY4201 ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4809]) ).
thf(4910,plain,
! [SV175: $i,SV976: $i,SV470: $i > $i] :
( ( ( ~ ( in @ ( sK117_SY4135 @ SV470 @ SV976 @ SV175 ) @ SV175 ) )
= $false )
| ( ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4810]) ).
thf(4911,plain,
! [SV175: $i,SV470: $i > $i,SV976: $i] :
( ( ( SV976
!= ( SV470 @ ( sK117_SY4135 @ SV470 @ SV976 @ SV175 ) ) )
= $false )
| ( ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4810]) ).
thf(4912,plain,
! [SV470: $i > $i,SV976: $i,SV175: $i,SV1060: $i] :
( ( ( ~ ( in @ SV1060 @ SV175 ) )
= $true )
| ( ( SV976
!= ( SV470 @ SV1060 ) )
= $true )
| ( ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4811]) ).
thf(4913,plain,
! [SV977: $i,SV470: $i > $i,SV175: $i] :
( ( ( ~ ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) ) )
= $false )
| ( ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4812]) ).
thf(4914,plain,
! [SV977: $i,SV175: $i,SV470: $i > $i] :
( ( ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
= $false )
| ( ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4812]) ).
thf(4915,plain,
! [SV977: $i,SV470: $i > $i,SV175: $i,SV1071: $i] :
( ( ( ~ ( ~ ( in @ SV1071 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SV1071 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) )
| ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 ) ) )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4813]) ).
thf(4916,plain,
! [SV979: $i,SV670: $i > $i > $o,SV180: $i,SV1052: $i,SV475: $i] :
( ( ( reflwellordering @ SV475 @ SV1052 )
= $false )
| ( ( ! [SY4187: $i] :
( ~ ( in @ SY4187 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY4188: $i] :
~ ( ~ ( SV670 @ SY4187 @ SY4188 )
| ~ ! [SY4189: $i] :
( ~ ( in @ SY4189 @ SV475 )
| ~ ( SV670 @ SY4187 @ SY4189 )
| ( in @ ( kpair @ SY4188 @ SY4189 ) @ SV1052 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV1052 @ ( breln1Set @ SV475 ) )
= $false )
| ( ( in @ SV979 @ SV475 )
= $false )
| ( ( SV670 @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV979 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4814]) ).
thf(4917,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( SV196 @ ( sK109_SY2855 @ SV816 @ SV196 ) )
= $true )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV196 @ ( sK80_SY4002 @ SV816 @ SV196 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4816]) ).
thf(4918,plain,
! [SV816: $i,SV196: $i > $o] :
( ( ( ! [SY4190: $i] :
( ~ ( SV196 @ SY4190 )
| ( ( sK109_SY2855 @ SV816 @ SV196 )
= SY4190 ) ) )
= $true )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV196 @ ( sK80_SY4002 @ SV816 @ SV196 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4817]) ).
thf(4919,plain,
! [SV816: $i,SV1078: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ SV1078 )
| ( ( sK101_SY2855 @ SV816 @ SV196 )
= SV1078 ) )
= $true )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV816
= ( sK80_SY4002 @ SV816 @ SV196 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4819]) ).
thf(4920,plain,
! [SV491: $i > $o,SV1053: $i,SV197: $i > $o] :
( ( ( SV197 @ SV1053 )
= $false )
| ( ( ~ ! [SY4191: $i] :
( ~ ( SV197 @ SY4191 )
| ( SV1053 = SY4191 ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4820]) ).
thf(4921,plain,
! [SV197: $i > $o,SV1054: $i,SV491: $i > $o] :
( ( ( SV491 @ SV1054 )
= $false )
| ( ( ~ ! [SY4192: $i] :
( ~ ( SV491 @ SY4192 )
| ( SV1054 = SY4192 ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4821]) ).
thf(4922,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4822]) ).
thf(4923,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4823]) ).
thf(4924,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) ) )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4824]) ).
thf(4925,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) ) )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4825]) ).
thf(4926,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) ) )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4826]) ).
thf(4927,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) ) )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4827]) ).
thf(4928,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4828]) ).
thf(4929,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4829]) ).
thf(4930,plain,
! [SV208: $i,SV501: $i,SV952: $o,SV818: $i,SV982: $i] :
( ( ( ~ ( in @ SV982 @ SV818 )
| SV952 )
= $false )
| ( SV952 = $true )
| ( ( in @ SV982 @ SV501 )
= $true )
| ( ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV982 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4830]) ).
thf(4931,plain,
! [SV208: $i,SV501: $i,SV952: $o,SV818: $i,SV982: $i] :
( ( ( ~ ( in @ SV982 @ SV818 ) )
= $false )
| ( SV952 = $true )
| ( SV952 = $false )
| ( ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV982 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4831]) ).
thf(4932,plain,
! [SV208: $i,SV818: $i,SV501: $i,SV982: $i,SV952: $o] :
( ( SV952 = $false )
| ( SV952 = $true )
| ( SV952 = $false )
| ( ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV982 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4831]) ).
thf(4933,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV983: $i] :
( ( ( ~ ( in @ SV983 @ SV818 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV983 @ SV501 )
= $true )
| ( ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV983 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4832]) ).
thf(4934,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV983: $i] :
( ( ( ~ ( in @ SV983 @ SV818 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV983 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4833]) ).
thf(4935,plain,
! [SV208: $i,SV818: $i,SV501: $i,SV983: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV983 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4833]) ).
thf(4936,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV984: $i] :
( ( ( ~ ( in @ SV984 @ SV818 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV984 @ SV501 )
= $true )
| ( ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV984 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4834]) ).
thf(4937,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV984: $i] :
( ( ( ~ ( in @ SV984 @ SV818 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV984 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4835]) ).
thf(4938,plain,
! [SV208: $i,SV818: $i,SV501: $i,SV984: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV984 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4835]) ).
thf(4939,plain,
! [SV216: $i,SV1061: $o,SV819: $i,SV508: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| SV1061 )
| SV1061 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4836]) ).
thf(4940,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i,SV1061: $o] :
( ( SV1061 = $false )
| ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| SV1061 )
| SV1061 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4836]) ).
thf(4941,plain,
! [SV216: $i,SV819: $i,SV508: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $true )
| $true )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4837]) ).
thf(4942,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $true )
| $true )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4837]) ).
thf(4943,plain,
! [SV216: $i,SV819: $i,SV508: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $false )
| $false )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4838]) ).
thf(4944,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $false )
| $false )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4838]) ).
thf(4945,plain,
! [SV226: $i,SV1040: $i,SV1066: $i] :
( ( ( in @ SV1066 @ SV1040 )
= $false )
| ( ( in @ SV1066 @ SV226 )
= $true )
| ( ( in @ SV1040 @ ( sK2_SY2943 @ SV226 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4839]) ).
thf(4946,plain,
! [SV1056: $i,SV226: $i,SV1041: $i] :
( ( ( ~ ( in @ SV1041 @ SV226 ) )
= $true )
| ( ( ~ ( in @ SV1056 @ SV226 ) )
= $true )
| ( ( ~ ! [SY4193: $i] :
( ~ ( in @ SY4193 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SV1041 @ SY4193 )
| ( in @ SV1056 @ SY4193 ) )
| ~ ( ~ ( in @ SV1056 @ SY4193 )
| ( in @ SV1041 @ SY4193 ) ) ) )
| ( SV1041 = SV1056 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4840]) ).
thf(4947,plain,
! [SV226: $i,SV1014: $i,SV1002: $i] :
( ( ( ! [SY4166: $i] :
( ~ ( in @ SY4166 @ SV1002 )
| ( in @ SY4166 @ SV1014 ) ) )
= $true )
| ( ( ! [SY4167: $i] :
( ~ ( in @ SY4167 @ SV1014 )
| ( in @ SY4167 @ SV1002 ) ) )
= $true )
| ( ( in @ SV1002 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( in @ SV1014 @ ( sK2_SY2943 @ SV226 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4841]) ).
thf(4948,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( ~ ( in @ SV1079 @ SV955 ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( ~ ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4842]) ).
thf(4949,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( in @ SV1072 @ SV955 )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( ~ ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4843]) ).
thf(4950,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1003: $i] :
( ( ( ~ ( ~ ( in @ ( sK129_SY4159 @ SV1003 @ SV230 @ SV520 ) @ SV520 )
| ~ ( SV230 @ ( sK129_SY4159 @ SV1003 @ SV230 @ SV520 ) @ SV1003 ) ) )
= $true )
| ( ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
= $false )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4844]) ).
thf(4951,plain,
! [SV1003: $i,SV230: $i > $i > $o,SV520: $i,SV1073: $i] :
( ( ( ~ ( ~ ( in @ SV1073 @ SV520 )
| ~ ( SV230 @ SV1073 @ SV1003 ) ) )
= $false )
| ( ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
= $true )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4845]) ).
thf(4952,plain,
! [SV520: $i,SV230: $i > $i > $o,SV957: $i] :
( ( ( ! [SY4211: $i] :
~ ( ~ ( ~ ( in @ SY4211 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
| ~ ! [SY3587: $i] :
~ ~ ( ~ ( in @ SY3587 @ SV520 )
| ~ ( SV230 @ SY3587 @ SY4211 ) ) )
| ~ ( ~ ~ ! [SY3588: $i] :
~ ~ ( ~ ( in @ SY3588 @ SV520 )
| ~ ( SV230 @ SY3588 @ SY4211 ) )
| ( in @ SY4211 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) ) ) ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4846]) ).
thf(4953,plain,
! [SV520: $i,SV230: $i > $i > $o,SV957: $i,SV1080: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
| ~ ! [SY4217: $i] :
~ ~ ( ~ ( in @ SY4217 @ SV520 )
| ~ ( SV230 @ SY4217 @ SV1080 ) ) )
| ~ ( ~ ~ ! [SY4218: $i] :
~ ~ ( ~ ( in @ SY4218 @ SV520 )
| ~ ( SV230 @ SY4218 @ SV1080 ) )
| ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) ) ) ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4847]) ).
thf(4954,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( in @ ( sK122_SY4194 @ SV829 @ SV549 @ SV260 ) @ SV260 )
= $true )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4848]) ).
thf(4955,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK110_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK122_SY4194 @ SV829 @ SV549 @ SV260 ) ) @ SV829 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4849]) ).
thf(4956,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( in @ ( kpair @ ( sK110_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK122_SY4194 @ SV829 @ SV549 @ SV260 ) ) @ SV549 )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4849]) ).
thf(4957,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( in @ ( sK123_SY4022 @ SV549 @ SV829 @ SV260 ) @ SV260 )
= $true )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4850]) ).
thf(4958,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK133_SY4205 @ SV829 @ SV549 @ SV260 ) @ SV260 )
| ~ ( in @ ( kpair @ ( sK123_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK133_SY4205 @ SV829 @ SV549 @ SV260 ) ) @ SV829 )
| ( in @ ( kpair @ ( sK123_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK133_SY4205 @ SV829 @ SV549 @ SV260 ) ) @ SV549 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4851]) ).
thf(4959,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( ~ ( in @ ( sK131_SY4022 @ SV549 @ SV829 @ SV260 ) @ SV260 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV549 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4852]) ).
thf(4960,plain,
! [SV829: $i,SV549: $i,SV260: $i] :
( ( ( ! [SY4214: $i] :
( ~ ( in @ SY4214 @ SV260 )
| ~ ( in @ ( kpair @ ( sK131_SY4022 @ SV549 @ SV829 @ SV260 ) @ SY4214 ) @ SV829 )
| ( in @ ( kpair @ ( sK131_SY4022 @ SV549 @ SV829 @ SV260 ) @ SY4214 ) @ SV549 ) ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV549 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4852]) ).
thf(4961,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( in @ ( sK124_SY4022 @ SV549 @ SV829 @ SV260 ) @ SV260 )
= $true )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4853]) ).
thf(4962,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK134_SY4206 @ SV829 @ SV549 @ SV260 ) @ SV260 )
| ~ ( in @ ( kpair @ ( sK124_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK134_SY4206 @ SV829 @ SV549 @ SV260 ) ) @ SV829 )
| ( in @ ( kpair @ ( sK124_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK134_SY4206 @ SV829 @ SV549 @ SV260 ) ) @ SV549 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4854]) ).
thf(4963,plain,
! [SV280: $i,SV963: $i,SV568: $i,SV1007: $i,SV836: $i,SV1062: $o] :
( ( ( ~ ( in @ ( sK135_SY4199 @ SV1062 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ ( sK135_SY4199 @ SV1062 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) ) @ SV568 )
| ~ ( in @ ( kpair @ ( sK135_SY4199 @ SV1062 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV1007 ) @ SV836 )
| SV1062 )
= $false )
| ( SV1062 = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4855]) ).
thf(4964,plain,
! [SV280: $i,SV963: $i,SV568: $i,SV1007: $i,SV836: $i] :
( ( ( ~ ( in @ ( sK136_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ ( sK136_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) ) @ SV568 )
| ~ ( in @ ( kpair @ ( sK136_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV1007 ) @ SV836 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4856]) ).
thf(4965,plain,
! [SV280: $i,SV963: $i,SV568: $i,SV1007: $i,SV836: $i] :
( ( ( ~ ( in @ ( sK137_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV280 )
| ~ ( in @ ( kpair @ SV963 @ ( sK137_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) ) @ SV568 )
| ~ ( in @ ( kpair @ ( sK137_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV1007 ) @ SV836 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4857]) ).
thf(4966,plain,
! [SV837: $i,SV1044: $i,SV1057: $i,SV288: $i > $o] :
( ( ( SV288 @ SV1057 )
= $false )
| ( ( SV1044 = SV1057 )
= $true )
| ( ( SV288 @ SV1044 )
= $false )
| ( ( SV288 @ SV837 )
= $false )
| ( ( SV288 @ ( sK83_SY4034 @ SV837 @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4858]) ).
thf(4967,plain,
! [SV299: $i,SV840: $i,SV584: $i] :
( ( ( in @ ( sK118_SY4036 @ SV584 @ SV840 @ SV299 ) @ SV840 )
= $true )
| ( ( SV584 = SV840 )
= $true )
| ( ( in @ ( sK70_SY4035 @ SV840 @ SV584 @ SV299 ) @ SV584 )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4862]) ).
thf(4968,plain,
! [SV301: $i,SV734: $i,SV911: $i,SV1046: $i,SV586: $i,SV1067: $i] :
( ( ( in @ SV1067 @ SV586 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV1046 @ SV1067 ) @ SV911 )
| ( in @ ( kpair @ SV1046 @ SV1067 ) @ SV734 ) )
= $true )
| ( ( in @ SV1046 @ SV301 )
= $false )
| ( ( in @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) @ SV301 )
= $true )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4865]) ).
thf(4969,plain,
! [SV301: $i,SV586: $i,SV734: $i,SV911: $i,SV1063: $i,SV1027: $i] :
( ( ( ~ ( in @ ( kpair @ SV1027 @ SV1063 ) @ SV911 ) )
= $true )
| ( ( in @ ( kpair @ SV1027 @ SV1063 ) @ SV734 )
= $true )
| ( ( in @ SV1063 @ SV586 )
= $false )
| ( ( in @ SV1027 @ SV301 )
= $false )
| ( ( ( ap @ SV301 @ SV586 @ SV734 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) )
= ( ap @ SV301 @ SV586 @ SV911 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) ) )
= $false )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4866]) ).
thf(4970,plain,
! [SV848: $i,SV1068: $i,SV316: $i > $o] :
( ( ( ~ ( ~ ( SV316 @ SV1068 )
| ( SV1068
= ( sK113_SY3190 @ SV848 @ SV316 ) ) ) )
= $false )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV316 @ ( sK85_SY4045 @ SV848 @ SV316 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4867]) ).
thf(4971,plain,
! [SV316: $i > $o,SV848: $i,SV1068: $i] :
( ( ( ~ ( ( SV1068
!= ( sK113_SY3190 @ SV848 @ SV316 ) )
| ( SV316 @ SV1068 ) ) )
= $false )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV316 @ ( sK85_SY4045 @ SV848 @ SV316 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4867]) ).
thf(4972,plain,
! [SV848: $i,SV1064: $i,SV316: $i > $o] :
( ( ( ~ ( SV316 @ SV1064 )
| ( SV1064
= ( sK104_SY3190 @ SV848 @ SV316 ) ) )
= $true )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV848
= ( sK85_SY4045 @ SV848 @ SV316 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4868]) ).
thf(4973,plain,
! [SV316: $i > $o,SV848: $i,SV1064: $i] :
( ( ( ( SV1064
!= ( sK104_SY3190 @ SV848 @ SV316 ) )
| ( SV316 @ SV1064 ) )
= $true )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV848
= ( sK85_SY4045 @ SV848 @ SV316 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4869]) ).
thf(4974,plain,
! [SV322: $i,SV851: $i,SV1059: $i] :
( ( ( in @ SV1059 @ ( sK51_SY3211 @ SV851 @ SV322 ) )
= $false )
| ( ( ~ ( in @ SV1059 @ SV322 ) )
= $true )
| ( ( in @ SV851 @ SV322 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4870]) ).
thf(4975,plain,
! [SV44: $i,SV1049: $i,SV353: $i > $o] :
( ( ( SV353 @ SV1049 )
= $false )
| ( ( in @ SV1049 @ SV44 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV44
@ ^ [SY3241: $i] : ( SV353 @ SY3241 ) ) )
= $true )
| ( ( SV353 @ ( sK36_SY3943 @ SV353 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4872]) ).
thf(4976,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ ( sK119_SY2468 @ SV766 @ SV59 ) ) )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4875]) ).
thf(4977,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ~ ! [SY4200: $i] :
( ~ ( SV59 @ SY4200 )
| ( ( sK119_SY2468 @ SV766 @ SV59 )
= SY4200 ) ) )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4875]) ).
thf(4978,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( SV59 @ ( sK114_SY2468 @ SV766 @ SV59 ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4876]) ).
thf(4979,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ! [SY4196: $i] :
( ~ ( SV59 @ SY4196 )
| ( ( sK114_SY2468 @ SV766 @ SV59 )
= SY4196 ) ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4877]) ).
thf(4980,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( SV59 @ ( sK115_SY2468 @ SV766 @ SV59 ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4878]) ).
thf(4981,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ! [SY4197: $i] :
( ~ ( SV59 @ SY4197 )
| ( ( sK115_SY2468 @ SV766 @ SV59 )
= SY4197 ) ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4879]) ).
thf(4982,plain,
! [SV766: $i,SV1081: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ SV1081 )
| ( ( sK106_SY2468 @ SV766 @ SV59 )
= SV1081 ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4881]) ).
thf(4983,plain,
! [SV767: $i,SV1082: $i,SV60: $i > $o] :
( ( ( ~ ( SV60 @ SV1082 )
| ( ( sK107_SY2472 @ SV767 @ SV60 )
= SV1082 ) )
= $true )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV60 @ ( sK76_SY3951 @ SV767 @ SV60 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4883]) ).
thf(4984,plain,
! [SV767: $i,SV1074: $i,SV60: $i > $o] :
( ( ( ~ ( SV60 @ SV1074 ) )
= $true )
| ( ( ( sK96_SY2472 @ SV767 @ SV60 )
= SV1074 )
= $true )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV767
= ( sK76_SY3951 @ SV767 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4884]) ).
thf(4985,plain,
! [SV78: $i,SV927: $i,SV382: $i,SV994: $i,SV773: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) ) @ SV382 ) ) )
= $false )
| ( ( in @ ( kpair @ SV927 @ SV994 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
= $false )
| ( ( in @ SV994 @ SV78 )
= $false )
| ( ( in @ SV927 @ SV78 )
= $false )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4885]) ).
thf(4986,plain,
! [SV78: $i,SV927: $i,SV382: $i,SV994: $i,SV773: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) @ SV994 ) @ SV773 ) )
= $false )
| ( ( in @ ( kpair @ SV927 @ SV994 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
= $false )
| ( ( in @ SV994 @ SV78 )
= $false )
| ( ( in @ SV927 @ SV78 )
= $false )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4885]) ).
thf(4987,plain,
! [SV781: $i,SV1075: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV1075 ) )
= $true )
| ( ( ( sK97_SY2565 @ SV781 @ SV100 )
= SV1075 )
= $true )
| ( ( SV100 @ ( sK53_SY2563 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4886]) ).
thf(4988,plain,
! [SV781: $i,SV1083: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV1083 )
| ( ( sK108_SY2565 @ SV781 @ SV100 )
= SV1083 ) )
= $true )
| ( ( SV100 @ ( sK61_SY4131 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4888]) ).
thf(4989,plain,
! [SV781: $i,SV1076: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV1076 ) )
= $true )
| ( ( ( sK98_SY2565 @ SV781 @ SV100 )
= SV1076 )
= $true )
| ( ( ( sK53_SY2563 @ SV781 @ SV100 )
= ( sK61_SY4131 @ SV781 @ SV100 ) )
= $false )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4889]) ).
thf(4990,plain,
! [SV420: $i,SV788: $i > $o,SV122: $i,SV865: $i > $o] :
( ( ( ~ ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) ) )
= $false )
| ( ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) )
= $true )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4890]) ).
thf(4991,plain,
! [SV122: $i,SV420: $i,SV865: $i > $o,SV788: $i > $o] :
( ( ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) )
= $false )
| ( ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) )
= $true )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4890]) ).
thf(4992,plain,
! [SV420: $i,SV788: $i > $o,SV122: $i,SV865: $i > $o] :
( ( ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
= $true )
| ( ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
= $false )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4891]) ).
thf(4993,plain,
! [SV428: $i,SV131: $i,SV939: $i,SV792: $i,SV998: $i,SV1034: $i] :
( ( ( in @ ( kpair @ SV1034 @ SV998 ) @ SV792 )
= $false )
| ( ( in @ ( kpair @ SV939 @ SV998 ) @ ( breln1compset @ SV131 @ SV428 @ SV792 ) )
= $true )
| ( ( in @ ( kpair @ SV939 @ SV1034 ) @ SV428 )
= $false )
| ( ( in @ SV1034 @ SV131 )
= $false )
| ( ( in @ SV998 @ SV131 )
= $false )
| ( ( in @ SV939 @ SV131 )
= $false )
| ( ( breln1 @ SV131 @ SV792 )
= $false )
| ( ( breln1 @ SV131 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4893]) ).
thf(4994,plain,
! [SV436: $i,SV650: $i,SV870: $i,SV140: $i] :
( ( ( in @ ( sK125_SY4198 @ SV140 @ SV870 @ SV650 @ SV436 ) @ SV436 )
= $true )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SV140 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4894]) ).
thf(4995,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK116_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK125_SY4198 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV870 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SV140 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4895]) ).
thf(4996,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( in @ ( kpair @ ( sK116_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK125_SY4198 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV650 )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SV140 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4895]) ).
thf(4997,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( in @ ( sK126_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SV140 )
= $true )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) @ SV436 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4896]) ).
thf(4998,plain,
! [SV436: $i,SV650: $i,SV870: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK138_SY4207 @ SV140 @ SV870 @ SV650 @ SV436 ) @ SV436 )
| ~ ( in @ ( kpair @ ( sK126_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK138_SY4207 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV870 )
| ( in @ ( kpair @ ( sK126_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK138_SY4207 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV650 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) @ SV436 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4897]) ).
thf(4999,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( ~ ( in @ ( sK132_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SV140 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV650 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4898]) ).
thf(5000,plain,
! [SV140: $i,SV870: $i,SV650: $i,SV436: $i] :
( ( ( ! [SY4215: $i] :
( ~ ( in @ SY4215 @ SV436 )
| ~ ( in @ ( kpair @ ( sK132_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SY4215 ) @ SV870 )
| ( in @ ( kpair @ ( sK132_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SY4215 ) @ SV650 ) ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV650 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4898]) ).
thf(5001,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( in @ ( sK127_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SV140 )
= $true )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4899]) ).
thf(5002,plain,
! [SV436: $i,SV650: $i,SV870: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK139_SY4208 @ SV140 @ SV870 @ SV650 @ SV436 ) @ SV436 )
| ~ ( in @ ( kpair @ ( sK127_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK139_SY4208 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV870 )
| ( in @ ( kpair @ ( sK127_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK139_SY4208 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV650 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4900]) ).
thf(5003,plain,
! [SV146: $i,SV1051: $i,SV442: $i > $o] :
( ( ( SV442 @ SV1051 )
= $false )
| ( ( in @ SV1051 @ SV146 )
= $false )
| ( ( ex1 @ SV146
@ ^ [SY3410: $i] : ( SV442 @ SY3410 ) )
= $true )
| ( ( SV442 @ ( sK38_SY3987 @ SV442 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4902]) ).
thf(5004,plain,
! [SV1010: $i,SV448: $i > $o,SV152: $i > $o] :
( ( ( SV152 @ ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4904]) ).
thf(5005,plain,
! [SV1010: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV1010
= ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $false )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4905]) ).
thf(5006,plain,
! [SV448: $i > $o,SV1077: $i,SV152: $i > $o] :
( ( ( ~ ( ~ ( SV152 @ SV1077 )
| ~ ! [SY4216: $i] :
( ~ ( SV152 @ SY4216 )
| ( SV1077 = SY4216 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4906]) ).
thf(5007,plain,
! [SV448: $i > $o,SV1069: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ SV1069 )
| ~ ! [SY4209: $i] :
( ~ ( SV152 @ SY4209 )
| ( SV1069 = SY4209 ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4907]) ).
thf(5008,plain,
! [SV448: $i > $o,SV1070: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ SV1070 )
| ~ ! [SY4210: $i] :
( ~ ( SV152 @ SY4210 )
| ( SV1070 = SY4210 ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4908]) ).
thf(5009,plain,
! [SV448: $i > $o,SV1065: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ SV1065 ) )
= $true )
| ( ( ~ ! [SY4201: $i] :
( ~ ( SV152 @ SY4201 )
| ( SV1065 = SY4201 ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4909]) ).
thf(5010,plain,
! [SV175: $i,SV976: $i,SV470: $i > $i] :
( ( ( in @ ( sK117_SY4135 @ SV470 @ SV976 @ SV175 ) @ SV175 )
= $true )
| ( ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4910]) ).
thf(5011,plain,
! [SV175: $i,SV470: $i > $i,SV976: $i] :
( ( ( SV976
= ( SV470 @ ( sK117_SY4135 @ SV470 @ SV976 @ SV175 ) ) )
= $true )
| ( ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4911]) ).
thf(5012,plain,
! [SV470: $i > $i,SV976: $i,SV175: $i,SV1060: $i] :
( ( ( in @ SV1060 @ SV175 )
= $false )
| ( ( SV976
!= ( SV470 @ SV1060 ) )
= $true )
| ( ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4912]) ).
thf(5013,plain,
! [SV977: $i,SV470: $i > $i,SV175: $i] :
( ( ( ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) ) )
= $true )
| ( ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4913]) ).
thf(5014,plain,
! [SV977: $i,SV470: $i > $i,SV175: $i,SV1071: $i] :
( ( ( ~ ( in @ SV1071 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SV1071 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) )
| ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 ) ) )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4915]) ).
thf(5015,plain,
! [SV979: $i,SV1052: $i,SV670: $i > $i > $o,SV475: $i,SV180: $i,SV1084: $i] :
( ( ( ~ ( in @ SV1084 @ SV180 )
| ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY4219: $i] :
~ ( ~ ( SV670 @ SV1084 @ SY4219 )
| ~ ! [SY4220: $i] :
( ~ ( in @ SY4220 @ SV475 )
| ~ ( SV670 @ SV1084 @ SY4220 )
| ( in @ ( kpair @ SY4219 @ SY4220 ) @ SV1052 ) ) ) ) ) )
= $true )
| ( ( reflwellordering @ SV475 @ SV1052 )
= $false )
| ( ( in @ SV1052 @ ( breln1Set @ SV475 ) )
= $false )
| ( ( in @ SV979 @ SV475 )
= $false )
| ( ( SV670 @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV979 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4916]) ).
thf(5016,plain,
! [SV816: $i,SV1085: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ SV1085 )
| ( ( sK109_SY2855 @ SV816 @ SV196 )
= SV1085 ) )
= $true )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV196 @ ( sK80_SY4002 @ SV816 @ SV196 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4918]) ).
thf(5017,plain,
! [SV816: $i,SV1078: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ SV1078 ) )
= $true )
| ( ( ( sK101_SY2855 @ SV816 @ SV196 )
= SV1078 )
= $true )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV816
= ( sK80_SY4002 @ SV816 @ SV196 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4919]) ).
thf(5018,plain,
! [SV491: $i > $o,SV1053: $i,SV197: $i > $o] :
( ( ( ! [SY4191: $i] :
( ~ ( SV197 @ SY4191 )
| ( SV1053 = SY4191 ) ) )
= $false )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4920]) ).
thf(5019,plain,
! [SV197: $i > $o,SV1054: $i,SV491: $i > $o] :
( ( ( ! [SY4192: $i] :
( ~ ( SV491 @ SY4192 )
| ( SV1054 = SY4192 ) ) )
= $false )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4921]) ).
thf(5020,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) ) )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4922]) ).
thf(5021,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) ) )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4923]) ).
thf(5022,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4924]) ).
thf(5023,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4925]) ).
thf(5024,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4926]) ).
thf(5025,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4927]) ).
thf(5026,plain,
! [SV491: $i > $o,SV1086: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ SV1086 )
| ~ ! [SY4221: $i] :
( ~ ( SV197 @ SY4221 )
| ( SV1086 = SY4221 ) ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4928]) ).
thf(5027,plain,
! [SV197: $i > $o,SV1087: $i,SV491: $i > $o] :
( ( ( ~ ~ ( ~ ( SV491 @ SV1087 )
| ~ ! [SY4222: $i] :
( ~ ( SV491 @ SY4222 )
| ( SV1087 = SY4222 ) ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4929]) ).
thf(5028,plain,
! [SV208: $i,SV501: $i,SV952: $o,SV818: $i,SV982: $i] :
( ( ( ~ ( in @ SV982 @ SV818 ) )
= $false )
| ( SV952 = $true )
| ( ( in @ SV982 @ SV501 )
= $true )
| ( ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV982 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4930]) ).
thf(5029,plain,
! [SV208: $i,SV818: $i,SV501: $i,SV982: $i,SV952: $o] :
( ( SV952 = $false )
| ( SV952 = $true )
| ( ( in @ SV982 @ SV501 )
= $true )
| ( ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV982 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4930]) ).
thf(5030,plain,
! [SV208: $i,SV501: $i,SV952: $o,SV818: $i,SV982: $i] :
( ( ( in @ SV982 @ SV818 )
= $true )
| ( SV952 = $true )
| ( SV952 = $false )
| ( ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV982 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4931]) ).
thf(5031,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV983: $i] :
( ( ( ~ ( in @ SV983 @ SV818 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV983 @ SV501 )
= $true )
| ( ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV983 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4933]) ).
thf(5032,plain,
! [SV208: $i,SV818: $i,SV501: $i,SV983: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV983 @ SV501 )
= $true )
| ( ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV983 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4933]) ).
thf(5033,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV983: $i] :
( ( ( in @ SV983 @ SV818 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV983 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4934]) ).
thf(5034,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV984: $i] :
( ( ( ~ ( in @ SV984 @ SV818 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV984 @ SV501 )
= $true )
| ( ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV984 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4936]) ).
thf(5035,plain,
! [SV208: $i,SV818: $i,SV501: $i,SV984: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV984 @ SV501 )
= $true )
| ( ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV984 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4936]) ).
thf(5036,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV984: $i] :
( ( ( in @ SV984 @ SV818 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV984 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4937]) ).
thf(5037,plain,
! [SV216: $i,SV1061: $o,SV819: $i,SV508: $i,SV1001: $i,SV953: $i] :
( ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
= $true )
| ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| SV1061 )
| SV1061 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4939]) ).
thf(5038,plain,
! [SV216: $i,SV508: $i,SV1061: $o,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| SV1061 ) )
= $true )
| ( SV1061 = $true )
| ( SV1061 = $false )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4940]) ).
thf(5039,plain,
! [SV216: $i,SV819: $i,SV508: $i,SV1001: $i,SV953: $i] :
( ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
= $true )
| ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $true )
| $true )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4941]) ).
thf(5040,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4942]) ).
thf(5041,plain,
! [SV216: $i,SV819: $i,SV508: $i,SV1001: $i,SV953: $i] :
( ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
= $true )
| ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $false )
| $false )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4943]) ).
thf(5042,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4944]) ).
thf(5043,plain,
! [SV1056: $i,SV226: $i,SV1041: $i] :
( ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( ~ ( in @ SV1056 @ SV226 ) )
= $true )
| ( ( ~ ! [SY4193: $i] :
( ~ ( in @ SY4193 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SV1041 @ SY4193 )
| ( in @ SV1056 @ SY4193 ) )
| ~ ( ~ ( in @ SV1056 @ SY4193 )
| ( in @ SV1041 @ SY4193 ) ) ) )
| ( SV1041 = SV1056 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4946]) ).
thf(5044,plain,
! [SV226: $i,SV1014: $i,SV1002: $i,SV1088: $i] :
( ( ( ~ ( in @ SV1088 @ SV1002 )
| ( in @ SV1088 @ SV1014 ) )
= $true )
| ( ( ! [SY4167: $i] :
( ~ ( in @ SY4167 @ SV1014 )
| ( in @ SY4167 @ SV1002 ) ) )
= $true )
| ( ( in @ SV1002 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( in @ SV1014 @ ( sK2_SY2943 @ SV226 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4947]) ).
thf(5045,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( in @ SV1079 @ SV955 )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( ~ ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4948]) ).
thf(5046,plain,
! [SV1072: $i,SV955: $i,SV226: $i] :
( ( ( ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4949]) ).
thf(5047,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1003: $i] :
( ( ( ~ ( in @ ( sK129_SY4159 @ SV1003 @ SV230 @ SV520 ) @ SV520 )
| ~ ( SV230 @ ( sK129_SY4159 @ SV1003 @ SV230 @ SV520 ) @ SV1003 ) )
= $false )
| ( ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
= $false )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4950]) ).
thf(5048,plain,
! [SV1003: $i,SV230: $i > $i > $o,SV520: $i,SV1073: $i] :
( ( ( ~ ( in @ SV1073 @ SV520 )
| ~ ( SV230 @ SV1073 @ SV1003 ) )
= $true )
| ( ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
= $true )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4951]) ).
thf(5049,plain,
! [SV520: $i,SV230: $i > $i > $o,SV957: $i,SV1089: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
| ~ ! [SY4223: $i] :
~ ~ ( ~ ( in @ SY4223 @ SV520 )
| ~ ( SV230 @ SY4223 @ SV1089 ) ) )
| ~ ( ~ ~ ! [SY4224: $i] :
~ ~ ( ~ ( in @ SY4224 @ SV520 )
| ~ ( SV230 @ SY4224 @ SV1089 ) )
| ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) ) ) ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4952]) ).
thf(5050,plain,
! [SV520: $i,SV230: $i > $i > $o,SV957: $i,SV1080: $i] :
( ( ( ~ ( ~ ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
| ~ ! [SY4217: $i] :
~ ~ ( ~ ( in @ SY4217 @ SV520 )
| ~ ( SV230 @ SY4217 @ SV1080 ) ) )
| ~ ( ~ ~ ! [SY4218: $i] :
~ ~ ( ~ ( in @ SY4218 @ SV520 )
| ~ ( SV230 @ SY4218 @ SV1080 ) )
| ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) ) ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4953]) ).
thf(5051,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( in @ ( kpair @ ( sK110_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK122_SY4194 @ SV829 @ SV549 @ SV260 ) ) @ SV829 )
= $true )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4955]) ).
thf(5052,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK133_SY4205 @ SV829 @ SV549 @ SV260 ) @ SV260 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4958]) ).
thf(5053,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK123_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK133_SY4205 @ SV829 @ SV549 @ SV260 ) ) @ SV829 )
| ( in @ ( kpair @ ( sK123_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK133_SY4205 @ SV829 @ SV549 @ SV260 ) ) @ SV549 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4958]) ).
thf(5054,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( in @ ( sK131_SY4022 @ SV549 @ SV829 @ SV260 ) @ SV260 )
= $true )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV549 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4959]) ).
thf(5055,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK140_SY4214 @ SV829 @ SV549 @ SV260 ) @ SV260 )
| ~ ( in @ ( kpair @ ( sK131_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK140_SY4214 @ SV829 @ SV549 @ SV260 ) ) @ SV829 )
| ( in @ ( kpair @ ( sK131_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK140_SY4214 @ SV829 @ SV549 @ SV260 ) ) @ SV549 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV549 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4960]) ).
thf(5056,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK134_SY4206 @ SV829 @ SV549 @ SV260 ) @ SV260 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4962]) ).
thf(5057,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK124_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK134_SY4206 @ SV829 @ SV549 @ SV260 ) ) @ SV829 )
| ( in @ ( kpair @ ( sK124_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK134_SY4206 @ SV829 @ SV549 @ SV260 ) ) @ SV549 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4962]) ).
thf(5058,plain,
! [SV280: $i,SV963: $i,SV568: $i,SV1007: $i,SV836: $i,SV1062: $o] :
( ( ( ~ ( in @ ( sK135_SY4199 @ SV1062 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV280 ) )
= $false )
| ( SV1062 = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4963]) ).
thf(5059,plain,
! [SV280: $i,SV568: $i,SV1007: $i,SV836: $i,SV1062: $o,SV963: $i] :
( ( ( ~ ( in @ ( kpair @ SV963 @ ( sK135_SY4199 @ SV1062 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) ) @ SV568 )
| ~ ( in @ ( kpair @ ( sK135_SY4199 @ SV1062 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV1007 ) @ SV836 )
| SV1062 )
= $false )
| ( SV1062 = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4963]) ).
thf(5060,plain,
! [SV280: $i,SV963: $i,SV568: $i,SV1007: $i,SV836: $i] :
( ( ( ~ ( in @ ( sK136_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV280 ) )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4964]) ).
thf(5061,plain,
! [SV280: $i,SV568: $i,SV1007: $i,SV836: $i,SV963: $i] :
( ( ( ~ ( in @ ( kpair @ SV963 @ ( sK136_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) ) @ SV568 )
| ~ ( in @ ( kpair @ ( sK136_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV1007 ) @ SV836 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4964]) ).
thf(5062,plain,
! [SV280: $i,SV963: $i,SV568: $i,SV1007: $i,SV836: $i] :
( ( ( ~ ( in @ ( sK137_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV280 ) )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4965]) ).
thf(5063,plain,
! [SV280: $i,SV568: $i,SV1007: $i,SV836: $i,SV963: $i] :
( ( ( ~ ( in @ ( kpair @ SV963 @ ( sK137_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) ) @ SV568 )
| ~ ( in @ ( kpair @ ( sK137_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV1007 ) @ SV836 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4965]) ).
thf(5064,plain,
! [SV301: $i,SV586: $i,SV734: $i,SV911: $i,SV1067: $i,SV1046: $i] :
( ( ( ~ ( in @ ( kpair @ SV1046 @ SV1067 ) @ SV911 ) )
= $true )
| ( ( in @ ( kpair @ SV1046 @ SV1067 ) @ SV734 )
= $true )
| ( ( in @ SV1067 @ SV586 )
= $false )
| ( ( in @ SV1046 @ SV301 )
= $false )
| ( ( in @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) @ SV301 )
= $true )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4968]) ).
thf(5065,plain,
! [SV301: $i,SV586: $i,SV734: $i,SV911: $i,SV1063: $i,SV1027: $i] :
( ( ( in @ ( kpair @ SV1027 @ SV1063 ) @ SV911 )
= $false )
| ( ( in @ ( kpair @ SV1027 @ SV1063 ) @ SV734 )
= $true )
| ( ( in @ SV1063 @ SV586 )
= $false )
| ( ( in @ SV1027 @ SV301 )
= $false )
| ( ( ( ap @ SV301 @ SV586 @ SV734 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) )
= ( ap @ SV301 @ SV586 @ SV911 @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) ) )
= $false )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4969]) ).
thf(5066,plain,
! [SV848: $i,SV1068: $i,SV316: $i > $o] :
( ( ( ~ ( SV316 @ SV1068 )
| ( SV1068
= ( sK113_SY3190 @ SV848 @ SV316 ) ) )
= $true )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV316 @ ( sK85_SY4045 @ SV848 @ SV316 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4970]) ).
thf(5067,plain,
! [SV316: $i > $o,SV848: $i,SV1068: $i] :
( ( ( ( SV1068
!= ( sK113_SY3190 @ SV848 @ SV316 ) )
| ( SV316 @ SV1068 ) )
= $true )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV316 @ ( sK85_SY4045 @ SV848 @ SV316 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4971]) ).
thf(5068,plain,
! [SV848: $i,SV1064: $i,SV316: $i > $o] :
( ( ( ~ ( SV316 @ SV1064 ) )
= $true )
| ( ( SV1064
= ( sK104_SY3190 @ SV848 @ SV316 ) )
= $true )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV848
= ( sK85_SY4045 @ SV848 @ SV316 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4972]) ).
thf(5069,plain,
! [SV316: $i > $o,SV848: $i,SV1064: $i] :
( ( ( SV1064
!= ( sK104_SY3190 @ SV848 @ SV316 ) )
= $true )
| ( ( SV316 @ SV1064 )
= $true )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV848
= ( sK85_SY4045 @ SV848 @ SV316 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4973]) ).
thf(5070,plain,
! [SV851: $i,SV322: $i,SV1059: $i] :
( ( ( in @ SV1059 @ SV322 )
= $false )
| ( ( in @ SV1059 @ ( sK51_SY3211 @ SV851 @ SV322 ) )
= $false )
| ( ( in @ SV851 @ SV322 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4974]) ).
thf(5071,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( SV59 @ ( sK119_SY2468 @ SV766 @ SV59 ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4976]) ).
thf(5072,plain,
! [SV766: $i,SV59: $i > $o] :
( ( ( ! [SY4200: $i] :
( ~ ( SV59 @ SY4200 )
| ( ( sK119_SY2468 @ SV766 @ SV59 )
= SY4200 ) ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4977]) ).
thf(5073,plain,
! [SV766: $i,SV1090: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ SV1090 )
| ( ( sK114_SY2468 @ SV766 @ SV59 )
= SV1090 ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4979]) ).
thf(5074,plain,
! [SV766: $i,SV1091: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ SV1091 )
| ( ( sK115_SY2468 @ SV766 @ SV59 )
= SV1091 ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4981]) ).
thf(5075,plain,
! [SV766: $i,SV1081: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ SV1081 ) )
= $true )
| ( ( ( sK106_SY2468 @ SV766 @ SV59 )
= SV1081 )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4982]) ).
thf(5076,plain,
! [SV767: $i,SV1082: $i,SV60: $i > $o] :
( ( ( ~ ( SV60 @ SV1082 ) )
= $true )
| ( ( ( sK107_SY2472 @ SV767 @ SV60 )
= SV1082 )
= $true )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV60 @ ( sK76_SY3951 @ SV767 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4983]) ).
thf(5077,plain,
! [SV767: $i,SV1074: $i,SV60: $i > $o] :
( ( ( SV60 @ SV1074 )
= $false )
| ( ( ( sK96_SY2472 @ SV767 @ SV60 )
= SV1074 )
= $true )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV767
= ( sK76_SY3951 @ SV767 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4984]) ).
thf(5078,plain,
! [SV78: $i,SV927: $i,SV382: $i,SV994: $i,SV773: $i] :
( ( ( ~ ( ~ ( in @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) ) @ SV382 ) ) )
= $true )
| ( ( in @ ( kpair @ SV927 @ SV994 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
= $false )
| ( ( in @ SV994 @ SV78 )
= $false )
| ( ( in @ SV927 @ SV78 )
= $false )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4985]) ).
thf(5079,plain,
! [SV78: $i,SV927: $i,SV382: $i,SV994: $i,SV773: $i] :
( ( ( in @ ( kpair @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) @ SV994 ) @ SV773 )
= $true )
| ( ( in @ ( kpair @ SV927 @ SV994 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
= $false )
| ( ( in @ SV994 @ SV78 )
= $false )
| ( ( in @ SV927 @ SV78 )
= $false )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4986]) ).
thf(5080,plain,
! [SV781: $i,SV1075: $i,SV100: $i > $o] :
( ( ( SV100 @ SV1075 )
= $false )
| ( ( ( sK97_SY2565 @ SV781 @ SV100 )
= SV1075 )
= $true )
| ( ( SV100 @ ( sK53_SY2563 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4987]) ).
thf(5081,plain,
! [SV781: $i,SV1083: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV1083 ) )
= $true )
| ( ( ( sK108_SY2565 @ SV781 @ SV100 )
= SV1083 )
= $true )
| ( ( SV100 @ ( sK61_SY4131 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4988]) ).
thf(5082,plain,
! [SV781: $i,SV1076: $i,SV100: $i > $o] :
( ( ( SV100 @ SV1076 )
= $false )
| ( ( ( sK98_SY2565 @ SV781 @ SV100 )
= SV1076 )
= $true )
| ( ( ( sK53_SY2563 @ SV781 @ SV100 )
= ( sK61_SY4131 @ SV781 @ SV100 ) )
= $false )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4989]) ).
thf(5083,plain,
! [SV420: $i,SV788: $i > $o,SV122: $i,SV865: $i > $o] :
( ( ( SV865 @ ( sK77_SY4133 @ SV122 @ SV788 @ SV865 @ SV420 ) )
= $true )
| ( ( SV788 @ ( sK54_SY4052 @ SV865 @ SV788 @ SV420 @ SV122 ) )
= $true )
| ( ( ( dsetconstr @ SV122
@ ^ [SY3975: $i] : ( SV788 @ SY3975 ) )
= ( dsetconstr @ SV420
@ ^ [SY4055: $i] : ( SV865 @ SY4055 ) ) )
= $true )
| ( ( SV122 = SV420 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4990]) ).
thf(5084,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( in @ ( kpair @ ( sK116_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK125_SY4198 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV870 )
= $true )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ SV140 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4995]) ).
thf(5085,plain,
! [SV436: $i,SV650: $i,SV870: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK138_SY4207 @ SV140 @ SV870 @ SV650 @ SV436 ) @ SV436 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) @ SV436 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4998]) ).
thf(5086,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK126_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK138_SY4207 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV870 )
| ( in @ ( kpair @ ( sK126_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK138_SY4207 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV650 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) @ SV436 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4998]) ).
thf(5087,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( in @ ( sK132_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ SV140 )
= $true )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV650 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4999]) ).
thf(5088,plain,
! [SV436: $i,SV650: $i,SV870: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK141_SY4215 @ SV140 @ SV870 @ SV650 @ SV436 ) @ SV436 )
| ~ ( in @ ( kpair @ ( sK132_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK141_SY4215 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV870 )
| ( in @ ( kpair @ ( sK132_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK141_SY4215 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV650 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV650 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5000]) ).
thf(5089,plain,
! [SV436: $i,SV650: $i,SV870: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK139_SY4208 @ SV140 @ SV870 @ SV650 @ SV436 ) @ SV436 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5002]) ).
thf(5090,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK127_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK139_SY4208 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV870 )
| ( in @ ( kpair @ ( sK127_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK139_SY4208 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV650 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5002]) ).
thf(5091,plain,
! [SV1010: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV152 @ ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5004]) ).
thf(5092,plain,
! [SV1010: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV1010
= ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $false )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5005]) ).
thf(5093,plain,
! [SV448: $i > $o,SV1077: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ SV1077 )
| ~ ! [SY4216: $i] :
( ~ ( SV152 @ SY4216 )
| ( SV1077 = SY4216 ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5006]) ).
thf(5094,plain,
! [SV448: $i > $o,SV1069: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ SV1069 ) )
= $true )
| ( ( ~ ! [SY4209: $i] :
( ~ ( SV152 @ SY4209 )
| ( SV1069 = SY4209 ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5007]) ).
thf(5095,plain,
! [SV448: $i > $o,SV1070: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ SV1070 ) )
= $true )
| ( ( ~ ! [SY4210: $i] :
( ~ ( SV152 @ SY4210 )
| ( SV1070 = SY4210 ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5008]) ).
thf(5096,plain,
! [SV448: $i > $o,SV1065: $i,SV152: $i > $o] :
( ( ( SV152 @ SV1065 )
= $false )
| ( ( ~ ! [SY4201: $i] :
( ~ ( SV152 @ SY4201 )
| ( SV1065 = SY4201 ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5009]) ).
thf(5097,plain,
! [SV175: $i,SV1060: $i,SV470: $i > $i,SV976: $i] :
( ( ( SV976
= ( SV470 @ SV1060 ) )
= $false )
| ( ( in @ SV1060 @ SV175 )
= $false )
| ( ( in @ SV976 @ ( sK3_SY3462 @ SV470 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5012]) ).
thf(5098,plain,
! [SV977: $i,SV470: $i > $i,SV175: $i] :
( ( ( ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) ) )
= $false )
| ( ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5013]) ).
thf(5099,plain,
! [SV977: $i,SV470: $i > $i,SV175: $i,SV1071: $i] :
( ( ( ~ ( in @ SV1071 @ SV175 ) )
= $true )
| ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SV1071 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) )
| ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 ) ) )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5014]) ).
thf(5100,plain,
! [SV979: $i,SV1052: $i,SV670: $i > $i > $o,SV475: $i,SV180: $i,SV1084: $i] :
( ( ( ~ ( in @ SV1084 @ SV180 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY4219: $i] :
~ ( ~ ( SV670 @ SV1084 @ SY4219 )
| ~ ! [SY4220: $i] :
( ~ ( in @ SY4220 @ SV475 )
| ~ ( SV670 @ SV1084 @ SY4220 )
| ( in @ ( kpair @ SY4219 @ SY4220 ) @ SV1052 ) ) ) ) )
= $true )
| ( ( reflwellordering @ SV475 @ SV1052 )
= $false )
| ( ( in @ SV1052 @ ( breln1Set @ SV475 ) )
= $false )
| ( ( in @ SV979 @ SV475 )
= $false )
| ( ( SV670 @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV979 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5015]) ).
thf(5101,plain,
! [SV816: $i,SV1085: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ SV1085 ) )
= $true )
| ( ( ( sK109_SY2855 @ SV816 @ SV196 )
= SV1085 )
= $true )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV196 @ ( sK80_SY4002 @ SV816 @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5016]) ).
thf(5102,plain,
! [SV816: $i,SV1078: $i,SV196: $i > $o] :
( ( ( SV196 @ SV1078 )
= $false )
| ( ( ( sK101_SY2855 @ SV816 @ SV196 )
= SV1078 )
= $true )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV816
= ( sK80_SY4002 @ SV816 @ SV196 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5017]) ).
thf(5103,plain,
! [SV1053: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
| ( SV1053
= ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5018]) ).
thf(5104,plain,
! [SV1054: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
| ( SV1054
= ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) ) )
= $false )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5019]) ).
thf(5105,plain,
! [SV491: $i > $o,SV197: $i > $o] :
( ( ( ! [SY2860: $i] :
~ ~ ( ~ ( SV197 @ SY2860 )
| ~ ! [SY2861: $i] :
( ~ ( SV197 @ SY2861 )
| ( SY2860 = SY2861 ) ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5020]) ).
thf(5106,plain,
! [SV197: $i > $o,SV491: $i > $o] :
( ( ( ! [SY3521: $i] :
~ ~ ( ~ ( SV491 @ SY3521 )
| ~ ! [SY3522: $i] :
( ~ ( SV491 @ SY3522 )
| ( SY3521 = SY3522 ) ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5021]) ).
thf(5107,plain,
! [SV491: $i > $o,SV1092: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ SV1092 )
| ~ ! [SY4225: $i] :
( ~ ( SV197 @ SY4225 )
| ( SV1092 = SY4225 ) ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5022]) ).
thf(5108,plain,
! [SV197: $i > $o,SV1093: $i,SV491: $i > $o] :
( ( ( ~ ~ ( ~ ( SV491 @ SV1093 )
| ~ ! [SY4226: $i] :
( ~ ( SV491 @ SY4226 )
| ( SV1093 = SY4226 ) ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5023]) ).
thf(5109,plain,
! [SV491: $i > $o,SV1094: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ SV1094 )
| ~ ! [SY4227: $i] :
( ~ ( SV197 @ SY4227 )
| ( SV1094 = SY4227 ) ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5024]) ).
thf(5110,plain,
! [SV197: $i > $o,SV1095: $i,SV491: $i > $o] :
( ( ( ~ ~ ( ~ ( SV491 @ SV1095 )
| ~ ! [SY4228: $i] :
( ~ ( SV491 @ SY4228 )
| ( SV1095 = SY4228 ) ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5025]) ).
thf(5111,plain,
! [SV491: $i > $o,SV1086: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ SV1086 )
| ~ ! [SY4221: $i] :
( ~ ( SV197 @ SY4221 )
| ( SV1086 = SY4221 ) ) ) )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5026]) ).
thf(5112,plain,
! [SV197: $i > $o,SV1087: $i,SV491: $i > $o] :
( ( ( ~ ( ~ ( SV491 @ SV1087 )
| ~ ! [SY4222: $i] :
( ~ ( SV491 @ SY4222 )
| ( SV1087 = SY4222 ) ) ) )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5027]) ).
thf(5113,plain,
! [SV208: $i,SV501: $i,SV952: $o,SV818: $i,SV982: $i] :
( ( ( in @ SV982 @ SV818 )
= $true )
| ( SV952 = $true )
| ( ( in @ SV982 @ SV501 )
= $true )
| ( ( in @ SV982 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV982 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5028]) ).
thf(5114,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV983: $i] :
( ( ( in @ SV983 @ SV818 )
= $true )
| ( $true = $true )
| ( ( in @ SV983 @ SV501 )
= $true )
| ( ( in @ SV983 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV983 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5031]) ).
thf(5115,plain,
! [SV208: $i,SV501: $i,SV818: $i,SV984: $i] :
( ( ( in @ SV984 @ SV818 )
= $true )
| ( $false = $true )
| ( ( in @ SV984 @ SV501 )
= $true )
| ( ( in @ SV984 @ ( binunion @ SV501 @ SV818 ) )
= $false )
| ( ( in @ SV984 @ SV208 )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV208 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5034]) ).
thf(5116,plain,
! [SV216: $i,SV508: $i,SV1061: $o,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| SV1061 ) )
= $true )
| ( SV1061 = $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5037]) ).
thf(5117,plain,
! [SV216: $i,SV508: $i,SV1061: $o,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| SV1061 )
= $false )
| ( SV1061 = $true )
| ( SV1061 = $false )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5038]) ).
thf(5118,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5039]) ).
thf(5119,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5040]) ).
thf(5120,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5041]) ).
thf(5121,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5042]) ).
thf(5122,plain,
! [SV1041: $i,SV226: $i,SV1056: $i] :
( ( ( in @ SV1056 @ SV226 )
= $false )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( ~ ! [SY4193: $i] :
( ~ ( in @ SY4193 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SV1041 @ SY4193 )
| ( in @ SV1056 @ SY4193 ) )
| ~ ( ~ ( in @ SV1056 @ SY4193 )
| ( in @ SV1041 @ SY4193 ) ) ) )
| ( SV1041 = SV1056 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5043]) ).
thf(5123,plain,
! [SV226: $i,SV1014: $i,SV1002: $i,SV1088: $i] :
( ( ( ~ ( in @ SV1088 @ SV1002 ) )
= $true )
| ( ( in @ SV1088 @ SV1014 )
= $true )
| ( ( ! [SY4167: $i] :
( ~ ( in @ SY4167 @ SV1014 )
| ( in @ SY4167 @ SV1002 ) ) )
= $true )
| ( ( in @ SV1002 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( in @ SV1014 @ ( sK2_SY2943 @ SV226 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5044]) ).
thf(5124,plain,
! [SV1079: $i,SV955: $i,SV226: $i] :
( ( ( ! [SY4116: $i] :
~ ~ ! [SY4117: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY4116 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4117 @ SV955 ) )
| ~ ~ ~ ! [SY4118: $i] :
~ ~ ( ~ ( in @ SY4118 @ SY4116 )
| ~ ( in @ SY4118 @ SV955 ) ) )
| ~ ! [SY3866: $i] :
( ~ ( in @ SY3866 @ ( sK2_SY2943 @ SV226 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3866 )
| ( in @ SX6 @ SY4116 ) )
| ( in @ SY4117 @ SY3866 ) ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5045]) ).
thf(5125,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( ~ ~ ! [SY4229: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4229 @ SV955 ) )
| ~ ~ ~ ! [SY4230: $i] :
~ ~ ( ~ ( in @ SY4230 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
| ~ ( in @ SY4230 @ SV955 ) ) )
| ~ ! [SY4231: $i] :
( ~ ( in @ SY4231 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4232: $i] :
( ~ ( in @ SY4232 @ SY4231 )
| ( in @ SY4232 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) ) )
| ( in @ SY4229 @ SY4231 ) ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5046]) ).
thf(5126,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1003: $i] :
( ( ( ~ ( in @ ( sK129_SY4159 @ SV1003 @ SV230 @ SV520 ) @ SV520 ) )
= $false )
| ( ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
= $false )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5047]) ).
thf(5127,plain,
! [SV520: $i,SV1003: $i,SV230: $i > $i > $o] :
( ( ( ~ ( SV230 @ ( sK129_SY4159 @ SV1003 @ SV230 @ SV520 ) @ SV1003 ) )
= $false )
| ( ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
= $false )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5047]) ).
thf(5128,plain,
! [SV1003: $i,SV230: $i > $i > $o,SV520: $i,SV1073: $i] :
( ( ( ~ ( in @ SV1073 @ SV520 ) )
= $true )
| ( ( ~ ( SV230 @ SV1073 @ SV1003 ) )
= $true )
| ( ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
= $true )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5048]) ).
thf(5129,plain,
! [SV520: $i,SV230: $i > $i > $o,SV957: $i,SV1089: $i] :
( ( ( ~ ( ~ ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
| ~ ! [SY4223: $i] :
~ ~ ( ~ ( in @ SY4223 @ SV520 )
| ~ ( SV230 @ SY4223 @ SV1089 ) ) )
| ~ ( ~ ~ ! [SY4224: $i] :
~ ~ ( ~ ( in @ SY4224 @ SV520 )
| ~ ( SV230 @ SY4224 @ SV1089 ) )
| ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) ) ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5049]) ).
thf(5130,plain,
! [SV520: $i,SV230: $i > $i > $o,SV957: $i,SV1080: $i] :
( ( ( ~ ( ~ ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
| ~ ! [SY4217: $i] :
~ ~ ( ~ ( in @ SY4217 @ SV520 )
| ~ ( SV230 @ SY4217 @ SV1080 ) ) ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5050]) ).
thf(5131,plain,
! [SV957: $i,SV1080: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ~ ( ~ ~ ! [SY4218: $i] :
~ ~ ( ~ ( in @ SY4218 @ SV520 )
| ~ ( SV230 @ SY4218 @ SV1080 ) )
| ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) ) ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5050]) ).
thf(5132,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( in @ ( sK133_SY4205 @ SV829 @ SV549 @ SV260 ) @ SV260 )
= $true )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5052]) ).
thf(5133,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK123_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK133_SY4205 @ SV829 @ SV549 @ SV260 ) ) @ SV829 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5053]) ).
thf(5134,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( in @ ( kpair @ ( sK123_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK133_SY4205 @ SV829 @ SV549 @ SV260 ) ) @ SV549 )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5053]) ).
thf(5135,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK140_SY4214 @ SV829 @ SV549 @ SV260 ) @ SV260 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV549 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5055]) ).
thf(5136,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK131_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK140_SY4214 @ SV829 @ SV549 @ SV260 ) ) @ SV829 )
| ( in @ ( kpair @ ( sK131_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK140_SY4214 @ SV829 @ SV549 @ SV260 ) ) @ SV549 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV549 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5055]) ).
thf(5137,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( in @ ( sK134_SY4206 @ SV829 @ SV549 @ SV260 ) @ SV260 )
= $true )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5056]) ).
thf(5138,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK124_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK134_SY4206 @ SV829 @ SV549 @ SV260 ) ) @ SV829 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5057]) ).
thf(5139,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( in @ ( kpair @ ( sK124_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK134_SY4206 @ SV829 @ SV549 @ SV260 ) ) @ SV549 )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5057]) ).
thf(5140,plain,
! [SV280: $i,SV963: $i,SV568: $i,SV1007: $i,SV836: $i,SV1062: $o] :
( ( ( in @ ( sK135_SY4199 @ SV1062 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV280 )
= $true )
| ( SV1062 = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5058]) ).
thf(5141,plain,
! [SV280: $i,SV568: $i,SV1007: $i,SV836: $i,SV1062: $o,SV963: $i] :
( ( ( ~ ( in @ ( kpair @ SV963 @ ( sK135_SY4199 @ SV1062 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) ) @ SV568 ) )
= $false )
| ( SV1062 = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5059]) ).
thf(5142,plain,
! [SV280: $i,SV963: $i,SV568: $i,SV1007: $i,SV836: $i,SV1062: $o] :
( ( ( ~ ( in @ ( kpair @ ( sK135_SY4199 @ SV1062 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV1007 ) @ SV836 )
| SV1062 )
= $false )
| ( SV1062 = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5059]) ).
thf(5143,plain,
! [SV280: $i,SV963: $i,SV568: $i,SV1007: $i,SV836: $i] :
( ( ( in @ ( sK136_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV280 )
= $true )
| ( $true = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5060]) ).
thf(5144,plain,
! [SV280: $i,SV568: $i,SV1007: $i,SV836: $i,SV963: $i] :
( ( ( ~ ( in @ ( kpair @ SV963 @ ( sK136_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) ) @ SV568 ) )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5061]) ).
thf(5145,plain,
! [SV280: $i,SV963: $i,SV568: $i,SV1007: $i,SV836: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK136_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV1007 ) @ SV836 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5061]) ).
thf(5146,plain,
! [SV280: $i,SV963: $i,SV568: $i,SV1007: $i,SV836: $i] :
( ( ( in @ ( sK137_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV280 )
= $true )
| ( $false = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5062]) ).
thf(5147,plain,
! [SV280: $i,SV568: $i,SV1007: $i,SV836: $i,SV963: $i] :
( ( ( ~ ( in @ ( kpair @ SV963 @ ( sK137_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) ) @ SV568 ) )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5063]) ).
thf(5148,plain,
! [SV280: $i,SV963: $i,SV568: $i,SV1007: $i,SV836: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK137_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV1007 ) @ SV836 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5063]) ).
thf(5149,plain,
! [SV301: $i,SV586: $i,SV734: $i,SV911: $i,SV1067: $i,SV1046: $i] :
( ( ( in @ ( kpair @ SV1046 @ SV1067 ) @ SV911 )
= $false )
| ( ( in @ ( kpair @ SV1046 @ SV1067 ) @ SV734 )
= $true )
| ( ( in @ SV1067 @ SV586 )
= $false )
| ( ( in @ SV1046 @ SV301 )
= $false )
| ( ( in @ ( sK84_SY4087 @ SV911 @ SV734 @ SV586 @ SV301 ) @ SV301 )
= $true )
| ( ( func @ SV301 @ SV586 @ SV911 )
= $false )
| ( ( func @ SV301 @ SV586 @ SV734 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5064]) ).
thf(5150,plain,
! [SV848: $i,SV1068: $i,SV316: $i > $o] :
( ( ( ~ ( SV316 @ SV1068 ) )
= $true )
| ( ( SV1068
= ( sK113_SY3190 @ SV848 @ SV316 ) )
= $true )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV316 @ ( sK85_SY4045 @ SV848 @ SV316 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5066]) ).
thf(5151,plain,
! [SV316: $i > $o,SV848: $i,SV1068: $i] :
( ( ( SV1068
!= ( sK113_SY3190 @ SV848 @ SV316 ) )
= $true )
| ( ( SV316 @ SV1068 )
= $true )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV316 @ ( sK85_SY4045 @ SV848 @ SV316 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5067]) ).
thf(5152,plain,
! [SV848: $i,SV1064: $i,SV316: $i > $o] :
( ( ( SV316 @ SV1064 )
= $false )
| ( ( SV1064
= ( sK104_SY3190 @ SV848 @ SV316 ) )
= $true )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV848
= ( sK85_SY4045 @ SV848 @ SV316 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5068]) ).
thf(5153,plain,
! [SV316: $i > $o,SV848: $i,SV1064: $i] :
( ( ( SV1064
= ( sK104_SY3190 @ SV848 @ SV316 ) )
= $false )
| ( ( SV316 @ SV1064 )
= $true )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV848
= ( sK85_SY4045 @ SV848 @ SV316 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5069]) ).
thf(5154,plain,
! [SV766: $i,SV1096: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ SV1096 )
| ( ( sK119_SY2468 @ SV766 @ SV59 )
= SV1096 ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5072]) ).
thf(5155,plain,
! [SV766: $i,SV1090: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ SV1090 ) )
= $true )
| ( ( ( sK114_SY2468 @ SV766 @ SV59 )
= SV1090 )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5073]) ).
thf(5156,plain,
! [SV766: $i,SV1091: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ SV1091 ) )
= $true )
| ( ( ( sK115_SY2468 @ SV766 @ SV59 )
= SV1091 )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5074]) ).
thf(5157,plain,
! [SV766: $i,SV1081: $i,SV59: $i > $o] :
( ( ( SV59 @ SV1081 )
= $false )
| ( ( ( sK106_SY2468 @ SV766 @ SV59 )
= SV1081 )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5075]) ).
thf(5158,plain,
! [SV767: $i,SV1082: $i,SV60: $i > $o] :
( ( ( SV60 @ SV1082 )
= $false )
| ( ( ( sK107_SY2472 @ SV767 @ SV60 )
= SV1082 )
= $true )
| ( ( SV60 @ SV767 )
= $false )
| ( ( SV60 @ ( sK76_SY3951 @ SV767 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5076]) ).
thf(5159,plain,
! [SV78: $i,SV927: $i,SV382: $i,SV994: $i,SV773: $i] :
( ( ( ~ ( in @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) @ SV78 )
| ~ ( in @ ( kpair @ SV927 @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) ) @ SV382 ) )
= $false )
| ( ( in @ ( kpair @ SV927 @ SV994 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
= $false )
| ( ( in @ SV994 @ SV78 )
= $false )
| ( ( in @ SV927 @ SV78 )
= $false )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5078]) ).
thf(5160,plain,
! [SV781: $i,SV1083: $i,SV100: $i > $o] :
( ( ( SV100 @ SV1083 )
= $false )
| ( ( ( sK108_SY2565 @ SV781 @ SV100 )
= SV1083 )
= $true )
| ( ( SV100 @ ( sK61_SY4131 @ SV781 @ SV100 ) )
= $true )
| ( ( SV100 @ SV781 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5081]) ).
thf(5161,plain,
! [SV436: $i,SV650: $i,SV870: $i,SV140: $i] :
( ( ( in @ ( sK138_SY4207 @ SV140 @ SV870 @ SV650 @ SV436 ) @ SV436 )
= $true )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) @ SV436 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5085]) ).
thf(5162,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK126_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK138_SY4207 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV870 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) @ SV436 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5086]) ).
thf(5163,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( in @ ( kpair @ ( sK126_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK138_SY4207 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV650 )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) @ SV436 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5086]) ).
thf(5164,plain,
! [SV436: $i,SV650: $i,SV870: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK141_SY4215 @ SV140 @ SV870 @ SV650 @ SV436 ) @ SV436 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV650 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5088]) ).
thf(5165,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK132_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK141_SY4215 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV870 )
| ( in @ ( kpair @ ( sK132_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK141_SY4215 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV650 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV650 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5088]) ).
thf(5166,plain,
! [SV436: $i,SV650: $i,SV870: $i,SV140: $i] :
( ( ( in @ ( sK139_SY4208 @ SV140 @ SV870 @ SV650 @ SV436 ) @ SV436 )
= $true )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5089]) ).
thf(5167,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK127_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK139_SY4208 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV870 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5090]) ).
thf(5168,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( in @ ( kpair @ ( sK127_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK139_SY4208 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV650 )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5090]) ).
thf(5169,plain,
! [SV1010: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV152 @ ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5091]) ).
thf(5170,plain,
! [SV1010: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV1010
= ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $false )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5092]) ).
thf(5171,plain,
! [SV448: $i > $o,SV1077: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ SV1077 ) )
= $true )
| ( ( ~ ! [SY4216: $i] :
( ~ ( SV152 @ SY4216 )
| ( SV1077 = SY4216 ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5093]) ).
thf(5172,plain,
! [SV448: $i > $o,SV1069: $i,SV152: $i > $o] :
( ( ( SV152 @ SV1069 )
= $false )
| ( ( ~ ! [SY4209: $i] :
( ~ ( SV152 @ SY4209 )
| ( SV1069 = SY4209 ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5094]) ).
thf(5173,plain,
! [SV448: $i > $o,SV1070: $i,SV152: $i > $o] :
( ( ( SV152 @ SV1070 )
= $false )
| ( ( ~ ! [SY4210: $i] :
( ~ ( SV152 @ SY4210 )
| ( SV1070 = SY4210 ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5095]) ).
thf(5174,plain,
! [SV448: $i > $o,SV1065: $i,SV152: $i > $o] :
( ( ( ! [SY4201: $i] :
( ~ ( SV152 @ SY4201 )
| ( SV1065 = SY4201 ) ) )
= $false )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5096]) ).
thf(5175,plain,
! [SV175: $i,SV470: $i > $i,SV977: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK145_SY4165 @ SV977 @ SV470 @ SV175 ) @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ ( sK145_SY4165 @ SV977 @ SV470 @ SV175 ) ) ) ) )
= $false )
| ( ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5098]) ).
thf(5176,plain,
! [SV977: $i,SV470: $i > $i,SV175: $i,SV1071: $i] :
( ( ( in @ SV1071 @ SV175 )
= $false )
| ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SV1071 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) )
| ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 ) ) )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5099]) ).
thf(5177,plain,
! [SV979: $i,SV1052: $i,SV670: $i > $i > $o,SV475: $i,SV180: $i,SV1084: $i] :
( ( ( in @ SV1084 @ SV180 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV475
@ ^ [SY4219: $i] :
~ ( ~ ( SV670 @ SV1084 @ SY4219 )
| ~ ! [SY4220: $i] :
( ~ ( in @ SY4220 @ SV475 )
| ~ ( SV670 @ SV1084 @ SY4220 )
| ( in @ ( kpair @ SY4219 @ SY4220 ) @ SV1052 ) ) ) ) )
= $true )
| ( ( reflwellordering @ SV475 @ SV1052 )
= $false )
| ( ( in @ SV1052 @ ( breln1Set @ SV475 ) )
= $false )
| ( ( in @ SV979 @ SV475 )
= $false )
| ( ( SV670 @ ( sK29_SY3805 @ SV670 @ SV475 @ SV180 ) @ SV979 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5100]) ).
thf(5178,plain,
! [SV816: $i,SV1085: $i,SV196: $i > $o] :
( ( ( SV196 @ SV1085 )
= $false )
| ( ( ( sK109_SY2855 @ SV816 @ SV196 )
= SV1085 )
= $true )
| ( ( SV196 @ SV816 )
= $false )
| ( ( SV196 @ ( sK80_SY4002 @ SV816 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5101]) ).
thf(5179,plain,
! [SV1053: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5103]) ).
thf(5180,plain,
! [SV197: $i > $o,SV491: $i > $o,SV1053: $i] :
( ( ( SV1053
= ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $false )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5103]) ).
thf(5181,plain,
! [SV1054: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) ) )
= $false )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5104]) ).
thf(5182,plain,
! [SV491: $i > $o,SV197: $i > $o,SV1054: $i] :
( ( ( SV1054
= ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $false )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5104]) ).
thf(5183,plain,
! [SV491: $i > $o,SV1097: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ SV1097 )
| ~ ! [SY4233: $i] :
( ~ ( SV197 @ SY4233 )
| ( SV1097 = SY4233 ) ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5105]) ).
thf(5184,plain,
! [SV197: $i > $o,SV1098: $i,SV491: $i > $o] :
( ( ( ~ ~ ( ~ ( SV491 @ SV1098 )
| ~ ! [SY4234: $i] :
( ~ ( SV491 @ SY4234 )
| ( SV1098 = SY4234 ) ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5106]) ).
thf(5185,plain,
! [SV491: $i > $o,SV1092: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ SV1092 )
| ~ ! [SY4225: $i] :
( ~ ( SV197 @ SY4225 )
| ( SV1092 = SY4225 ) ) ) )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5107]) ).
thf(5186,plain,
! [SV197: $i > $o,SV1093: $i,SV491: $i > $o] :
( ( ( ~ ( ~ ( SV491 @ SV1093 )
| ~ ! [SY4226: $i] :
( ~ ( SV491 @ SY4226 )
| ( SV1093 = SY4226 ) ) ) )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5108]) ).
thf(5187,plain,
! [SV491: $i > $o,SV1094: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ SV1094 )
| ~ ! [SY4227: $i] :
( ~ ( SV197 @ SY4227 )
| ( SV1094 = SY4227 ) ) ) )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5109]) ).
thf(5188,plain,
! [SV197: $i > $o,SV1095: $i,SV491: $i > $o] :
( ( ( ~ ( ~ ( SV491 @ SV1095 )
| ~ ! [SY4228: $i] :
( ~ ( SV491 @ SY4228 )
| ( SV1095 = SY4228 ) ) ) )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5110]) ).
thf(5189,plain,
! [SV491: $i > $o,SV1086: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1086 )
| ~ ! [SY4221: $i] :
( ~ ( SV197 @ SY4221 )
| ( SV1086 = SY4221 ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5111]) ).
thf(5190,plain,
! [SV197: $i > $o,SV1087: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1087 )
| ~ ! [SY4222: $i] :
( ~ ( SV491 @ SY4222 )
| ( SV1087 = SY4222 ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5112]) ).
thf(5191,plain,
! [SV216: $i,SV508: $i,SV1061: $o,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| SV1061 )
= $false )
| ( SV1061 = $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5116]) ).
thf(5192,plain,
! [SV216: $i,SV508: $i,SV1061: $o,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 ) )
= $false )
| ( SV1061 = $true )
| ( SV1061 = $false )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5117]) ).
thf(5193,plain,
! [SV216: $i,SV819: $i,SV508: $i,SV1001: $i,SV953: $i,SV1061: $o] :
( ( SV1061 = $false )
| ( SV1061 = $true )
| ( SV1061 = $false )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5117]) ).
thf(5194,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5118]) ).
thf(5195,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5119]) ).
thf(5196,plain,
! [SV216: $i,SV819: $i,SV508: $i,SV1001: $i,SV953: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5119]) ).
thf(5197,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5120]) ).
thf(5198,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5121]) ).
thf(5199,plain,
! [SV216: $i,SV819: $i,SV508: $i,SV1001: $i,SV953: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5121]) ).
thf(5200,plain,
! [SV1056: $i,SV1041: $i,SV226: $i] :
( ( ( ~ ! [SY4193: $i] :
( ~ ( in @ SY4193 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SV1041 @ SY4193 )
| ( in @ SV1056 @ SY4193 ) )
| ~ ( ~ ( in @ SV1056 @ SY4193 )
| ( in @ SV1041 @ SY4193 ) ) ) ) )
= $true )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5122]) ).
thf(5201,plain,
! [SV226: $i,SV1014: $i,SV1002: $i,SV1088: $i] :
( ( ( in @ SV1088 @ SV1002 )
= $false )
| ( ( in @ SV1088 @ SV1014 )
= $true )
| ( ( ! [SY4167: $i] :
( ~ ( in @ SY4167 @ SV1014 )
| ( in @ SY4167 @ SV1002 ) ) )
= $true )
| ( ( in @ SV1002 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( in @ SV1014 @ ( sK2_SY2943 @ SV226 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5123]) ).
thf(5202,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( ~ ~ ! [SY4235: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4235 @ SV955 ) )
| ~ ~ ~ ! [SY4236: $i] :
~ ~ ( ~ ( in @ SY4236 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
| ~ ( in @ SY4236 @ SV955 ) ) )
| ~ ! [SY4237: $i] :
( ~ ( in @ SY4237 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4238: $i] :
( ~ ( in @ SY4238 @ SY4237 )
| ( in @ SY4238 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) ) )
| ( in @ SY4235 @ SY4237 ) ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5124]) ).
thf(5203,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( ~ ! [SY4229: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4229 @ SV955 ) )
| ~ ~ ~ ! [SY4230: $i] :
~ ~ ( ~ ( in @ SY4230 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
| ~ ( in @ SY4230 @ SV955 ) ) )
| ~ ! [SY4231: $i] :
( ~ ( in @ SY4231 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4232: $i] :
( ~ ( in @ SY4232 @ SY4231 )
| ( in @ SY4232 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) ) )
| ( in @ SY4229 @ SY4231 ) ) ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5125]) ).
thf(5204,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1003: $i] :
( ( ( in @ ( sK129_SY4159 @ SV1003 @ SV230 @ SV520 ) @ SV520 )
= $true )
| ( ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
= $false )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5126]) ).
thf(5205,plain,
! [SV520: $i,SV1003: $i,SV230: $i > $i > $o] :
( ( ( SV230 @ ( sK129_SY4159 @ SV1003 @ SV230 @ SV520 ) @ SV1003 )
= $true )
| ( ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
= $false )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5127]) ).
thf(5206,plain,
! [SV1003: $i,SV230: $i > $i > $o,SV520: $i,SV1073: $i] :
( ( ( in @ SV1073 @ SV520 )
= $false )
| ( ( ~ ( SV230 @ SV1073 @ SV1003 ) )
= $true )
| ( ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
= $true )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5128]) ).
thf(5207,plain,
! [SV520: $i,SV230: $i > $i > $o,SV957: $i,SV1089: $i] :
( ( ( ~ ( ~ ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
| ~ ! [SY4223: $i] :
~ ~ ( ~ ( in @ SY4223 @ SV520 )
| ~ ( SV230 @ SY4223 @ SV1089 ) ) ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5129]) ).
thf(5208,plain,
! [SV957: $i,SV1089: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ~ ( ~ ~ ! [SY4224: $i] :
~ ~ ( ~ ( in @ SY4224 @ SV520 )
| ~ ( SV230 @ SY4224 @ SV1089 ) )
| ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) ) ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5129]) ).
thf(5209,plain,
! [SV520: $i,SV230: $i > $i > $o,SV957: $i,SV1080: $i] :
( ( ( ~ ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
| ~ ! [SY4217: $i] :
~ ~ ( ~ ( in @ SY4217 @ SV520 )
| ~ ( SV230 @ SY4217 @ SV1080 ) ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5130]) ).
thf(5210,plain,
! [SV957: $i,SV1080: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ~ ~ ! [SY4218: $i] :
~ ~ ( ~ ( in @ SY4218 @ SV520 )
| ~ ( SV230 @ SY4218 @ SV1080 ) )
| ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5131]) ).
thf(5211,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( in @ ( kpair @ ( sK123_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK133_SY4205 @ SV829 @ SV549 @ SV260 ) ) @ SV829 )
= $true )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) @ SV260 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5133]) ).
thf(5212,plain,
! [SV260: $i,SV549: $i,SV829: $i] :
( ( ( in @ ( sK140_SY4214 @ SV829 @ SV549 @ SV260 ) @ SV260 )
= $true )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV549 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5135]) ).
thf(5213,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK131_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK140_SY4214 @ SV829 @ SV549 @ SV260 ) ) @ SV829 ) )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV549 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5136]) ).
thf(5214,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( in @ ( kpair @ ( sK131_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK140_SY4214 @ SV829 @ SV549 @ SV260 ) ) @ SV549 )
= $false )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV549 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5136]) ).
thf(5215,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( in @ ( kpair @ ( sK124_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK134_SY4206 @ SV829 @ SV549 @ SV260 ) ) @ SV829 )
= $true )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5138]) ).
thf(5216,plain,
! [SV280: $i,SV568: $i,SV1007: $i,SV836: $i,SV1062: $o,SV963: $i] :
( ( ( in @ ( kpair @ SV963 @ ( sK135_SY4199 @ SV1062 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) ) @ SV568 )
= $true )
| ( SV1062 = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5141]) ).
thf(5217,plain,
! [SV280: $i,SV963: $i,SV568: $i,SV1007: $i,SV836: $i,SV1062: $o] :
( ( ( ~ ( in @ ( kpair @ ( sK135_SY4199 @ SV1062 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV1007 ) @ SV836 ) )
= $false )
| ( SV1062 = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5142]) ).
thf(5218,plain,
! [SV836: $i,SV568: $i,SV280: $i,SV1007: $i,SV963: $i,SV1062: $o] :
( ( SV1062 = $false )
| ( SV1062 = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5142]) ).
thf(5219,plain,
! [SV280: $i,SV568: $i,SV1007: $i,SV836: $i,SV963: $i] :
( ( ( in @ ( kpair @ SV963 @ ( sK136_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) ) @ SV568 )
= $true )
| ( $true = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5144]) ).
thf(5220,plain,
! [SV280: $i,SV963: $i,SV568: $i,SV1007: $i,SV836: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK136_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV1007 ) @ SV836 ) )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5145]) ).
thf(5221,plain,
! [SV836: $i,SV568: $i,SV280: $i,SV1007: $i,SV963: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5145]) ).
thf(5222,plain,
! [SV280: $i,SV568: $i,SV1007: $i,SV836: $i,SV963: $i] :
( ( ( in @ ( kpair @ SV963 @ ( sK137_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) ) @ SV568 )
= $true )
| ( $false = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5147]) ).
thf(5223,plain,
! [SV280: $i,SV963: $i,SV568: $i,SV1007: $i,SV836: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK137_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV1007 ) @ SV836 ) )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5148]) ).
thf(5224,plain,
! [SV836: $i,SV568: $i,SV280: $i,SV1007: $i,SV963: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5148]) ).
thf(5225,plain,
! [SV848: $i,SV1068: $i,SV316: $i > $o] :
( ( ( SV316 @ SV1068 )
= $false )
| ( ( SV1068
= ( sK113_SY3190 @ SV848 @ SV316 ) )
= $true )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV316 @ ( sK85_SY4045 @ SV848 @ SV316 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5150]) ).
thf(5226,plain,
! [SV316: $i > $o,SV848: $i,SV1068: $i] :
( ( ( SV1068
= ( sK113_SY3190 @ SV848 @ SV316 ) )
= $false )
| ( ( SV316 @ SV1068 )
= $true )
| ( ( SV316 @ SV848 )
= $false )
| ( ( SV316 @ ( sK85_SY4045 @ SV848 @ SV316 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5151]) ).
thf(5227,plain,
! [SV766: $i,SV1096: $i,SV59: $i > $o] :
( ( ( ~ ( SV59 @ SV1096 ) )
= $true )
| ( ( ( sK119_SY2468 @ SV766 @ SV59 )
= SV1096 )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5154]) ).
thf(5228,plain,
! [SV766: $i,SV1090: $i,SV59: $i > $o] :
( ( ( SV59 @ SV1090 )
= $false )
| ( ( ( sK114_SY2468 @ SV766 @ SV59 )
= SV1090 )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5155]) ).
thf(5229,plain,
! [SV766: $i,SV1091: $i,SV59: $i > $o] :
( ( ( SV59 @ SV1091 )
= $false )
| ( ( ( sK115_SY2468 @ SV766 @ SV59 )
= SV1091 )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $false )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5156]) ).
thf(5230,plain,
! [SV78: $i,SV927: $i,SV382: $i,SV994: $i,SV773: $i] :
( ( ( ~ ( in @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) @ SV78 ) )
= $false )
| ( ( in @ ( kpair @ SV927 @ SV994 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
= $false )
| ( ( in @ SV994 @ SV78 )
= $false )
| ( ( in @ SV927 @ SV78 )
= $false )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5159]) ).
thf(5231,plain,
! [SV78: $i,SV382: $i,SV994: $i,SV773: $i,SV927: $i] :
( ( ( ~ ( in @ ( kpair @ SV927 @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) ) @ SV382 ) )
= $false )
| ( ( in @ ( kpair @ SV927 @ SV994 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
= $false )
| ( ( in @ SV994 @ SV78 )
= $false )
| ( ( in @ SV927 @ SV78 )
= $false )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5159]) ).
thf(5232,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( in @ ( kpair @ ( sK126_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK138_SY4207 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV870 )
= $true )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) @ SV436 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5162]) ).
thf(5233,plain,
! [SV436: $i,SV650: $i,SV870: $i,SV140: $i] :
( ( ( in @ ( sK141_SY4215 @ SV140 @ SV870 @ SV650 @ SV436 ) @ SV436 )
= $true )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV650 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5164]) ).
thf(5234,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK132_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK141_SY4215 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV870 ) )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV650 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5165]) ).
thf(5235,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( in @ ( kpair @ ( sK132_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK141_SY4215 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV650 )
= $false )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV650 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5165]) ).
thf(5236,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( in @ ( kpair @ ( sK127_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK139_SY4208 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV870 )
= $true )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5167]) ).
thf(5237,plain,
! [SV1010: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV152 @ ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5169]) ).
thf(5238,plain,
! [SV1010: $i,SV152: $i > $o,SV1099: $i,SV448: $i > $o] :
( ( ( ~ ~ ( ~ ( SV448 @ SV1099 )
| ~ ! [SY4239: $i] :
( ~ ( SV448 @ SY4239 )
| ( SV1099 = SY4239 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV1010
= ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $false )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5170]) ).
thf(5239,plain,
! [SV448: $i > $o,SV1077: $i,SV152: $i > $o] :
( ( ( SV152 @ SV1077 )
= $false )
| ( ( ~ ! [SY4216: $i] :
( ~ ( SV152 @ SY4216 )
| ( SV1077 = SY4216 ) ) )
= $true )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5171]) ).
thf(5240,plain,
! [SV448: $i > $o,SV1069: $i,SV152: $i > $o] :
( ( ( ! [SY4209: $i] :
( ~ ( SV152 @ SY4209 )
| ( SV1069 = SY4209 ) ) )
= $false )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5172]) ).
thf(5241,plain,
! [SV448: $i > $o,SV1070: $i,SV152: $i > $o] :
( ( ( ! [SY4210: $i] :
( ~ ( SV152 @ SY4210 )
| ( SV1070 = SY4210 ) ) )
= $false )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5173]) ).
thf(5242,plain,
! [SV1065: $i,SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
| ( SV1065
= ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) ) )
= $false )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5174]) ).
thf(5243,plain,
! [SV175: $i,SV470: $i > $i,SV977: $i] :
( ( ( ~ ( ~ ( in @ ( sK145_SY4165 @ SV977 @ SV470 @ SV175 ) @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ ( sK145_SY4165 @ SV977 @ SV470 @ SV175 ) ) ) ) )
= $true )
| ( ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5175]) ).
thf(5244,plain,
! [SV1071: $i,SV977: $i,SV175: $i,SV470: $i > $i] :
( ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
= ( SV470 @ SV1071 ) )
= $false )
| ( ( in @ SV1071 @ SV175 )
= $false )
| ( ( ~ ( ~ ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) )
| ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 ) ) )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5176]) ).
thf(5245,plain,
! [SV1053: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( SV197 @ ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $true )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5179]) ).
thf(5246,plain,
! [SV1053: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $false )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV1053
= ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5180]) ).
thf(5247,plain,
! [SV1054: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( SV491 @ ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $true )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5181]) ).
thf(5248,plain,
! [SV1054: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $false )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV1054
= ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5182]) ).
thf(5249,plain,
! [SV491: $i > $o,SV1097: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ SV1097 )
| ~ ! [SY4233: $i] :
( ~ ( SV197 @ SY4233 )
| ( SV1097 = SY4233 ) ) ) )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5183]) ).
thf(5250,plain,
! [SV197: $i > $o,SV1098: $i,SV491: $i > $o] :
( ( ( ~ ( ~ ( SV491 @ SV1098 )
| ~ ! [SY4234: $i] :
( ~ ( SV491 @ SY4234 )
| ( SV1098 = SY4234 ) ) ) )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5184]) ).
thf(5251,plain,
! [SV491: $i > $o,SV1092: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1092 )
| ~ ! [SY4225: $i] :
( ~ ( SV197 @ SY4225 )
| ( SV1092 = SY4225 ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5185]) ).
thf(5252,plain,
! [SV197: $i > $o,SV1093: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1093 )
| ~ ! [SY4226: $i] :
( ~ ( SV491 @ SY4226 )
| ( SV1093 = SY4226 ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5186]) ).
thf(5253,plain,
! [SV491: $i > $o,SV1094: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1094 )
| ~ ! [SY4227: $i] :
( ~ ( SV197 @ SY4227 )
| ( SV1094 = SY4227 ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5187]) ).
thf(5254,plain,
! [SV197: $i > $o,SV1095: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1095 )
| ~ ! [SY4228: $i] :
( ~ ( SV491 @ SY4228 )
| ( SV1095 = SY4228 ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5188]) ).
thf(5255,plain,
! [SV491: $i > $o,SV1086: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1086 ) )
= $true )
| ( ( ~ ! [SY4221: $i] :
( ~ ( SV197 @ SY4221 )
| ( SV1086 = SY4221 ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5189]) ).
thf(5256,plain,
! [SV197: $i > $o,SV1087: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1087 ) )
= $true )
| ( ( ~ ! [SY4222: $i] :
( ~ ( SV491 @ SY4222 )
| ( SV1087 = SY4222 ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5190]) ).
thf(5257,plain,
! [SV216: $i,SV508: $i,SV1061: $o,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 ) )
= $false )
| ( SV1061 = $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5191]) ).
thf(5258,plain,
! [SV216: $i,SV819: $i,SV508: $i,SV1001: $i,SV953: $i,SV1061: $o] :
( ( SV1061 = $false )
| ( SV1061 = $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5191]) ).
thf(5259,plain,
! [SV216: $i,SV508: $i,SV1061: $o,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
= $true )
| ( SV1061 = $true )
| ( SV1061 = $false )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5192]) ).
thf(5260,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 ) )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5194]) ).
thf(5261,plain,
! [SV216: $i,SV819: $i,SV508: $i,SV1001: $i,SV953: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5194]) ).
thf(5262,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5195]) ).
thf(5263,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( ~ ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 ) )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5197]) ).
thf(5264,plain,
! [SV216: $i,SV819: $i,SV508: $i,SV1001: $i,SV953: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5197]) ).
thf(5265,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5198]) ).
thf(5266,plain,
! [SV1056: $i,SV1041: $i,SV226: $i] :
( ( ( ! [SY4193: $i] :
( ~ ( in @ SY4193 @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SV1041 @ SY4193 )
| ( in @ SV1056 @ SY4193 ) )
| ~ ( ~ ( in @ SV1056 @ SY4193 )
| ( in @ SV1041 @ SY4193 ) ) ) ) )
= $false )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5200]) ).
thf(5267,plain,
! [SV226: $i,SV1088: $i,SV1002: $i,SV1014: $i,SV1100: $i] :
( ( ( ~ ( in @ SV1100 @ SV1014 )
| ( in @ SV1100 @ SV1002 ) )
= $true )
| ( ( in @ SV1088 @ SV1014 )
= $true )
| ( ( in @ SV1088 @ SV1002 )
= $false )
| ( ( in @ SV1002 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( in @ SV1014 @ ( sK2_SY2943 @ SV226 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5201]) ).
thf(5268,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( ~ ! [SY4235: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4235 @ SV955 ) )
| ~ ~ ~ ! [SY4236: $i] :
~ ~ ( ~ ( in @ SY4236 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
| ~ ( in @ SY4236 @ SV955 ) ) )
| ~ ! [SY4237: $i] :
( ~ ( in @ SY4237 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4238: $i] :
( ~ ( in @ SY4238 @ SY4237 )
| ( in @ SY4238 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) ) )
| ( in @ SY4235 @ SY4237 ) ) ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5202]) ).
thf(5269,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( ! [SY4229: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4229 @ SV955 ) )
| ~ ~ ~ ! [SY4230: $i] :
~ ~ ( ~ ( in @ SY4230 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
| ~ ( in @ SY4230 @ SV955 ) ) )
| ~ ! [SY4231: $i] :
( ~ ( in @ SY4231 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4232: $i] :
( ~ ( in @ SY4232 @ SY4231 )
| ( in @ SY4232 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) ) )
| ( in @ SY4229 @ SY4231 ) ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5203]) ).
thf(5270,plain,
! [SV520: $i,SV1003: $i,SV1073: $i,SV230: $i > $i > $o] :
( ( ( SV230 @ SV1073 @ SV1003 )
= $false )
| ( ( in @ SV1073 @ SV520 )
= $false )
| ( ( in @ SV1003 @ ( sK56_SY3585 @ SV230 @ SV520 ) )
= $true )
| ( ( in @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV520 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5206]) ).
thf(5271,plain,
! [SV520: $i,SV230: $i > $i > $o,SV957: $i,SV1089: $i] :
( ( ( ~ ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
| ~ ! [SY4223: $i] :
~ ~ ( ~ ( in @ SY4223 @ SV520 )
| ~ ( SV230 @ SY4223 @ SV1089 ) ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5207]) ).
thf(5272,plain,
! [SV957: $i,SV1089: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ~ ~ ! [SY4224: $i] :
~ ~ ( ~ ( in @ SY4224 @ SV520 )
| ~ ( SV230 @ SY4224 @ SV1089 ) )
| ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5208]) ).
thf(5273,plain,
! [SV520: $i,SV230: $i > $i > $o,SV957: $i,SV1080: $i] :
( ( ( ~ ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) ) )
= $true )
| ( ( ~ ! [SY4217: $i] :
~ ~ ( ~ ( in @ SY4217 @ SV520 )
| ~ ( SV230 @ SY4217 @ SV1080 ) ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5209]) ).
thf(5274,plain,
! [SV957: $i,SV1080: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ~ ~ ! [SY4218: $i] :
~ ~ ( ~ ( in @ SY4218 @ SV520 )
| ~ ( SV230 @ SY4218 @ SV1080 ) ) )
= $true )
| ( ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5210]) ).
thf(5275,plain,
! [SV260: $i,SV829: $i,SV549: $i] :
( ( ( in @ ( kpair @ ( sK131_SY4022 @ SV549 @ SV829 @ SV260 ) @ ( sK140_SY4214 @ SV829 @ SV549 @ SV260 ) ) @ SV829 )
= $true )
| ( ( SV549 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK67_SY4020 @ SV829 @ SV549 @ SV260 ) @ ( sK89_SY4150 @ SV549 @ SV829 @ SV260 ) ) @ SV549 )
= $true )
| ( ( breln1 @ SV260 @ SV829 )
= $false )
| ( ( breln1 @ SV260 @ SV549 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5213]) ).
thf(5276,plain,
! [SV280: $i,SV963: $i,SV568: $i,SV1007: $i,SV836: $i,SV1062: $o] :
( ( ( in @ ( kpair @ ( sK135_SY4199 @ SV1062 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV1007 ) @ SV836 )
= $true )
| ( SV1062 = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5217]) ).
thf(5277,plain,
! [SV280: $i,SV963: $i,SV568: $i,SV1007: $i,SV836: $i] :
( ( ( in @ ( kpair @ ( sK136_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV1007 ) @ SV836 )
= $true )
| ( $true = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5220]) ).
thf(5278,plain,
! [SV280: $i,SV963: $i,SV568: $i,SV1007: $i,SV836: $i] :
( ( ( in @ ( kpair @ ( sK137_SX0 @ SV836 @ SV1007 @ SV568 @ SV963 @ SV280 ) @ SV1007 ) @ SV836 )
= $true )
| ( $false = $true )
| ( ( in @ ( kpair @ SV963 @ SV1007 ) @ ( breln1compset @ SV280 @ SV568 @ SV836 ) )
= $false )
| ( ( in @ SV1007 @ SV280 )
= $false )
| ( ( in @ SV963 @ SV280 )
= $false )
| ( ( breln1 @ SV280 @ SV836 )
= $false )
| ( ( breln1 @ SV280 @ SV568 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5223]) ).
thf(5279,plain,
! [SV766: $i,SV1096: $i,SV59: $i > $o] :
( ( ( SV59 @ SV1096 )
= $false )
| ( ( ( sK119_SY2468 @ SV766 @ SV59 )
= SV1096 )
= $true )
| ( ( SV59 @ ( sK37_SY3950 @ SV766 @ SV59 ) )
= $true )
| ( ( ( sK37_SY3950 @ SV766 @ SV59 )
= SV766 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5227]) ).
thf(5280,plain,
! [SV78: $i,SV927: $i,SV382: $i,SV994: $i,SV773: $i] :
( ( ( in @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) @ SV78 )
= $true )
| ( ( in @ ( kpair @ SV927 @ SV994 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
= $false )
| ( ( in @ SV994 @ SV78 )
= $false )
| ( ( in @ SV927 @ SV78 )
= $false )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5230]) ).
thf(5281,plain,
! [SV78: $i,SV382: $i,SV994: $i,SV773: $i,SV927: $i] :
( ( ( in @ ( kpair @ SV927 @ ( sK120_SY4151 @ SV773 @ SV994 @ SV382 @ SV927 @ SV78 ) ) @ SV382 )
= $true )
| ( ( in @ ( kpair @ SV927 @ SV994 ) @ ( breln1compset @ SV78 @ SV382 @ SV773 ) )
= $false )
| ( ( in @ SV994 @ SV78 )
= $false )
| ( ( in @ SV927 @ SV78 )
= $false )
| ( ( breln1 @ SV78 @ SV773 )
= $false )
| ( ( breln1 @ SV78 @ SV382 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5231]) ).
thf(5282,plain,
! [SV140: $i,SV436: $i,SV870: $i,SV650: $i] :
( ( ( in @ ( kpair @ ( sK132_SY4061 @ SV650 @ SV870 @ SV436 @ SV140 ) @ ( sK141_SY4215 @ SV140 @ SV870 @ SV650 @ SV436 ) ) @ SV870 )
= $true )
| ( ( SV650 = SV870 )
= $true )
| ( ( in @ ( kpair @ ( sK78_SY4059 @ SV870 @ SV650 @ SV436 @ SV140 ) @ ( sK90_SY4153 @ SV140 @ SV650 @ SV870 @ SV436 ) ) @ SV650 )
= $true )
| ( ( breln @ SV140 @ SV436 @ SV870 )
= $false )
| ( ( breln @ SV140 @ SV436 @ SV650 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5234]) ).
thf(5283,plain,
! [SV1010: $i,SV152: $i > $o,SV1101: $i,SV448: $i > $o] :
( ( ( ~ ~ ( ~ ( SV448 @ SV1101 )
| ~ ! [SY4240: $i] :
( ~ ( SV448 @ SY4240 )
| ( SV1101 = SY4240 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV152 @ ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5237]) ).
thf(5284,plain,
! [SV1010: $i,SV152: $i > $o,SV1099: $i,SV448: $i > $o] :
( ( ( ~ ( ~ ( SV448 @ SV1099 )
| ~ ! [SY4239: $i] :
( ~ ( SV448 @ SY4239 )
| ( SV1099 = SY4239 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV1010
= ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $false )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5238]) ).
thf(5285,plain,
! [SV448: $i > $o,SV1077: $i,SV152: $i > $o] :
( ( ( ! [SY4216: $i] :
( ~ ( SV152 @ SY4216 )
| ( SV1077 = SY4216 ) ) )
= $false )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5239]) ).
thf(5286,plain,
! [SV1069: $i,SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
| ( SV1069
= ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) ) )
= $false )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5240]) ).
thf(5287,plain,
! [SV1070: $i,SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
| ( SV1070
= ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) ) )
= $false )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5241]) ).
thf(5288,plain,
! [SV1065: $i,SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) ) )
= $false )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5242]) ).
thf(5289,plain,
! [SV152: $i > $o,SV448: $i > $o,SV1065: $i] :
( ( ( SV1065
= ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $false )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5242]) ).
thf(5290,plain,
! [SV175: $i,SV470: $i > $i,SV977: $i] :
( ( ( ~ ( in @ ( sK145_SY4165 @ SV977 @ SV470 @ SV175 ) @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ ( sK145_SY4165 @ SV977 @ SV470 @ SV175 ) ) ) )
= $false )
| ( ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5243]) ).
thf(5291,plain,
! [SV1071: $i,SV977: $i,SV470: $i > $i,SV175: $i] :
( ( ( ~ ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) )
| ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 ) )
= $false )
| ( ( in @ SV1071 @ SV175 )
= $false )
| ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
= ( SV470 @ SV1071 ) )
= $false )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5244]) ).
thf(5292,plain,
! [SV1053: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $false )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV197 @ ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5245]) ).
thf(5293,plain,
! [SV197: $i > $o,SV1053: $i,SV491: $i > $o] :
( ( ( ~ ~ ( ~ ( SV491 @ ( sK150_SY3519 @ SV1053 @ SV197 @ SV491 ) )
| ~ ! [SY4241: $i] :
( ~ ( SV491 @ SY4241 )
| ( ( sK150_SY3519 @ SV1053 @ SV197 @ SV491 )
= SY4241 ) ) ) )
= $false )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV1053
= ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5246]) ).
thf(5294,plain,
! [SV1054: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $false )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV491 @ ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5247]) ).
thf(5295,plain,
! [SV491: $i > $o,SV1054: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ ( sK151_SY2866 @ SV1054 @ SV491 @ SV197 ) )
| ~ ! [SY4242: $i] :
( ~ ( SV197 @ SY4242 )
| ( ( sK151_SY2866 @ SV1054 @ SV491 @ SV197 )
= SY4242 ) ) ) )
= $false )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV1054
= ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5248]) ).
thf(5296,plain,
! [SV491: $i > $o,SV1097: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1097 )
| ~ ! [SY4233: $i] :
( ~ ( SV197 @ SY4233 )
| ( SV1097 = SY4233 ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5249]) ).
thf(5297,plain,
! [SV197: $i > $o,SV1098: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1098 )
| ~ ! [SY4234: $i] :
( ~ ( SV491 @ SY4234 )
| ( SV1098 = SY4234 ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5250]) ).
thf(5298,plain,
! [SV491: $i > $o,SV1092: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1092 ) )
= $true )
| ( ( ~ ! [SY4225: $i] :
( ~ ( SV197 @ SY4225 )
| ( SV1092 = SY4225 ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5251]) ).
thf(5299,plain,
! [SV197: $i > $o,SV1093: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1093 ) )
= $true )
| ( ( ~ ! [SY4226: $i] :
( ~ ( SV491 @ SY4226 )
| ( SV1093 = SY4226 ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5252]) ).
thf(5300,plain,
! [SV491: $i > $o,SV1094: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1094 ) )
= $true )
| ( ( ~ ! [SY4227: $i] :
( ~ ( SV197 @ SY4227 )
| ( SV1094 = SY4227 ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5253]) ).
thf(5301,plain,
! [SV197: $i > $o,SV1095: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1095 ) )
= $true )
| ( ( ~ ! [SY4228: $i] :
( ~ ( SV491 @ SY4228 )
| ( SV1095 = SY4228 ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5254]) ).
thf(5302,plain,
! [SV491: $i > $o,SV1086: $i,SV197: $i > $o] :
( ( ( SV197 @ SV1086 )
= $false )
| ( ( ~ ! [SY4221: $i] :
( ~ ( SV197 @ SY4221 )
| ( SV1086 = SY4221 ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5255]) ).
thf(5303,plain,
! [SV197: $i > $o,SV1087: $i,SV491: $i > $o] :
( ( ( SV491 @ SV1087 )
= $false )
| ( ( ~ ! [SY4222: $i] :
( ~ ( SV491 @ SY4222 )
| ( SV1087 = SY4222 ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5256]) ).
thf(5304,plain,
! [SV216: $i,SV508: $i,SV1061: $o,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
= $true )
| ( SV1061 = $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5257]) ).
thf(5305,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
= $true )
| ( $true = $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5260]) ).
thf(5306,plain,
! [SV216: $i,SV508: $i,SV819: $i,SV1001: $i,SV953: $i] :
( ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV819 )
= $true )
| ( $false = $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ SV508 )
= $true )
| ( ( in @ ( kpair @ SV953 @ SV1001 ) @ ( binunion @ SV508 @ SV819 ) )
= $false )
| ( ( in @ SV1001 @ SV216 )
= $false )
| ( ( in @ SV953 @ SV216 )
= $false )
| ( ( breln1 @ SV216 @ SV819 )
= $false )
| ( ( breln1 @ SV216 @ SV508 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5263]) ).
thf(5307,plain,
! [SV226: $i,SV1041: $i,SV1056: $i] :
( ( ( ~ ( in @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( ~ ( ~ ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
| ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) ) )
| ~ ( ~ ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
| ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) ) ) ) )
= $false )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5266]) ).
thf(5308,plain,
! [SV226: $i,SV1088: $i,SV1002: $i,SV1014: $i,SV1100: $i] :
( ( ( ~ ( in @ SV1100 @ SV1014 ) )
= $true )
| ( ( in @ SV1100 @ SV1002 )
= $true )
| ( ( in @ SV1088 @ SV1014 )
= $true )
| ( ( in @ SV1088 @ SV1002 )
= $false )
| ( ( in @ SV1002 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( in @ SV1014 @ ( sK2_SY2943 @ SV226 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5267]) ).
thf(5309,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( ! [SY4235: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ SY4235 @ SV955 ) )
| ~ ~ ~ ! [SY4236: $i] :
~ ~ ( ~ ( in @ SY4236 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
| ~ ( in @ SY4236 @ SV955 ) ) )
| ~ ! [SY4237: $i] :
( ~ ( in @ SY4237 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4238: $i] :
( ~ ( in @ SY4238 @ SY4237 )
| ( in @ SY4238 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) ) )
| ( in @ SY4235 @ SY4237 ) ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5268]) ).
thf(5310,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SV955 ) )
| ~ ~ ~ ! [SY4230: $i] :
~ ~ ( ~ ( in @ SY4230 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
| ~ ( in @ SY4230 @ SV955 ) ) )
| ~ ! [SY4244: $i] :
( ~ ( in @ SY4244 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4232: $i] :
( ~ ( in @ SY4232 @ SY4244 )
| ( in @ SY4232 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) ) )
| ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SY4244 ) ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5269]) ).
thf(5311,plain,
! [SV520: $i,SV230: $i > $i > $o,SV957: $i,SV1089: $i] :
( ( ( ~ ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) ) )
= $true )
| ( ( ~ ! [SY4223: $i] :
~ ~ ( ~ ( in @ SY4223 @ SV520 )
| ~ ( SV230 @ SY4223 @ SV1089 ) ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5271]) ).
thf(5312,plain,
! [SV957: $i,SV1089: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ~ ~ ! [SY4224: $i] :
~ ~ ( ~ ( in @ SY4224 @ SV520 )
| ~ ( SV230 @ SY4224 @ SV1089 ) ) )
= $true )
| ( ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5272]) ).
thf(5313,plain,
! [SV520: $i,SV230: $i > $i > $o,SV957: $i,SV1080: $i] :
( ( ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $false )
| ( ( ~ ! [SY4217: $i] :
~ ~ ( ~ ( in @ SY4217 @ SV520 )
| ~ ( SV230 @ SY4217 @ SV1080 ) ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5273]) ).
thf(5314,plain,
! [SV957: $i,SV1080: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ~ ! [SY4218: $i] :
~ ~ ( ~ ( in @ SY4218 @ SV520 )
| ~ ( SV230 @ SY4218 @ SV1080 ) ) )
= $false )
| ( ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5274]) ).
thf(5315,plain,
! [SV1010: $i,SV152: $i > $o,SV1101: $i,SV448: $i > $o] :
( ( ( ~ ( ~ ( SV448 @ SV1101 )
| ~ ! [SY4240: $i] :
( ~ ( SV448 @ SY4240 )
| ( SV1101 = SY4240 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV152 @ ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5283]) ).
thf(5316,plain,
! [SV1010: $i,SV152: $i > $o,SV1099: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1099 )
| ~ ! [SY4239: $i] :
( ~ ( SV448 @ SY4239 )
| ( SV1099 = SY4239 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV1010
= ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $false )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5284]) ).
thf(5317,plain,
! [SV1077: $i,SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
| ( SV1077
= ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) ) )
= $false )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5285]) ).
thf(5318,plain,
! [SV1069: $i,SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) ) )
= $false )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5286]) ).
thf(5319,plain,
! [SV152: $i > $o,SV448: $i > $o,SV1069: $i] :
( ( ( SV1069
= ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $false )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5286]) ).
thf(5320,plain,
! [SV1070: $i,SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) ) )
= $false )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5287]) ).
thf(5321,plain,
! [SV152: $i > $o,SV448: $i > $o,SV1070: $i] :
( ( ( SV1070
= ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $false )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5287]) ).
thf(5322,plain,
! [SV1065: $i,SV448: $i > $o,SV152: $i > $o] :
( ( ( SV152 @ ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5288]) ).
thf(5323,plain,
! [SV1065: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV1065
= ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5289]) ).
thf(5324,plain,
! [SV175: $i,SV470: $i > $i,SV977: $i] :
( ( ( ~ ( in @ ( sK145_SY4165 @ SV977 @ SV470 @ SV175 ) @ SV175 ) )
= $false )
| ( ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5290]) ).
thf(5325,plain,
! [SV977: $i,SV175: $i,SV470: $i > $i] :
( ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ ( sK145_SY4165 @ SV977 @ SV470 @ SV175 ) ) )
= $false )
| ( ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5290]) ).
thf(5326,plain,
! [SV1071: $i,SV977: $i,SV470: $i > $i,SV175: $i] :
( ( ( ~ ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) ) )
= $false )
| ( ( in @ SV1071 @ SV175 )
= $false )
| ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
= ( SV470 @ SV1071 ) )
= $false )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5291]) ).
thf(5327,plain,
! [SV1071: $i,SV977: $i,SV175: $i,SV470: $i > $i] :
( ( ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
= $false )
| ( ( in @ SV1071 @ SV175 )
= $false )
| ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
= ( SV470 @ SV1071 ) )
= $false )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5291]) ).
thf(5328,plain,
! [SV197: $i > $o,SV1053: $i,SV491: $i > $o] :
( ( ( ~ ~ ( ~ ( SV491 @ ( sK155_SY3519 @ SV1053 @ SV197 @ SV491 ) )
| ~ ! [SY4246: $i] :
( ~ ( SV491 @ SY4246 )
| ( ( sK155_SY3519 @ SV1053 @ SV197 @ SV491 )
= SY4246 ) ) ) )
= $false )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV197 @ ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5292]) ).
thf(5329,plain,
! [SV197: $i > $o,SV1053: $i,SV491: $i > $o] :
( ( ( ~ ( ~ ( SV491 @ ( sK150_SY3519 @ SV1053 @ SV197 @ SV491 ) )
| ~ ! [SY4241: $i] :
( ~ ( SV491 @ SY4241 )
| ( ( sK150_SY3519 @ SV1053 @ SV197 @ SV491 )
= SY4241 ) ) ) )
= $true )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV1053
= ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5293]) ).
thf(5330,plain,
! [SV491: $i > $o,SV1054: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ ( sK156_SY2866 @ SV1054 @ SV491 @ SV197 ) )
| ~ ! [SY4247: $i] :
( ~ ( SV197 @ SY4247 )
| ( ( sK156_SY2866 @ SV1054 @ SV491 @ SV197 )
= SY4247 ) ) ) )
= $false )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV491 @ ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5294]) ).
thf(5331,plain,
! [SV491: $i > $o,SV1054: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ ( sK151_SY2866 @ SV1054 @ SV491 @ SV197 ) )
| ~ ! [SY4242: $i] :
( ~ ( SV197 @ SY4242 )
| ( ( sK151_SY2866 @ SV1054 @ SV491 @ SV197 )
= SY4242 ) ) ) )
= $true )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV1054
= ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5295]) ).
thf(5332,plain,
! [SV491: $i > $o,SV1097: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1097 ) )
= $true )
| ( ( ~ ! [SY4233: $i] :
( ~ ( SV197 @ SY4233 )
| ( SV1097 = SY4233 ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5296]) ).
thf(5333,plain,
! [SV197: $i > $o,SV1098: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1098 ) )
= $true )
| ( ( ~ ! [SY4234: $i] :
( ~ ( SV491 @ SY4234 )
| ( SV1098 = SY4234 ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5297]) ).
thf(5334,plain,
! [SV491: $i > $o,SV1092: $i,SV197: $i > $o] :
( ( ( SV197 @ SV1092 )
= $false )
| ( ( ~ ! [SY4225: $i] :
( ~ ( SV197 @ SY4225 )
| ( SV1092 = SY4225 ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5298]) ).
thf(5335,plain,
! [SV197: $i > $o,SV1093: $i,SV491: $i > $o] :
( ( ( SV491 @ SV1093 )
= $false )
| ( ( ~ ! [SY4226: $i] :
( ~ ( SV491 @ SY4226 )
| ( SV1093 = SY4226 ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5299]) ).
thf(5336,plain,
! [SV491: $i > $o,SV1094: $i,SV197: $i > $o] :
( ( ( SV197 @ SV1094 )
= $false )
| ( ( ~ ! [SY4227: $i] :
( ~ ( SV197 @ SY4227 )
| ( SV1094 = SY4227 ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5300]) ).
thf(5337,plain,
! [SV197: $i > $o,SV1095: $i,SV491: $i > $o] :
( ( ( SV491 @ SV1095 )
= $false )
| ( ( ~ ! [SY4228: $i] :
( ~ ( SV491 @ SY4228 )
| ( SV1095 = SY4228 ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5301]) ).
thf(5338,plain,
! [SV491: $i > $o,SV1086: $i,SV197: $i > $o] :
( ( ( ! [SY4221: $i] :
( ~ ( SV197 @ SY4221 )
| ( SV1086 = SY4221 ) ) )
= $false )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5302]) ).
thf(5339,plain,
! [SV197: $i > $o,SV1087: $i,SV491: $i > $o] :
( ( ( ! [SY4222: $i] :
( ~ ( SV491 @ SY4222 )
| ( SV1087 = SY4222 ) ) )
= $false )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5303]) ).
thf(5340,plain,
! [SV226: $i,SV1041: $i,SV1056: $i] :
( ( ( ~ ( in @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) ) )
= $false )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5307]) ).
thf(5341,plain,
! [SV226: $i,SV1056: $i,SV1041: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
| ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) ) )
| ~ ( ~ ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
| ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) ) ) ) )
= $false )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5307]) ).
thf(5342,plain,
! [SV226: $i,SV1088: $i,SV1002: $i,SV1014: $i,SV1100: $i] :
( ( ( in @ SV1100 @ SV1014 )
= $false )
| ( ( in @ SV1100 @ SV1002 )
= $true )
| ( ( in @ SV1088 @ SV1014 )
= $true )
| ( ( in @ SV1088 @ SV1002 )
= $false )
| ( ( in @ SV1002 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( in @ SV1014 @ ( sK2_SY2943 @ SV226 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5308]) ).
thf(5343,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SV955 ) )
| ~ ~ ~ ! [SY4236: $i] :
~ ~ ( ~ ( in @ SY4236 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
| ~ ( in @ SY4236 @ SV955 ) ) )
| ~ ! [SY4249: $i] :
( ~ ( in @ SY4249 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4238: $i] :
( ~ ( in @ SY4238 @ SY4249 )
| ( in @ SY4238 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) ) )
| ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SY4249 ) ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5309]) ).
thf(5344,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SV955 ) )
| ~ ~ ~ ! [SY4230: $i] :
~ ~ ( ~ ( in @ SY4230 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
| ~ ( in @ SY4230 @ SV955 ) ) )
| ~ ! [SY4244: $i] :
( ~ ( in @ SY4244 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4232: $i] :
( ~ ( in @ SY4232 @ SY4244 )
| ( in @ SY4232 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) ) )
| ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SY4244 ) ) ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5310]) ).
thf(5345,plain,
! [SV520: $i,SV230: $i > $i > $o,SV957: $i,SV1089: $i] :
( ( ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $false )
| ( ( ~ ! [SY4223: $i] :
~ ~ ( ~ ( in @ SY4223 @ SV520 )
| ~ ( SV230 @ SY4223 @ SV1089 ) ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5311]) ).
thf(5346,plain,
! [SV957: $i,SV1089: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ~ ! [SY4224: $i] :
~ ~ ( ~ ( in @ SY4224 @ SV520 )
| ~ ( SV230 @ SY4224 @ SV1089 ) ) )
= $false )
| ( ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5312]) ).
thf(5347,plain,
! [SV957: $i,SV1080: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ! [SY4217: $i] :
~ ~ ( ~ ( in @ SY4217 @ SV520 )
| ~ ( SV230 @ SY4217 @ SV1080 ) ) )
= $false )
| ( ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5313]) ).
thf(5348,plain,
! [SV957: $i,SV1080: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ! [SY4218: $i] :
~ ~ ( ~ ( in @ SY4218 @ SV520 )
| ~ ( SV230 @ SY4218 @ SV1080 ) ) )
= $true )
| ( ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5314]) ).
thf(5349,plain,
! [SV1010: $i,SV152: $i > $o,SV1101: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1101 )
| ~ ! [SY4240: $i] :
( ~ ( SV448 @ SY4240 )
| ( SV1101 = SY4240 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV152 @ ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5315]) ).
thf(5350,plain,
! [SV1010: $i,SV152: $i > $o,SV1099: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1099 ) )
= $true )
| ( ( ~ ! [SY4239: $i] :
( ~ ( SV448 @ SY4239 )
| ( SV1099 = SY4239 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV1010
= ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $false )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5316]) ).
thf(5351,plain,
! [SV1077: $i,SV448: $i > $o,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) ) )
= $false )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5317]) ).
thf(5352,plain,
! [SV152: $i > $o,SV448: $i > $o,SV1077: $i] :
( ( ( SV1077
= ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $false )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5317]) ).
thf(5353,plain,
! [SV1069: $i,SV448: $i > $o,SV152: $i > $o] :
( ( ( SV152 @ ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5318]) ).
thf(5354,plain,
! [SV1069: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV1069
= ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5319]) ).
thf(5355,plain,
! [SV1070: $i,SV448: $i > $o,SV152: $i > $o] :
( ( ( SV152 @ ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5320]) ).
thf(5356,plain,
! [SV1070: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV1070
= ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5321]) ).
thf(5357,plain,
! [SV1065: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV152 @ ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5322]) ).
thf(5358,plain,
! [SV1065: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV1065
= ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5323]) ).
thf(5359,plain,
! [SV175: $i,SV470: $i > $i,SV977: $i] :
( ( ( in @ ( sK145_SY4165 @ SV977 @ SV470 @ SV175 ) @ SV175 )
= $true )
| ( ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5324]) ).
thf(5360,plain,
! [SV977: $i,SV175: $i,SV470: $i > $i] :
( ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
= ( SV470 @ ( sK145_SY4165 @ SV977 @ SV470 @ SV175 ) ) )
= $true )
| ( ( in @ ( sK88_SY4137 @ SV470 @ SV175 @ SV977 ) @ SV977 )
= $true )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5325]) ).
thf(5361,plain,
! [SV1071: $i,SV977: $i,SV470: $i > $i,SV175: $i] :
( ( ( ~ ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) ) )
= $true )
| ( ( in @ SV1071 @ SV175 )
= $false )
| ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
= ( SV470 @ SV1071 ) )
= $false )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5326]) ).
thf(5362,plain,
! [SV197: $i > $o,SV1053: $i,SV491: $i > $o] :
( ( ( ~ ( ~ ( SV491 @ ( sK155_SY3519 @ SV1053 @ SV197 @ SV491 ) )
| ~ ! [SY4246: $i] :
( ~ ( SV491 @ SY4246 )
| ( ( sK155_SY3519 @ SV1053 @ SV197 @ SV491 )
= SY4246 ) ) ) )
= $true )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV197 @ ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5328]) ).
thf(5363,plain,
! [SV197: $i > $o,SV1053: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK150_SY3519 @ SV1053 @ SV197 @ SV491 ) )
| ~ ! [SY4241: $i] :
( ~ ( SV491 @ SY4241 )
| ( ( sK150_SY3519 @ SV1053 @ SV197 @ SV491 )
= SY4241 ) ) )
= $false )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV1053
= ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5329]) ).
thf(5364,plain,
! [SV491: $i > $o,SV1054: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ ( sK156_SY2866 @ SV1054 @ SV491 @ SV197 ) )
| ~ ! [SY4247: $i] :
( ~ ( SV197 @ SY4247 )
| ( ( sK156_SY2866 @ SV1054 @ SV491 @ SV197 )
= SY4247 ) ) ) )
= $true )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV491 @ ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5330]) ).
thf(5365,plain,
! [SV491: $i > $o,SV1054: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK151_SY2866 @ SV1054 @ SV491 @ SV197 ) )
| ~ ! [SY4242: $i] :
( ~ ( SV197 @ SY4242 )
| ( ( sK151_SY2866 @ SV1054 @ SV491 @ SV197 )
= SY4242 ) ) )
= $false )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV1054
= ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5331]) ).
thf(5366,plain,
! [SV491: $i > $o,SV1097: $i,SV197: $i > $o] :
( ( ( SV197 @ SV1097 )
= $false )
| ( ( ~ ! [SY4233: $i] :
( ~ ( SV197 @ SY4233 )
| ( SV1097 = SY4233 ) ) )
= $true )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5332]) ).
thf(5367,plain,
! [SV197: $i > $o,SV1098: $i,SV491: $i > $o] :
( ( ( SV491 @ SV1098 )
= $false )
| ( ( ~ ! [SY4234: $i] :
( ~ ( SV491 @ SY4234 )
| ( SV1098 = SY4234 ) ) )
= $true )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5333]) ).
thf(5368,plain,
! [SV491: $i > $o,SV1092: $i,SV197: $i > $o] :
( ( ( ! [SY4225: $i] :
( ~ ( SV197 @ SY4225 )
| ( SV1092 = SY4225 ) ) )
= $false )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5334]) ).
thf(5369,plain,
! [SV197: $i > $o,SV1093: $i,SV491: $i > $o] :
( ( ( ! [SY4226: $i] :
( ~ ( SV491 @ SY4226 )
| ( SV1093 = SY4226 ) ) )
= $false )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5335]) ).
thf(5370,plain,
! [SV491: $i > $o,SV1094: $i,SV197: $i > $o] :
( ( ( ! [SY4227: $i] :
( ~ ( SV197 @ SY4227 )
| ( SV1094 = SY4227 ) ) )
= $false )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5336]) ).
thf(5371,plain,
! [SV197: $i > $o,SV1095: $i,SV491: $i > $o] :
( ( ( ! [SY4228: $i] :
( ~ ( SV491 @ SY4228 )
| ( SV1095 = SY4228 ) ) )
= $false )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5337]) ).
thf(5372,plain,
! [SV1086: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
| ( SV1086
= ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5338]) ).
thf(5373,plain,
! [SV1087: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
| ( SV1087
= ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) ) )
= $false )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5339]) ).
thf(5374,plain,
! [SV226: $i,SV1041: $i,SV1056: $i] :
( ( ( in @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
= $true )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5340]) ).
thf(5375,plain,
! [SV226: $i,SV1056: $i,SV1041: $i] :
( ( ( ~ ( ~ ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
| ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) ) )
| ~ ( ~ ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
| ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) ) ) )
= $true )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5341]) ).
thf(5376,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SV955 ) )
| ~ ~ ~ ! [SY4236: $i] :
~ ~ ( ~ ( in @ SY4236 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
| ~ ( in @ SY4236 @ SV955 ) ) )
| ~ ! [SY4249: $i] :
( ~ ( in @ SY4249 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4238: $i] :
( ~ ( in @ SY4238 @ SY4249 )
| ( in @ SY4238 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) ) )
| ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SY4249 ) ) ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5343]) ).
thf(5377,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SV955 ) )
| ~ ~ ~ ! [SY4230: $i] :
~ ~ ( ~ ( in @ SY4230 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
| ~ ( in @ SY4230 @ SV955 ) ) )
| ~ ! [SY4244: $i] :
( ~ ( in @ SY4244 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4232: $i] :
( ~ ( in @ SY4232 @ SY4244 )
| ( in @ SY4232 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) ) )
| ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SY4244 ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5344]) ).
thf(5378,plain,
! [SV957: $i,SV1089: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ! [SY4223: $i] :
~ ~ ( ~ ( in @ SY4223 @ SV520 )
| ~ ( SV230 @ SY4223 @ SV1089 ) ) )
= $false )
| ( ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5345]) ).
thf(5379,plain,
! [SV957: $i,SV1089: $i,SV230: $i > $i > $o,SV520: $i] :
( ( ( ! [SY4224: $i] :
~ ~ ( ~ ( in @ SY4224 @ SV520 )
| ~ ( SV230 @ SY4224 @ SV1089 ) ) )
= $true )
| ( ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5346]) ).
thf(5380,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1080: $i,SV957: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK160_SY4217 @ SV957 @ SV1080 @ SV230 @ SV520 ) @ SV520 )
| ~ ( SV230 @ ( sK160_SY4217 @ SV957 @ SV1080 @ SV230 @ SV520 ) @ SV1080 ) ) )
= $false )
| ( ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5347]) ).
thf(5381,plain,
! [SV957: $i,SV1080: $i,SV230: $i > $i > $o,SV520: $i,SV1102: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1102 @ SV520 )
| ~ ( SV230 @ SV1102 @ SV1080 ) ) )
= $true )
| ( ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5348]) ).
thf(5382,plain,
! [SV1010: $i,SV152: $i > $o,SV1101: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1101 ) )
= $true )
| ( ( ~ ! [SY4240: $i] :
( ~ ( SV448 @ SY4240 )
| ( SV1101 = SY4240 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV152 @ ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5349]) ).
thf(5383,plain,
! [SV1010: $i,SV152: $i > $o,SV1099: $i,SV448: $i > $o] :
( ( ( SV448 @ SV1099 )
= $false )
| ( ( ~ ! [SY4239: $i] :
( ~ ( SV448 @ SY4239 )
| ( SV1099 = SY4239 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV1010
= ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $false )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5350]) ).
thf(5384,plain,
! [SV1077: $i,SV448: $i > $o,SV152: $i > $o] :
( ( ( SV152 @ ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) )
| ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5351]) ).
thf(5385,plain,
! [SV1077: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV1077
= ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5352]) ).
thf(5386,plain,
! [SV1069: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV152 @ ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5353]) ).
thf(5387,plain,
! [SV1069: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV1069
= ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5354]) ).
thf(5388,plain,
! [SV1070: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV152 @ ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5355]) ).
thf(5389,plain,
! [SV1070: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV1070
= ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5356]) ).
thf(5390,plain,
! [SV1065: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV152 @ ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5357]) ).
thf(5391,plain,
! [SV1065: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV1065
= ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5358]) ).
thf(5392,plain,
! [SV1071: $i,SV977: $i,SV470: $i > $i,SV175: $i] :
( ( ( ! [SY4165: $i] :
~ ~ ( ~ ( in @ SY4165 @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ SY4165 ) ) ) )
= $false )
| ( ( in @ SV1071 @ SV175 )
= $false )
| ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
= ( SV470 @ SV1071 ) )
= $false )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5361]) ).
thf(5393,plain,
! [SV197: $i > $o,SV1053: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK155_SY3519 @ SV1053 @ SV197 @ SV491 ) )
| ~ ! [SY4246: $i] :
( ~ ( SV491 @ SY4246 )
| ( ( sK155_SY3519 @ SV1053 @ SV197 @ SV491 )
= SY4246 ) ) )
= $false )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV197 @ ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5362]) ).
thf(5394,plain,
! [SV197: $i > $o,SV1053: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK150_SY3519 @ SV1053 @ SV197 @ SV491 ) ) )
= $false )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV1053
= ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5363]) ).
thf(5395,plain,
! [SV197: $i > $o,SV1053: $i,SV491: $i > $o] :
( ( ( ~ ! [SY4241: $i] :
( ~ ( SV491 @ SY4241 )
| ( ( sK150_SY3519 @ SV1053 @ SV197 @ SV491 )
= SY4241 ) ) )
= $false )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV1053
= ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5363]) ).
thf(5396,plain,
! [SV491: $i > $o,SV1054: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK156_SY2866 @ SV1054 @ SV491 @ SV197 ) )
| ~ ! [SY4247: $i] :
( ~ ( SV197 @ SY4247 )
| ( ( sK156_SY2866 @ SV1054 @ SV491 @ SV197 )
= SY4247 ) ) )
= $false )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV491 @ ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5364]) ).
thf(5397,plain,
! [SV491: $i > $o,SV1054: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK151_SY2866 @ SV1054 @ SV491 @ SV197 ) ) )
= $false )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV1054
= ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5365]) ).
thf(5398,plain,
! [SV491: $i > $o,SV1054: $i,SV197: $i > $o] :
( ( ( ~ ! [SY4242: $i] :
( ~ ( SV197 @ SY4242 )
| ( ( sK151_SY2866 @ SV1054 @ SV491 @ SV197 )
= SY4242 ) ) )
= $false )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV1054
= ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5365]) ).
thf(5399,plain,
! [SV491: $i > $o,SV1097: $i,SV197: $i > $o] :
( ( ( ! [SY4233: $i] :
( ~ ( SV197 @ SY4233 )
| ( SV1097 = SY4233 ) ) )
= $false )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5366]) ).
thf(5400,plain,
! [SV197: $i > $o,SV1098: $i,SV491: $i > $o] :
( ( ( ! [SY4234: $i] :
( ~ ( SV491 @ SY4234 )
| ( SV1098 = SY4234 ) ) )
= $false )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5367]) ).
thf(5401,plain,
! [SV1092: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
| ( SV1092
= ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5368]) ).
thf(5402,plain,
! [SV1093: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
| ( SV1093
= ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) ) )
= $false )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5369]) ).
thf(5403,plain,
! [SV1094: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
| ( SV1094
= ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5370]) ).
thf(5404,plain,
! [SV1095: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
| ( SV1095
= ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) ) )
= $false )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5371]) ).
thf(5405,plain,
! [SV1086: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5372]) ).
thf(5406,plain,
! [SV197: $i > $o,SV491: $i > $o,SV1086: $i] :
( ( ( SV1086
= ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $false )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5372]) ).
thf(5407,plain,
! [SV1087: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) ) )
= $false )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5373]) ).
thf(5408,plain,
! [SV491: $i > $o,SV197: $i > $o,SV1087: $i] :
( ( ( SV1087
= ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $false )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5373]) ).
thf(5409,plain,
! [SV226: $i,SV1056: $i,SV1041: $i] :
( ( ( ~ ( ~ ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
| ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
| ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) ) ) )
= $true )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5375]) ).
thf(5410,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SV955 ) )
| ~ ~ ~ ! [SY4236: $i] :
~ ~ ( ~ ( in @ SY4236 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
| ~ ( in @ SY4236 @ SV955 ) ) )
| ~ ! [SY4249: $i] :
( ~ ( in @ SY4249 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4238: $i] :
( ~ ( in @ SY4238 @ SY4249 )
| ( in @ SY4238 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) ) )
| ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SY4249 ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5376]) ).
thf(5411,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SV955 ) )
| ~ ~ ~ ! [SY4230: $i] :
~ ~ ( ~ ( in @ SY4230 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
| ~ ( in @ SY4230 @ SV955 ) ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5377]) ).
thf(5412,plain,
! [SV955: $i,SV1072: $i,SV226: $i] :
( ( ( ~ ! [SY4244: $i] :
( ~ ( in @ SY4244 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4232: $i] :
( ~ ( in @ SY4232 @ SY4244 )
| ( in @ SY4232 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) ) )
| ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SY4244 ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5377]) ).
thf(5413,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1089: $i,SV957: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK165_SY4223 @ SV957 @ SV1089 @ SV230 @ SV520 ) @ SV520 )
| ~ ( SV230 @ ( sK165_SY4223 @ SV957 @ SV1089 @ SV230 @ SV520 ) @ SV1089 ) ) )
= $false )
| ( ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5378]) ).
thf(5414,plain,
! [SV957: $i,SV1089: $i,SV230: $i > $i > $o,SV520: $i,SV1103: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1103 @ SV520 )
| ~ ( SV230 @ SV1103 @ SV1089 ) ) )
= $true )
| ( ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5379]) ).
thf(5415,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1080: $i,SV957: $i] :
( ( ( ~ ( ~ ( in @ ( sK160_SY4217 @ SV957 @ SV1080 @ SV230 @ SV520 ) @ SV520 )
| ~ ( SV230 @ ( sK160_SY4217 @ SV957 @ SV1080 @ SV230 @ SV520 ) @ SV1080 ) ) )
= $true )
| ( ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5380]) ).
thf(5416,plain,
! [SV957: $i,SV1080: $i,SV230: $i > $i > $o,SV520: $i,SV1102: $i] :
( ( ( ~ ( ~ ( in @ SV1102 @ SV520 )
| ~ ( SV230 @ SV1102 @ SV1080 ) ) )
= $false )
| ( ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5381]) ).
thf(5417,plain,
! [SV1010: $i,SV152: $i > $o,SV1101: $i,SV448: $i > $o] :
( ( ( SV448 @ SV1101 )
= $false )
| ( ( ~ ! [SY4240: $i] :
( ~ ( SV448 @ SY4240 )
| ( SV1101 = SY4240 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV152 @ ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5382]) ).
thf(5418,plain,
! [SV1010: $i,SV152: $i > $o,SV1099: $i,SV448: $i > $o] :
( ( ( ! [SY4239: $i] :
( ~ ( SV448 @ SY4239 )
| ( SV1099 = SY4239 ) ) )
= $false )
| ( ( SV448 @ SV1099 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV1010
= ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $false )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5383]) ).
thf(5419,plain,
! [SV1077: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV152 @ ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5384]) ).
thf(5420,plain,
! [SV1077: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV1077
= ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5385]) ).
thf(5421,plain,
! [SV1069: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV152 @ ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5386]) ).
thf(5422,plain,
! [SV1069: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV1069
= ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5387]) ).
thf(5423,plain,
! [SV1070: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV152 @ ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5388]) ).
thf(5424,plain,
! [SV1070: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV1070
= ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5389]) ).
thf(5425,plain,
! [SV1065: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV152 @ ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5390]) ).
thf(5426,plain,
! [SV1065: $i,SV152: $i > $o,SV1104: $i,SV448: $i > $o] :
( ( ( ~ ~ ( ~ ( SV448 @ SV1104 )
| ~ ! [SY4251: $i] :
( ~ ( SV448 @ SY4251 )
| ( SV1104 = SY4251 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV1065
= ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5391]) ).
thf(5427,plain,
! [SV175: $i,SV470: $i > $i,SV977: $i,SV1071: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK166_SY4165 @ SV1071 @ SV977 @ SV470 @ SV175 ) @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ ( sK166_SY4165 @ SV1071 @ SV977 @ SV470 @ SV175 ) ) ) ) )
= $false )
| ( ( in @ SV1071 @ SV175 )
= $false )
| ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
= ( SV470 @ SV1071 ) )
= $false )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5392]) ).
thf(5428,plain,
! [SV197: $i > $o,SV1053: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK155_SY3519 @ SV1053 @ SV197 @ SV491 ) ) )
= $false )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV197 @ ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5393]) ).
thf(5429,plain,
! [SV197: $i > $o,SV1053: $i,SV491: $i > $o] :
( ( ( ~ ! [SY4246: $i] :
( ~ ( SV491 @ SY4246 )
| ( ( sK155_SY3519 @ SV1053 @ SV197 @ SV491 )
= SY4246 ) ) )
= $false )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV197 @ ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5393]) ).
thf(5430,plain,
! [SV197: $i > $o,SV1053: $i,SV491: $i > $o] :
( ( ( SV491 @ ( sK150_SY3519 @ SV1053 @ SV197 @ SV491 ) )
= $true )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV1053
= ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5394]) ).
thf(5431,plain,
! [SV197: $i > $o,SV1053: $i,SV491: $i > $o] :
( ( ( ! [SY4241: $i] :
( ~ ( SV491 @ SY4241 )
| ( ( sK150_SY3519 @ SV1053 @ SV197 @ SV491 )
= SY4241 ) ) )
= $true )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV1053
= ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5395]) ).
thf(5432,plain,
! [SV491: $i > $o,SV1054: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK156_SY2866 @ SV1054 @ SV491 @ SV197 ) ) )
= $false )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV491 @ ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5396]) ).
thf(5433,plain,
! [SV491: $i > $o,SV1054: $i,SV197: $i > $o] :
( ( ( ~ ! [SY4247: $i] :
( ~ ( SV197 @ SY4247 )
| ( ( sK156_SY2866 @ SV1054 @ SV491 @ SV197 )
= SY4247 ) ) )
= $false )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV491 @ ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5396]) ).
thf(5434,plain,
! [SV491: $i > $o,SV1054: $i,SV197: $i > $o] :
( ( ( SV197 @ ( sK151_SY2866 @ SV1054 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV1054
= ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5397]) ).
thf(5435,plain,
! [SV491: $i > $o,SV1054: $i,SV197: $i > $o] :
( ( ( ! [SY4242: $i] :
( ~ ( SV197 @ SY4242 )
| ( ( sK151_SY2866 @ SV1054 @ SV491 @ SV197 )
= SY4242 ) ) )
= $true )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV1054
= ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5398]) ).
thf(5436,plain,
! [SV1097: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
| ( SV1097
= ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5399]) ).
thf(5437,plain,
! [SV1098: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
| ( SV1098
= ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) ) )
= $false )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5400]) ).
thf(5438,plain,
! [SV1092: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5401]) ).
thf(5439,plain,
! [SV197: $i > $o,SV491: $i > $o,SV1092: $i] :
( ( ( SV1092
= ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $false )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5401]) ).
thf(5440,plain,
! [SV1093: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) ) )
= $false )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5402]) ).
thf(5441,plain,
! [SV491: $i > $o,SV197: $i > $o,SV1093: $i] :
( ( ( SV1093
= ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $false )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5402]) ).
thf(5442,plain,
! [SV1094: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5403]) ).
thf(5443,plain,
! [SV197: $i > $o,SV491: $i > $o,SV1094: $i] :
( ( ( SV1094
= ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $false )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5403]) ).
thf(5444,plain,
! [SV1095: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) ) )
= $false )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5404]) ).
thf(5445,plain,
! [SV491: $i > $o,SV197: $i > $o,SV1095: $i] :
( ( ( SV1095
= ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $false )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5404]) ).
thf(5446,plain,
! [SV1086: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( SV197 @ ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $true )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5405]) ).
thf(5447,plain,
! [SV1086: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $false )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV1086
= ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5406]) ).
thf(5448,plain,
! [SV1087: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( SV491 @ ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $true )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5407]) ).
thf(5449,plain,
! [SV1087: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $false )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5408]) ).
thf(5450,plain,
! [SV226: $i,SV1056: $i,SV1041: $i] :
( ( ( ~ ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
| ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
| ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) ) ) )
= $true )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5409]) ).
thf(5451,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SV955 ) )
| ~ ~ ~ ! [SY4236: $i] :
~ ~ ( ~ ( in @ SY4236 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
| ~ ( in @ SY4236 @ SV955 ) ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5410]) ).
thf(5452,plain,
! [SV955: $i,SV1079: $i,SV226: $i] :
( ( ( ~ ! [SY4249: $i] :
( ~ ( in @ SY4249 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4238: $i] :
( ~ ( in @ SY4238 @ SY4249 )
| ( in @ SY4238 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) ) )
| ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SY4249 ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5410]) ).
thf(5453,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SV955 ) )
| ~ ~ ~ ! [SY4230: $i] :
~ ~ ( ~ ( in @ SY4230 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
| ~ ( in @ SY4230 @ SV955 ) ) ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5411]) ).
thf(5454,plain,
! [SV955: $i,SV1072: $i,SV226: $i] :
( ( ( ! [SY4244: $i] :
( ~ ( in @ SY4244 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4232: $i] :
( ~ ( in @ SY4232 @ SY4244 )
| ( in @ SY4232 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) ) )
| ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SY4244 ) ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5412]) ).
thf(5455,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1089: $i,SV957: $i] :
( ( ( ~ ( ~ ( in @ ( sK165_SY4223 @ SV957 @ SV1089 @ SV230 @ SV520 ) @ SV520 )
| ~ ( SV230 @ ( sK165_SY4223 @ SV957 @ SV1089 @ SV230 @ SV520 ) @ SV1089 ) ) )
= $true )
| ( ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5413]) ).
thf(5456,plain,
! [SV957: $i,SV1089: $i,SV230: $i > $i > $o,SV520: $i,SV1103: $i] :
( ( ( ~ ( ~ ( in @ SV1103 @ SV520 )
| ~ ( SV230 @ SV1103 @ SV1089 ) ) )
= $false )
| ( ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5414]) ).
thf(5457,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1080: $i,SV957: $i] :
( ( ( ~ ( in @ ( sK160_SY4217 @ SV957 @ SV1080 @ SV230 @ SV520 ) @ SV520 )
| ~ ( SV230 @ ( sK160_SY4217 @ SV957 @ SV1080 @ SV230 @ SV520 ) @ SV1080 ) )
= $false )
| ( ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5415]) ).
thf(5458,plain,
! [SV957: $i,SV1080: $i,SV230: $i > $i > $o,SV520: $i,SV1102: $i] :
( ( ( ~ ( in @ SV1102 @ SV520 )
| ~ ( SV230 @ SV1102 @ SV1080 ) )
= $true )
| ( ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5416]) ).
thf(5459,plain,
! [SV1010: $i,SV152: $i > $o,SV1101: $i,SV448: $i > $o] :
( ( ( ! [SY4240: $i] :
( ~ ( SV448 @ SY4240 )
| ( SV1101 = SY4240 ) ) )
= $false )
| ( ( SV448 @ SV1101 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV152 @ ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5417]) ).
thf(5460,plain,
! [SV1099: $i,SV152: $i > $o,SV1010: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK169_SY4239 @ SV1010 @ SV152 @ SV1099 @ SV448 ) )
| ( SV1099
= ( sK169_SY4239 @ SV1010 @ SV152 @ SV1099 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1099 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV1010
= ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $false )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5418]) ).
thf(5461,plain,
! [SV1077: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ~ ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV152 @ ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5419]) ).
thf(5462,plain,
! [SV1077: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV1077
= ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5420]) ).
thf(5463,plain,
! [SV1069: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV152 @ ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5421]) ).
thf(5464,plain,
! [SV1069: $i,SV152: $i > $o,SV1105: $i,SV448: $i > $o] :
( ( ( ~ ~ ( ~ ( SV448 @ SV1105 )
| ~ ! [SY4252: $i] :
( ~ ( SV448 @ SY4252 )
| ( SV1105 = SY4252 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV1069
= ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5422]) ).
thf(5465,plain,
! [SV1070: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV152 @ ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5423]) ).
thf(5466,plain,
! [SV1070: $i,SV152: $i > $o,SV1106: $i,SV448: $i > $o] :
( ( ( ~ ~ ( ~ ( SV448 @ SV1106 )
| ~ ! [SY4253: $i] :
( ~ ( SV448 @ SY4253 )
| ( SV1106 = SY4253 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV1070
= ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5424]) ).
thf(5467,plain,
! [SV1065: $i,SV152: $i > $o,SV1107: $i,SV448: $i > $o] :
( ( ( ~ ~ ( ~ ( SV448 @ SV1107 )
| ~ ! [SY4254: $i] :
( ~ ( SV448 @ SY4254 )
| ( SV1107 = SY4254 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV152 @ ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5425]) ).
thf(5468,plain,
! [SV1065: $i,SV152: $i > $o,SV1104: $i,SV448: $i > $o] :
( ( ( ~ ( ~ ( SV448 @ SV1104 )
| ~ ! [SY4251: $i] :
( ~ ( SV448 @ SY4251 )
| ( SV1104 = SY4251 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV1065
= ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5426]) ).
thf(5469,plain,
! [SV175: $i,SV470: $i > $i,SV977: $i,SV1071: $i] :
( ( ( ~ ( ~ ( in @ ( sK166_SY4165 @ SV1071 @ SV977 @ SV470 @ SV175 ) @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ ( sK166_SY4165 @ SV1071 @ SV977 @ SV470 @ SV175 ) ) ) ) )
= $true )
| ( ( in @ SV1071 @ SV175 )
= $false )
| ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
= ( SV470 @ SV1071 ) )
= $false )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5427]) ).
thf(5470,plain,
! [SV197: $i > $o,SV1053: $i,SV491: $i > $o] :
( ( ( SV491 @ ( sK155_SY3519 @ SV1053 @ SV197 @ SV491 ) )
= $true )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV197 @ ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5428]) ).
thf(5471,plain,
! [SV197: $i > $o,SV1053: $i,SV491: $i > $o] :
( ( ( ! [SY4246: $i] :
( ~ ( SV491 @ SY4246 )
| ( ( sK155_SY3519 @ SV1053 @ SV197 @ SV491 )
= SY4246 ) ) )
= $true )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV197 @ ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5429]) ).
thf(5472,plain,
! [SV197: $i > $o,SV1053: $i,SV1108: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1108 )
| ( ( sK150_SY3519 @ SV1053 @ SV197 @ SV491 )
= SV1108 ) )
= $true )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV1053
= ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5431]) ).
thf(5473,plain,
! [SV491: $i > $o,SV1054: $i,SV197: $i > $o] :
( ( ( SV197 @ ( sK156_SY2866 @ SV1054 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV491 @ ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5432]) ).
thf(5474,plain,
! [SV491: $i > $o,SV1054: $i,SV197: $i > $o] :
( ( ( ! [SY4247: $i] :
( ~ ( SV197 @ SY4247 )
| ( ( sK156_SY2866 @ SV1054 @ SV491 @ SV197 )
= SY4247 ) ) )
= $true )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV491 @ ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5433]) ).
thf(5475,plain,
! [SV491: $i > $o,SV1054: $i,SV1109: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1109 )
| ( ( sK151_SY2866 @ SV1054 @ SV491 @ SV197 )
= SV1109 ) )
= $true )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV1054
= ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5435]) ).
thf(5476,plain,
! [SV1097: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5436]) ).
thf(5477,plain,
! [SV197: $i > $o,SV491: $i > $o,SV1097: $i] :
( ( ( SV1097
= ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $false )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5436]) ).
thf(5478,plain,
! [SV1098: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) ) )
= $false )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5437]) ).
thf(5479,plain,
! [SV491: $i > $o,SV197: $i > $o,SV1098: $i] :
( ( ( SV1098
= ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $false )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5437]) ).
thf(5480,plain,
! [SV1092: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( SV197 @ ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $true )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5438]) ).
thf(5481,plain,
! [SV1092: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $false )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV1092
= ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5439]) ).
thf(5482,plain,
! [SV1093: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( SV491 @ ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $true )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5440]) ).
thf(5483,plain,
! [SV1093: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $false )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV1093
= ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5441]) ).
thf(5484,plain,
! [SV1094: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( SV197 @ ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $true )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5442]) ).
thf(5485,plain,
! [SV1094: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $false )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV1094
= ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5443]) ).
thf(5486,plain,
! [SV1095: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( SV491 @ ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $true )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5444]) ).
thf(5487,plain,
! [SV1095: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $false )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV1095
= ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5445]) ).
thf(5488,plain,
! [SV1086: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $false )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV197 @ ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5446]) ).
thf(5489,plain,
! [SV197: $i > $o,SV1086: $i,SV491: $i > $o] :
( ( ( ~ ~ ( ~ ( SV491 @ ( sK170_SY3519 @ SV1086 @ SV197 @ SV491 ) )
| ~ ! [SY4255: $i] :
( ~ ( SV491 @ SY4255 )
| ( ( sK170_SY3519 @ SV1086 @ SV197 @ SV491 )
= SY4255 ) ) ) )
= $false )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV1086
= ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5447]) ).
thf(5490,plain,
! [SV1087: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $false )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV491 @ ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5448]) ).
thf(5491,plain,
! [SV491: $i > $o,SV1087: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ ( sK171_SY2866 @ SV1087 @ SV491 @ SV197 ) )
| ~ ! [SY4256: $i] :
( ~ ( SV197 @ SY4256 )
| ( ( sK171_SY2866 @ SV1087 @ SV491 @ SV197 )
= SY4256 ) ) ) )
= $false )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5449]) ).
thf(5492,plain,
! [SV226: $i,SV1056: $i,SV1041: $i] :
( ( ( ~ ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
| ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) ) ) )
= $true )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5450]) ).
thf(5493,plain,
! [SV226: $i,SV1041: $i,SV1056: $i] :
( ( ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
| ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) ) ) )
= $true )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5450]) ).
thf(5494,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SV955 ) )
| ~ ~ ~ ! [SY4236: $i] :
~ ~ ( ~ ( in @ SY4236 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
| ~ ( in @ SY4236 @ SV955 ) ) ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5451]) ).
thf(5495,plain,
! [SV955: $i,SV1079: $i,SV226: $i] :
( ( ( ! [SY4249: $i] :
( ~ ( in @ SY4249 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4238: $i] :
( ~ ( in @ SY4238 @ SY4249 )
| ( in @ SY4238 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) ) )
| ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SY4249 ) ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5452]) ).
thf(5496,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SV955 ) )
| ~ ~ ~ ! [SY4230: $i] :
~ ~ ( ~ ( in @ SY4230 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
| ~ ( in @ SY4230 @ SV955 ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5453]) ).
thf(5497,plain,
! [SV955: $i,SV1072: $i,SV226: $i,SV1110: $i] :
( ( ( ~ ( in @ SV1110 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4257: $i] :
( ~ ( in @ SY4257 @ SV1110 )
| ( in @ SY4257 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) ) )
| ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SV1110 ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5454]) ).
thf(5498,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1089: $i,SV957: $i] :
( ( ( ~ ( in @ ( sK165_SY4223 @ SV957 @ SV1089 @ SV230 @ SV520 ) @ SV520 )
| ~ ( SV230 @ ( sK165_SY4223 @ SV957 @ SV1089 @ SV230 @ SV520 ) @ SV1089 ) )
= $false )
| ( ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5455]) ).
thf(5499,plain,
! [SV957: $i,SV1089: $i,SV230: $i > $i > $o,SV520: $i,SV1103: $i] :
( ( ( ~ ( in @ SV1103 @ SV520 )
| ~ ( SV230 @ SV1103 @ SV1089 ) )
= $true )
| ( ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5456]) ).
thf(5500,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1080: $i,SV957: $i] :
( ( ( ~ ( in @ ( sK160_SY4217 @ SV957 @ SV1080 @ SV230 @ SV520 ) @ SV520 ) )
= $false )
| ( ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5457]) ).
thf(5501,plain,
! [SV520: $i,SV1080: $i,SV957: $i,SV230: $i > $i > $o] :
( ( ( ~ ( SV230 @ ( sK160_SY4217 @ SV957 @ SV1080 @ SV230 @ SV520 ) @ SV1080 ) )
= $false )
| ( ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5457]) ).
thf(5502,plain,
! [SV957: $i,SV1080: $i,SV230: $i > $i > $o,SV520: $i,SV1102: $i] :
( ( ( ~ ( in @ SV1102 @ SV520 ) )
= $true )
| ( ( ~ ( SV230 @ SV1102 @ SV1080 ) )
= $true )
| ( ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5458]) ).
thf(5503,plain,
! [SV1101: $i,SV152: $i > $o,SV1010: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK172_SY4240 @ SV1010 @ SV152 @ SV1101 @ SV448 ) )
| ( SV1101
= ( sK172_SY4240 @ SV1010 @ SV152 @ SV1101 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1101 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV152 @ ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5459]) ).
thf(5504,plain,
! [SV1099: $i,SV152: $i > $o,SV1010: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK169_SY4239 @ SV1010 @ SV152 @ SV1099 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1099 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV1010
= ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $false )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5460]) ).
thf(5505,plain,
! [SV448: $i > $o,SV152: $i > $o,SV1010: $i,SV1099: $i] :
( ( ( SV1099
= ( sK169_SY4239 @ SV1010 @ SV152 @ SV1099 @ SV448 ) )
= $false )
| ( ( SV448 @ SV1099 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV1010
= ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $false )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5460]) ).
thf(5506,plain,
! [SV1077: $i,SV152: $i > $o,SV448: $i > $o] :
( ( ( ! [SY3429: $i] :
~ ~ ( ~ ( SV448 @ SY3429 )
| ~ ! [SY3430: $i] :
( ~ ( SV448 @ SY3430 )
| ( SY3429 = SY3430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV152 @ ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5461]) ).
thf(5507,plain,
! [SV1077: $i,SV152: $i > $o,SV1111: $i,SV448: $i > $o] :
( ( ( ~ ~ ( ~ ( SV448 @ SV1111 )
| ~ ! [SY4258: $i] :
( ~ ( SV448 @ SY4258 )
| ( SV1111 = SY4258 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV1077
= ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5462]) ).
thf(5508,plain,
! [SV1069: $i,SV152: $i > $o,SV1112: $i,SV448: $i > $o] :
( ( ( ~ ~ ( ~ ( SV448 @ SV1112 )
| ~ ! [SY4259: $i] :
( ~ ( SV448 @ SY4259 )
| ( SV1112 = SY4259 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV152 @ ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5463]) ).
thf(5509,plain,
! [SV1069: $i,SV152: $i > $o,SV1105: $i,SV448: $i > $o] :
( ( ( ~ ( ~ ( SV448 @ SV1105 )
| ~ ! [SY4252: $i] :
( ~ ( SV448 @ SY4252 )
| ( SV1105 = SY4252 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV1069
= ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5464]) ).
thf(5510,plain,
! [SV1070: $i,SV152: $i > $o,SV1113: $i,SV448: $i > $o] :
( ( ( ~ ~ ( ~ ( SV448 @ SV1113 )
| ~ ! [SY4260: $i] :
( ~ ( SV448 @ SY4260 )
| ( SV1113 = SY4260 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV152 @ ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5465]) ).
thf(5511,plain,
! [SV1070: $i,SV152: $i > $o,SV1106: $i,SV448: $i > $o] :
( ( ( ~ ( ~ ( SV448 @ SV1106 )
| ~ ! [SY4253: $i] :
( ~ ( SV448 @ SY4253 )
| ( SV1106 = SY4253 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV1070
= ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5466]) ).
thf(5512,plain,
! [SV1065: $i,SV152: $i > $o,SV1107: $i,SV448: $i > $o] :
( ( ( ~ ( ~ ( SV448 @ SV1107 )
| ~ ! [SY4254: $i] :
( ~ ( SV448 @ SY4254 )
| ( SV1107 = SY4254 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV152 @ ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5467]) ).
thf(5513,plain,
! [SV1065: $i,SV152: $i > $o,SV1104: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1104 )
| ~ ! [SY4251: $i] :
( ~ ( SV448 @ SY4251 )
| ( SV1104 = SY4251 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV1065
= ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5468]) ).
thf(5514,plain,
! [SV175: $i,SV470: $i > $i,SV977: $i,SV1071: $i] :
( ( ( ~ ( in @ ( sK166_SY4165 @ SV1071 @ SV977 @ SV470 @ SV175 ) @ SV175 )
| ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ ( sK166_SY4165 @ SV1071 @ SV977 @ SV470 @ SV175 ) ) ) )
= $false )
| ( ( in @ SV1071 @ SV175 )
= $false )
| ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
= ( SV470 @ SV1071 ) )
= $false )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5469]) ).
thf(5515,plain,
! [SV197: $i > $o,SV1053: $i,SV1114: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1114 )
| ( ( sK155_SY3519 @ SV1053 @ SV197 @ SV491 )
= SV1114 ) )
= $true )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV197 @ ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5471]) ).
thf(5516,plain,
! [SV197: $i > $o,SV1053: $i,SV1108: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1108 ) )
= $true )
| ( ( ( sK150_SY3519 @ SV1053 @ SV197 @ SV491 )
= SV1108 )
= $true )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV1053
= ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5472]) ).
thf(5517,plain,
! [SV491: $i > $o,SV1054: $i,SV1115: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1115 )
| ( ( sK156_SY2866 @ SV1054 @ SV491 @ SV197 )
= SV1115 ) )
= $true )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV491 @ ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5474]) ).
thf(5518,plain,
! [SV491: $i > $o,SV1054: $i,SV1109: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1109 ) )
= $true )
| ( ( ( sK151_SY2866 @ SV1054 @ SV491 @ SV197 )
= SV1109 )
= $true )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV1054
= ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5475]) ).
thf(5519,plain,
! [SV1097: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( SV197 @ ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $true )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( ~ ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5476]) ).
thf(5520,plain,
! [SV1097: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $false )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5477]) ).
thf(5521,plain,
! [SV1098: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( SV491 @ ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $true )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( ~ ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5478]) ).
thf(5522,plain,
! [SV1098: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $false )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5479]) ).
thf(5523,plain,
! [SV1092: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $false )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV197 @ ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5480]) ).
thf(5524,plain,
! [SV197: $i > $o,SV1092: $i,SV491: $i > $o] :
( ( ( ~ ~ ( ~ ( SV491 @ ( sK173_SY3519 @ SV1092 @ SV197 @ SV491 ) )
| ~ ! [SY4261: $i] :
( ~ ( SV491 @ SY4261 )
| ( ( sK173_SY3519 @ SV1092 @ SV197 @ SV491 )
= SY4261 ) ) ) )
= $false )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV1092
= ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5481]) ).
thf(5525,plain,
! [SV1093: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $false )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV491 @ ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5482]) ).
thf(5526,plain,
! [SV491: $i > $o,SV1093: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ ( sK174_SY2866 @ SV1093 @ SV491 @ SV197 ) )
| ~ ! [SY4262: $i] :
( ~ ( SV197 @ SY4262 )
| ( ( sK174_SY2866 @ SV1093 @ SV491 @ SV197 )
= SY4262 ) ) ) )
= $false )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV1093
= ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5483]) ).
thf(5527,plain,
! [SV1094: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $false )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV197 @ ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5484]) ).
thf(5528,plain,
! [SV197: $i > $o,SV1094: $i,SV491: $i > $o] :
( ( ( ~ ~ ( ~ ( SV491 @ ( sK175_SY3519 @ SV1094 @ SV197 @ SV491 ) )
| ~ ! [SY4263: $i] :
( ~ ( SV491 @ SY4263 )
| ( ( sK175_SY3519 @ SV1094 @ SV197 @ SV491 )
= SY4263 ) ) ) )
= $false )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV1094
= ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5485]) ).
thf(5529,plain,
! [SV1095: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $false )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV491 @ ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5486]) ).
thf(5530,plain,
! [SV491: $i > $o,SV1095: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ ( sK176_SY2866 @ SV1095 @ SV491 @ SV197 ) )
| ~ ! [SY4264: $i] :
( ~ ( SV197 @ SY4264 )
| ( ( sK176_SY2866 @ SV1095 @ SV491 @ SV197 )
= SY4264 ) ) ) )
= $false )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV1095
= ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5487]) ).
thf(5531,plain,
! [SV197: $i > $o,SV1086: $i,SV491: $i > $o] :
( ( ( ~ ~ ( ~ ( SV491 @ ( sK177_SY3519 @ SV1086 @ SV197 @ SV491 ) )
| ~ ! [SY4265: $i] :
( ~ ( SV491 @ SY4265 )
| ( ( sK177_SY3519 @ SV1086 @ SV197 @ SV491 )
= SY4265 ) ) ) )
= $false )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV197 @ ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5488]) ).
thf(5532,plain,
! [SV197: $i > $o,SV1086: $i,SV491: $i > $o] :
( ( ( ~ ( ~ ( SV491 @ ( sK170_SY3519 @ SV1086 @ SV197 @ SV491 ) )
| ~ ! [SY4255: $i] :
( ~ ( SV491 @ SY4255 )
| ( ( sK170_SY3519 @ SV1086 @ SV197 @ SV491 )
= SY4255 ) ) ) )
= $true )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV1086
= ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5489]) ).
thf(5533,plain,
! [SV491: $i > $o,SV1087: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ ( sK178_SY2866 @ SV1087 @ SV491 @ SV197 ) )
| ~ ! [SY4266: $i] :
( ~ ( SV197 @ SY4266 )
| ( ( sK178_SY2866 @ SV1087 @ SV491 @ SV197 )
= SY4266 ) ) ) )
= $false )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV491 @ ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5490]) ).
thf(5534,plain,
! [SV491: $i > $o,SV1087: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ ( sK171_SY2866 @ SV1087 @ SV491 @ SV197 ) )
| ~ ! [SY4256: $i] :
( ~ ( SV197 @ SY4256 )
| ( ( sK171_SY2866 @ SV1087 @ SV491 @ SV197 )
= SY4256 ) ) ) )
= $true )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5491]) ).
thf(5535,plain,
! [SV226: $i,SV1056: $i,SV1041: $i] :
( ( ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
| ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) ) ) )
= $true )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5492]) ).
thf(5536,plain,
! [SV226: $i,SV1041: $i,SV1056: $i] :
( ( ( ~ ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
| ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) ) )
= $false )
| ( ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
= $false )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5493]) ).
thf(5537,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SV955 ) )
| ~ ~ ~ ! [SY4236: $i] :
~ ~ ( ~ ( in @ SY4236 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
| ~ ( in @ SY4236 @ SV955 ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5494]) ).
thf(5538,plain,
! [SV955: $i,SV1079: $i,SV226: $i,SV1116: $i] :
( ( ( ~ ( in @ SV1116 @ ( sK2_SY2943 @ SV226 ) )
| ! [SY4267: $i] :
( ~ ( in @ SY4267 @ SV1116 )
| ( in @ SY4267 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) ) )
| ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SV1116 ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5495]) ).
thf(5539,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SV955 ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5496]) ).
thf(5540,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( ~ ~ ~ ! [SY4230: $i] :
~ ~ ( ~ ( in @ SY4230 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
| ~ ( in @ SY4230 @ SV955 ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5496]) ).
thf(5541,plain,
! [SV955: $i,SV1072: $i,SV226: $i,SV1110: $i] :
( ( ( ~ ( in @ SV1110 @ ( sK2_SY2943 @ SV226 ) ) )
= $true )
| ( ( ! [SY4257: $i] :
( ~ ( in @ SY4257 @ SV1110 )
| ( in @ SY4257 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) ) )
| ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SV1110 ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5497]) ).
thf(5542,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1089: $i,SV957: $i] :
( ( ( ~ ( in @ ( sK165_SY4223 @ SV957 @ SV1089 @ SV230 @ SV520 ) @ SV520 ) )
= $false )
| ( ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5498]) ).
thf(5543,plain,
! [SV520: $i,SV1089: $i,SV957: $i,SV230: $i > $i > $o] :
( ( ( ~ ( SV230 @ ( sK165_SY4223 @ SV957 @ SV1089 @ SV230 @ SV520 ) @ SV1089 ) )
= $false )
| ( ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5498]) ).
thf(5544,plain,
! [SV957: $i,SV1089: $i,SV230: $i > $i > $o,SV520: $i,SV1103: $i] :
( ( ( ~ ( in @ SV1103 @ SV520 ) )
= $true )
| ( ( ~ ( SV230 @ SV1103 @ SV1089 ) )
= $true )
| ( ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5499]) ).
thf(5545,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1080: $i,SV957: $i] :
( ( ( in @ ( sK160_SY4217 @ SV957 @ SV1080 @ SV230 @ SV520 ) @ SV520 )
= $true )
| ( ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5500]) ).
thf(5546,plain,
! [SV520: $i,SV1080: $i,SV957: $i,SV230: $i > $i > $o] :
( ( ( SV230 @ ( sK160_SY4217 @ SV957 @ SV1080 @ SV230 @ SV520 ) @ SV1080 )
= $true )
| ( ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5501]) ).
thf(5547,plain,
! [SV957: $i,SV1080: $i,SV230: $i > $i > $o,SV520: $i,SV1102: $i] :
( ( ( in @ SV1102 @ SV520 )
= $false )
| ( ( ~ ( SV230 @ SV1102 @ SV1080 ) )
= $true )
| ( ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5502]) ).
thf(5548,plain,
! [SV1101: $i,SV152: $i > $o,SV1010: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK172_SY4240 @ SV1010 @ SV152 @ SV1101 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1101 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV152 @ ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5503]) ).
thf(5549,plain,
! [SV448: $i > $o,SV152: $i > $o,SV1010: $i,SV1101: $i] :
( ( ( SV1101
= ( sK172_SY4240 @ SV1010 @ SV152 @ SV1101 @ SV448 ) )
= $false )
| ( ( SV448 @ SV1101 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV152 @ ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5503]) ).
thf(5550,plain,
! [SV1099: $i,SV152: $i > $o,SV1010: $i,SV448: $i > $o] :
( ( ( SV448 @ ( sK169_SY4239 @ SV1010 @ SV152 @ SV1099 @ SV448 ) )
= $true )
| ( ( SV448 @ SV1099 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV1010
= ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $false )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5504]) ).
thf(5551,plain,
! [SV1077: $i,SV152: $i > $o,SV1117: $i,SV448: $i > $o] :
( ( ( ~ ~ ( ~ ( SV448 @ SV1117 )
| ~ ! [SY4268: $i] :
( ~ ( SV448 @ SY4268 )
| ( SV1117 = SY4268 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV152 @ ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5506]) ).
thf(5552,plain,
! [SV1077: $i,SV152: $i > $o,SV1111: $i,SV448: $i > $o] :
( ( ( ~ ( ~ ( SV448 @ SV1111 )
| ~ ! [SY4258: $i] :
( ~ ( SV448 @ SY4258 )
| ( SV1111 = SY4258 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV1077
= ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5507]) ).
thf(5553,plain,
! [SV1069: $i,SV152: $i > $o,SV1112: $i,SV448: $i > $o] :
( ( ( ~ ( ~ ( SV448 @ SV1112 )
| ~ ! [SY4259: $i] :
( ~ ( SV448 @ SY4259 )
| ( SV1112 = SY4259 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV152 @ ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5508]) ).
thf(5554,plain,
! [SV1069: $i,SV152: $i > $o,SV1105: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1105 )
| ~ ! [SY4252: $i] :
( ~ ( SV448 @ SY4252 )
| ( SV1105 = SY4252 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV1069
= ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5509]) ).
thf(5555,plain,
! [SV1070: $i,SV152: $i > $o,SV1113: $i,SV448: $i > $o] :
( ( ( ~ ( ~ ( SV448 @ SV1113 )
| ~ ! [SY4260: $i] :
( ~ ( SV448 @ SY4260 )
| ( SV1113 = SY4260 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV152 @ ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5510]) ).
thf(5556,plain,
! [SV1070: $i,SV152: $i > $o,SV1106: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1106 )
| ~ ! [SY4253: $i] :
( ~ ( SV448 @ SY4253 )
| ( SV1106 = SY4253 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV1070
= ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5511]) ).
thf(5557,plain,
! [SV1065: $i,SV152: $i > $o,SV1107: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1107 )
| ~ ! [SY4254: $i] :
( ~ ( SV448 @ SY4254 )
| ( SV1107 = SY4254 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV152 @ ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5512]) ).
thf(5558,plain,
! [SV1065: $i,SV152: $i > $o,SV1104: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1104 ) )
= $true )
| ( ( ~ ! [SY4251: $i] :
( ~ ( SV448 @ SY4251 )
| ( SV1104 = SY4251 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV1065
= ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5513]) ).
thf(5559,plain,
! [SV175: $i,SV470: $i > $i,SV977: $i,SV1071: $i] :
( ( ( ~ ( in @ ( sK166_SY4165 @ SV1071 @ SV977 @ SV470 @ SV175 ) @ SV175 ) )
= $false )
| ( ( in @ SV1071 @ SV175 )
= $false )
| ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
= ( SV470 @ SV1071 ) )
= $false )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5514]) ).
thf(5560,plain,
! [SV1071: $i,SV977: $i,SV175: $i,SV470: $i > $i] :
( ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
!= ( SV470 @ ( sK166_SY4165 @ SV1071 @ SV977 @ SV470 @ SV175 ) ) )
= $false )
| ( ( in @ SV1071 @ SV175 )
= $false )
| ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
= ( SV470 @ SV1071 ) )
= $false )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5514]) ).
thf(5561,plain,
! [SV197: $i > $o,SV1053: $i,SV1114: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1114 ) )
= $true )
| ( ( ( sK155_SY3519 @ SV1053 @ SV197 @ SV491 )
= SV1114 )
= $true )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV197 @ ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5515]) ).
thf(5562,plain,
! [SV197: $i > $o,SV1053: $i,SV1108: $i,SV491: $i > $o] :
( ( ( SV491 @ SV1108 )
= $false )
| ( ( ( sK150_SY3519 @ SV1053 @ SV197 @ SV491 )
= SV1108 )
= $true )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV1053
= ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5516]) ).
thf(5563,plain,
! [SV491: $i > $o,SV1054: $i,SV1115: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1115 ) )
= $true )
| ( ( ( sK156_SY2866 @ SV1054 @ SV491 @ SV197 )
= SV1115 )
= $true )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV491 @ ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5517]) ).
thf(5564,plain,
! [SV491: $i > $o,SV1054: $i,SV1109: $i,SV197: $i > $o] :
( ( ( SV197 @ SV1109 )
= $false )
| ( ( ( sK151_SY2866 @ SV1054 @ SV491 @ SV197 )
= SV1109 )
= $true )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV1054
= ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $false )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5518]) ).
thf(5565,plain,
! [SV1097: $i,SV197: $i > $o,SV491: $i > $o] :
( ( ( ! [SY3519: $i] :
~ ~ ( ~ ( SV491 @ SY3519 )
| ~ ! [SY3520: $i] :
( ~ ( SV491 @ SY3520 )
| ( SY3519 = SY3520 ) ) ) )
= $false )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV197 @ ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5519]) ).
thf(5566,plain,
! [SV197: $i > $o,SV1097: $i,SV491: $i > $o] :
( ( ( ~ ~ ( ~ ( SV491 @ ( sK179_SY3519 @ SV1097 @ SV197 @ SV491 ) )
| ~ ! [SY4269: $i] :
( ~ ( SV491 @ SY4269 )
| ( ( sK179_SY3519 @ SV1097 @ SV197 @ SV491 )
= SY4269 ) ) ) )
= $false )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5520]) ).
thf(5567,plain,
! [SV1098: $i,SV491: $i > $o,SV197: $i > $o] :
( ( ( ! [SY2866: $i] :
~ ~ ( ~ ( SV197 @ SY2866 )
| ~ ! [SY2867: $i] :
( ~ ( SV197 @ SY2867 )
| ( SY2866 = SY2867 ) ) ) )
= $false )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV491 @ ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5521]) ).
thf(5568,plain,
! [SV491: $i > $o,SV1098: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ ( sK180_SY2866 @ SV1098 @ SV491 @ SV197 ) )
| ~ ! [SY4270: $i] :
( ~ ( SV197 @ SY4270 )
| ( ( sK180_SY2866 @ SV1098 @ SV491 @ SV197 )
= SY4270 ) ) ) )
= $false )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5522]) ).
thf(5569,plain,
! [SV197: $i > $o,SV1092: $i,SV491: $i > $o] :
( ( ( ~ ~ ( ~ ( SV491 @ ( sK181_SY3519 @ SV1092 @ SV197 @ SV491 ) )
| ~ ! [SY4271: $i] :
( ~ ( SV491 @ SY4271 )
| ( ( sK181_SY3519 @ SV1092 @ SV197 @ SV491 )
= SY4271 ) ) ) )
= $false )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV197 @ ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5523]) ).
thf(5570,plain,
! [SV197: $i > $o,SV1092: $i,SV491: $i > $o] :
( ( ( ~ ( ~ ( SV491 @ ( sK173_SY3519 @ SV1092 @ SV197 @ SV491 ) )
| ~ ! [SY4261: $i] :
( ~ ( SV491 @ SY4261 )
| ( ( sK173_SY3519 @ SV1092 @ SV197 @ SV491 )
= SY4261 ) ) ) )
= $true )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV1092
= ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5524]) ).
thf(5571,plain,
! [SV491: $i > $o,SV1093: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ ( sK182_SY2866 @ SV1093 @ SV491 @ SV197 ) )
| ~ ! [SY4272: $i] :
( ~ ( SV197 @ SY4272 )
| ( ( sK182_SY2866 @ SV1093 @ SV491 @ SV197 )
= SY4272 ) ) ) )
= $false )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV491 @ ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5525]) ).
thf(5572,plain,
! [SV491: $i > $o,SV1093: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ ( sK174_SY2866 @ SV1093 @ SV491 @ SV197 ) )
| ~ ! [SY4262: $i] :
( ~ ( SV197 @ SY4262 )
| ( ( sK174_SY2866 @ SV1093 @ SV491 @ SV197 )
= SY4262 ) ) ) )
= $true )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV1093
= ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5526]) ).
thf(5573,plain,
! [SV197: $i > $o,SV1094: $i,SV491: $i > $o] :
( ( ( ~ ~ ( ~ ( SV491 @ ( sK183_SY3519 @ SV1094 @ SV197 @ SV491 ) )
| ~ ! [SY4273: $i] :
( ~ ( SV491 @ SY4273 )
| ( ( sK183_SY3519 @ SV1094 @ SV197 @ SV491 )
= SY4273 ) ) ) )
= $false )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV197 @ ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5527]) ).
thf(5574,plain,
! [SV197: $i > $o,SV1094: $i,SV491: $i > $o] :
( ( ( ~ ( ~ ( SV491 @ ( sK175_SY3519 @ SV1094 @ SV197 @ SV491 ) )
| ~ ! [SY4263: $i] :
( ~ ( SV491 @ SY4263 )
| ( ( sK175_SY3519 @ SV1094 @ SV197 @ SV491 )
= SY4263 ) ) ) )
= $true )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV1094
= ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5528]) ).
thf(5575,plain,
! [SV491: $i > $o,SV1095: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ ( sK184_SY2866 @ SV1095 @ SV491 @ SV197 ) )
| ~ ! [SY4274: $i] :
( ~ ( SV197 @ SY4274 )
| ( ( sK184_SY2866 @ SV1095 @ SV491 @ SV197 )
= SY4274 ) ) ) )
= $false )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV491 @ ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5529]) ).
thf(5576,plain,
! [SV491: $i > $o,SV1095: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ ( sK176_SY2866 @ SV1095 @ SV491 @ SV197 ) )
| ~ ! [SY4264: $i] :
( ~ ( SV197 @ SY4264 )
| ( ( sK176_SY2866 @ SV1095 @ SV491 @ SV197 )
= SY4264 ) ) ) )
= $true )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV1095
= ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5530]) ).
thf(5577,plain,
! [SV197: $i > $o,SV1086: $i,SV491: $i > $o] :
( ( ( ~ ( ~ ( SV491 @ ( sK177_SY3519 @ SV1086 @ SV197 @ SV491 ) )
| ~ ! [SY4265: $i] :
( ~ ( SV491 @ SY4265 )
| ( ( sK177_SY3519 @ SV1086 @ SV197 @ SV491 )
= SY4265 ) ) ) )
= $true )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV197 @ ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5531]) ).
thf(5578,plain,
! [SV197: $i > $o,SV1086: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK170_SY3519 @ SV1086 @ SV197 @ SV491 ) )
| ~ ! [SY4255: $i] :
( ~ ( SV491 @ SY4255 )
| ( ( sK170_SY3519 @ SV1086 @ SV197 @ SV491 )
= SY4255 ) ) )
= $false )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV1086
= ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5532]) ).
thf(5579,plain,
! [SV491: $i > $o,SV1087: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ ( sK178_SY2866 @ SV1087 @ SV491 @ SV197 ) )
| ~ ! [SY4266: $i] :
( ~ ( SV197 @ SY4266 )
| ( ( sK178_SY2866 @ SV1087 @ SV491 @ SV197 )
= SY4266 ) ) ) )
= $true )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV491 @ ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5533]) ).
thf(5580,plain,
! [SV491: $i > $o,SV1087: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK171_SY2866 @ SV1087 @ SV491 @ SV197 ) )
| ~ ! [SY4256: $i] :
( ~ ( SV197 @ SY4256 )
| ( ( sK171_SY2866 @ SV1087 @ SV491 @ SV197 )
= SY4256 ) ) )
= $false )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5534]) ).
thf(5581,plain,
! [SV226: $i,SV1041: $i,SV1056: $i] :
( ( ( ~ ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
| ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) ) )
= $false )
| ( ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
= $true )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5535]) ).
thf(5582,plain,
! [SV226: $i,SV1041: $i,SV1056: $i] :
( ( ( ~ ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) ) )
= $false )
| ( ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
= $false )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5536]) ).
thf(5583,plain,
! [SV226: $i,SV1056: $i,SV1041: $i] :
( ( ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
= $false )
| ( ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
= $false )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5536]) ).
thf(5584,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SV955 ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5537]) ).
thf(5585,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( ~ ~ ~ ! [SY4236: $i] :
~ ~ ( ~ ( in @ SY4236 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
| ~ ( in @ SY4236 @ SV955 ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5537]) ).
thf(5586,plain,
! [SV955: $i,SV1079: $i,SV226: $i,SV1116: $i] :
( ( ( ~ ( in @ SV1116 @ ( sK2_SY2943 @ SV226 ) ) )
= $true )
| ( ( ! [SY4267: $i] :
( ~ ( in @ SY4267 @ SV1116 )
| ( in @ SY4267 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) ) )
| ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SV1116 ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5538]) ).
thf(5587,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( ~ ( ~ ( in @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SV955 ) ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5539]) ).
thf(5588,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( ~ ~ ! [SY4230: $i] :
~ ~ ( ~ ( in @ SY4230 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
| ~ ( in @ SY4230 @ SV955 ) ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5540]) ).
thf(5589,plain,
! [SV955: $i,SV1072: $i,SV226: $i,SV1110: $i] :
( ( ( in @ SV1110 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( ! [SY4257: $i] :
( ~ ( in @ SY4257 @ SV1110 )
| ( in @ SY4257 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) ) )
| ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SV1110 ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5541]) ).
thf(5590,plain,
! [SV520: $i,SV230: $i > $i > $o,SV1089: $i,SV957: $i] :
( ( ( in @ ( sK165_SY4223 @ SV957 @ SV1089 @ SV230 @ SV520 ) @ SV520 )
= $true )
| ( ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5542]) ).
thf(5591,plain,
! [SV520: $i,SV1089: $i,SV957: $i,SV230: $i > $i > $o] :
( ( ( SV230 @ ( sK165_SY4223 @ SV957 @ SV1089 @ SV230 @ SV520 ) @ SV1089 )
= $true )
| ( ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5543]) ).
thf(5592,plain,
! [SV957: $i,SV1089: $i,SV230: $i > $i > $o,SV520: $i,SV1103: $i] :
( ( ( in @ SV1103 @ SV520 )
= $false )
| ( ( ~ ( SV230 @ SV1103 @ SV1089 ) )
= $true )
| ( ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5544]) ).
thf(5593,plain,
! [SV957: $i,SV520: $i,SV1080: $i,SV1102: $i,SV230: $i > $i > $o] :
( ( ( SV230 @ SV1102 @ SV1080 )
= $false )
| ( ( in @ SV1102 @ SV520 )
= $false )
| ( ( in @ SV1080 @ ( sK121_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV957
= ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5547]) ).
thf(5594,plain,
! [SV1101: $i,SV152: $i > $o,SV1010: $i,SV448: $i > $o] :
( ( ( SV448 @ ( sK172_SY4240 @ SV1010 @ SV152 @ SV1101 @ SV448 ) )
= $true )
| ( ( SV448 @ SV1101 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1010 )
= $false )
| ( ( SV152 @ ( sK128_SY4163 @ SV448 @ SV1010 @ SV152 ) )
= $true )
| ( ( ( sK12_SY3425 @ SV448 @ SV152 )
= ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5548]) ).
thf(5595,plain,
! [SV1077: $i,SV152: $i > $o,SV1117: $i,SV448: $i > $o] :
( ( ( ~ ( ~ ( SV448 @ SV1117 )
| ~ ! [SY4268: $i] :
( ~ ( SV448 @ SY4268 )
| ( SV1117 = SY4268 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV152 @ ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5551]) ).
thf(5596,plain,
! [SV1077: $i,SV152: $i > $o,SV1111: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1111 )
| ~ ! [SY4258: $i] :
( ~ ( SV448 @ SY4258 )
| ( SV1111 = SY4258 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV1077
= ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5552]) ).
thf(5597,plain,
! [SV1069: $i,SV152: $i > $o,SV1112: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1112 )
| ~ ! [SY4259: $i] :
( ~ ( SV448 @ SY4259 )
| ( SV1112 = SY4259 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV152 @ ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5553]) ).
thf(5598,plain,
! [SV1069: $i,SV152: $i > $o,SV1105: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1105 ) )
= $true )
| ( ( ~ ! [SY4252: $i] :
( ~ ( SV448 @ SY4252 )
| ( SV1105 = SY4252 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV1069
= ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5554]) ).
thf(5599,plain,
! [SV1070: $i,SV152: $i > $o,SV1113: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1113 )
| ~ ! [SY4260: $i] :
( ~ ( SV448 @ SY4260 )
| ( SV1113 = SY4260 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV152 @ ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5555]) ).
thf(5600,plain,
! [SV1070: $i,SV152: $i > $o,SV1106: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1106 ) )
= $true )
| ( ( ~ ! [SY4253: $i] :
( ~ ( SV448 @ SY4253 )
| ( SV1106 = SY4253 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV1070
= ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5556]) ).
thf(5601,plain,
! [SV1065: $i,SV152: $i > $o,SV1107: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1107 ) )
= $true )
| ( ( ~ ! [SY4254: $i] :
( ~ ( SV448 @ SY4254 )
| ( SV1107 = SY4254 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV152 @ ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5557]) ).
thf(5602,plain,
! [SV1065: $i,SV152: $i > $o,SV1104: $i,SV448: $i > $o] :
( ( ( SV448 @ SV1104 )
= $false )
| ( ( ~ ! [SY4251: $i] :
( ~ ( SV448 @ SY4251 )
| ( SV1104 = SY4251 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV1065
= ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5558]) ).
thf(5603,plain,
! [SV175: $i,SV470: $i > $i,SV977: $i,SV1071: $i] :
( ( ( in @ ( sK166_SY4165 @ SV1071 @ SV977 @ SV470 @ SV175 ) @ SV175 )
= $true )
| ( ( in @ SV1071 @ SV175 )
= $false )
| ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
= ( SV470 @ SV1071 ) )
= $false )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5559]) ).
thf(5604,plain,
! [SV1071: $i,SV977: $i,SV175: $i,SV470: $i > $i] :
( ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
= ( SV470 @ ( sK166_SY4165 @ SV1071 @ SV977 @ SV470 @ SV175 ) ) )
= $true )
| ( ( in @ SV1071 @ SV175 )
= $false )
| ( ( ( sK88_SY4137 @ SV470 @ SV175 @ SV977 )
= ( SV470 @ SV1071 ) )
= $false )
| ( ( ( sK3_SY3462 @ SV470 @ SV175 )
= SV977 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5560]) ).
thf(5605,plain,
! [SV197: $i > $o,SV1053: $i,SV1114: $i,SV491: $i > $o] :
( ( ( SV491 @ SV1114 )
= $false )
| ( ( ( sK155_SY3519 @ SV1053 @ SV197 @ SV491 )
= SV1114 )
= $true )
| ( ( SV197 @ SV1053 )
= $false )
| ( ( SV197 @ ( sK142_SY4191 @ SV491 @ SV1053 @ SV197 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5561]) ).
thf(5606,plain,
! [SV491: $i > $o,SV1054: $i,SV1115: $i,SV197: $i > $o] :
( ( ( SV197 @ SV1115 )
= $false )
| ( ( ( sK156_SY2866 @ SV1054 @ SV491 @ SV197 )
= SV1115 )
= $true )
| ( ( SV491 @ SV1054 )
= $false )
| ( ( SV491 @ ( sK143_SY4192 @ SV197 @ SV1054 @ SV491 ) )
= $true )
| ( ( ( sK13_SY3515 @ SV491 @ SV197 )
= ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5563]) ).
thf(5607,plain,
! [SV197: $i > $o,SV1097: $i,SV491: $i > $o] :
( ( ( ~ ~ ( ~ ( SV491 @ ( sK185_SY3519 @ SV1097 @ SV197 @ SV491 ) )
| ~ ! [SY4275: $i] :
( ~ ( SV491 @ SY4275 )
| ( ( sK185_SY3519 @ SV1097 @ SV197 @ SV491 )
= SY4275 ) ) ) )
= $false )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV197 @ ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5565]) ).
thf(5608,plain,
! [SV197: $i > $o,SV1097: $i,SV491: $i > $o] :
( ( ( ~ ( ~ ( SV491 @ ( sK179_SY3519 @ SV1097 @ SV197 @ SV491 ) )
| ~ ! [SY4269: $i] :
( ~ ( SV491 @ SY4269 )
| ( ( sK179_SY3519 @ SV1097 @ SV197 @ SV491 )
= SY4269 ) ) ) )
= $true )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5566]) ).
thf(5609,plain,
! [SV491: $i > $o,SV1098: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ ( sK186_SY2866 @ SV1098 @ SV491 @ SV197 ) )
| ~ ! [SY4276: $i] :
( ~ ( SV197 @ SY4276 )
| ( ( sK186_SY2866 @ SV1098 @ SV491 @ SV197 )
= SY4276 ) ) ) )
= $false )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV491 @ ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5567]) ).
thf(5610,plain,
! [SV491: $i > $o,SV1098: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ ( sK180_SY2866 @ SV1098 @ SV491 @ SV197 ) )
| ~ ! [SY4270: $i] :
( ~ ( SV197 @ SY4270 )
| ( ( sK180_SY2866 @ SV1098 @ SV491 @ SV197 )
= SY4270 ) ) ) )
= $true )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5568]) ).
thf(5611,plain,
! [SV197: $i > $o,SV1092: $i,SV491: $i > $o] :
( ( ( ~ ( ~ ( SV491 @ ( sK181_SY3519 @ SV1092 @ SV197 @ SV491 ) )
| ~ ! [SY4271: $i] :
( ~ ( SV491 @ SY4271 )
| ( ( sK181_SY3519 @ SV1092 @ SV197 @ SV491 )
= SY4271 ) ) ) )
= $true )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV197 @ ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5569]) ).
thf(5612,plain,
! [SV197: $i > $o,SV1092: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK173_SY3519 @ SV1092 @ SV197 @ SV491 ) )
| ~ ! [SY4261: $i] :
( ~ ( SV491 @ SY4261 )
| ( ( sK173_SY3519 @ SV1092 @ SV197 @ SV491 )
= SY4261 ) ) )
= $false )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV1092
= ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5570]) ).
thf(5613,plain,
! [SV491: $i > $o,SV1093: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ ( sK182_SY2866 @ SV1093 @ SV491 @ SV197 ) )
| ~ ! [SY4272: $i] :
( ~ ( SV197 @ SY4272 )
| ( ( sK182_SY2866 @ SV1093 @ SV491 @ SV197 )
= SY4272 ) ) ) )
= $true )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV491 @ ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5571]) ).
thf(5614,plain,
! [SV491: $i > $o,SV1093: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK174_SY2866 @ SV1093 @ SV491 @ SV197 ) )
| ~ ! [SY4262: $i] :
( ~ ( SV197 @ SY4262 )
| ( ( sK174_SY2866 @ SV1093 @ SV491 @ SV197 )
= SY4262 ) ) )
= $false )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV1093
= ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5572]) ).
thf(5615,plain,
! [SV197: $i > $o,SV1094: $i,SV491: $i > $o] :
( ( ( ~ ( ~ ( SV491 @ ( sK183_SY3519 @ SV1094 @ SV197 @ SV491 ) )
| ~ ! [SY4273: $i] :
( ~ ( SV491 @ SY4273 )
| ( ( sK183_SY3519 @ SV1094 @ SV197 @ SV491 )
= SY4273 ) ) ) )
= $true )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV197 @ ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5573]) ).
thf(5616,plain,
! [SV197: $i > $o,SV1094: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK175_SY3519 @ SV1094 @ SV197 @ SV491 ) )
| ~ ! [SY4263: $i] :
( ~ ( SV491 @ SY4263 )
| ( ( sK175_SY3519 @ SV1094 @ SV197 @ SV491 )
= SY4263 ) ) )
= $false )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV1094
= ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5574]) ).
thf(5617,plain,
! [SV491: $i > $o,SV1095: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ ( sK184_SY2866 @ SV1095 @ SV491 @ SV197 ) )
| ~ ! [SY4274: $i] :
( ~ ( SV197 @ SY4274 )
| ( ( sK184_SY2866 @ SV1095 @ SV491 @ SV197 )
= SY4274 ) ) ) )
= $true )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV491 @ ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5575]) ).
thf(5618,plain,
! [SV491: $i > $o,SV1095: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK176_SY2866 @ SV1095 @ SV491 @ SV197 ) )
| ~ ! [SY4264: $i] :
( ~ ( SV197 @ SY4264 )
| ( ( sK176_SY2866 @ SV1095 @ SV491 @ SV197 )
= SY4264 ) ) )
= $false )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV1095
= ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5576]) ).
thf(5619,plain,
! [SV197: $i > $o,SV1086: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK177_SY3519 @ SV1086 @ SV197 @ SV491 ) )
| ~ ! [SY4265: $i] :
( ~ ( SV491 @ SY4265 )
| ( ( sK177_SY3519 @ SV1086 @ SV197 @ SV491 )
= SY4265 ) ) )
= $false )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV197 @ ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5577]) ).
thf(5620,plain,
! [SV197: $i > $o,SV1086: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK170_SY3519 @ SV1086 @ SV197 @ SV491 ) ) )
= $false )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV1086
= ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5578]) ).
thf(5621,plain,
! [SV197: $i > $o,SV1086: $i,SV491: $i > $o] :
( ( ( ~ ! [SY4255: $i] :
( ~ ( SV491 @ SY4255 )
| ( ( sK170_SY3519 @ SV1086 @ SV197 @ SV491 )
= SY4255 ) ) )
= $false )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV1086
= ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5578]) ).
thf(5622,plain,
! [SV491: $i > $o,SV1087: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK178_SY2866 @ SV1087 @ SV491 @ SV197 ) )
| ~ ! [SY4266: $i] :
( ~ ( SV197 @ SY4266 )
| ( ( sK178_SY2866 @ SV1087 @ SV491 @ SV197 )
= SY4266 ) ) )
= $false )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV491 @ ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5579]) ).
thf(5623,plain,
! [SV491: $i > $o,SV1087: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK171_SY2866 @ SV1087 @ SV491 @ SV197 ) ) )
= $false )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5580]) ).
thf(5624,plain,
! [SV491: $i > $o,SV1087: $i,SV197: $i > $o] :
( ( ( ~ ! [SY4256: $i] :
( ~ ( SV197 @ SY4256 )
| ( ( sK171_SY2866 @ SV1087 @ SV491 @ SV197 )
= SY4256 ) ) )
= $false )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5580]) ).
thf(5625,plain,
! [SV226: $i,SV1041: $i,SV1056: $i] :
( ( ( ~ ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) ) )
= $false )
| ( ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
= $true )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5581]) ).
thf(5626,plain,
! [SV226: $i,SV1056: $i,SV1041: $i] :
( ( ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
= $false )
| ( ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
= $true )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5581]) ).
thf(5627,plain,
! [SV226: $i,SV1041: $i,SV1056: $i] :
( ( ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
= $true )
| ( ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
= $false )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5582]) ).
thf(5628,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( ~ ( ~ ( in @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SV955 ) ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5584]) ).
thf(5629,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( ~ ~ ! [SY4236: $i] :
~ ~ ( ~ ( in @ SY4236 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
| ~ ( in @ SY4236 @ SV955 ) ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5585]) ).
thf(5630,plain,
! [SV955: $i,SV1079: $i,SV226: $i,SV1116: $i] :
( ( ( in @ SV1116 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( ! [SY4267: $i] :
( ~ ( in @ SY4267 @ SV1116 )
| ( in @ SY4267 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) ) )
| ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SV1116 ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5586]) ).
thf(5631,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( ~ ( in @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SV955 ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5587]) ).
thf(5632,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( ~ ! [SY4230: $i] :
~ ~ ( ~ ( in @ SY4230 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
| ~ ( in @ SY4230 @ SV955 ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5588]) ).
thf(5633,plain,
! [SV226: $i,SV955: $i,SV1072: $i,SV1110: $i] :
( ( ( ! [SY4257: $i] :
( ~ ( in @ SY4257 @ SV1110 )
| ( in @ SY4257 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) ) ) )
= $true )
| ( ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SV1110 )
= $true )
| ( ( in @ SV1110 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5589]) ).
thf(5634,plain,
! [SV957: $i,SV520: $i,SV1089: $i,SV1103: $i,SV230: $i > $i > $o] :
( ( ( SV230 @ SV1103 @ SV1089 )
= $false )
| ( ( in @ SV1103 @ SV520 )
= $false )
| ( ( in @ SV1089 @ ( sK130_SY3585 @ SV957 @ SV230 @ SV520 ) )
= $true )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ SV957 )
= $false )
| ( ( SV230 @ ( sK14_SY3582 @ SV230 @ SV520 ) @ ( sK103_SY4121 @ SV957 @ SV520 @ SV230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5592]) ).
thf(5635,plain,
! [SV1077: $i,SV152: $i > $o,SV1117: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1117 )
| ~ ! [SY4268: $i] :
( ~ ( SV448 @ SY4268 )
| ( SV1117 = SY4268 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV152 @ ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5595]) ).
thf(5636,plain,
! [SV1077: $i,SV152: $i > $o,SV1111: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1111 ) )
= $true )
| ( ( ~ ! [SY4258: $i] :
( ~ ( SV448 @ SY4258 )
| ( SV1111 = SY4258 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV1077
= ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5596]) ).
thf(5637,plain,
! [SV1069: $i,SV152: $i > $o,SV1112: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1112 ) )
= $true )
| ( ( ~ ! [SY4259: $i] :
( ~ ( SV448 @ SY4259 )
| ( SV1112 = SY4259 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV152 @ ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5597]) ).
thf(5638,plain,
! [SV1069: $i,SV152: $i > $o,SV1105: $i,SV448: $i > $o] :
( ( ( SV448 @ SV1105 )
= $false )
| ( ( ~ ! [SY4252: $i] :
( ~ ( SV448 @ SY4252 )
| ( SV1105 = SY4252 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV1069
= ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5598]) ).
thf(5639,plain,
! [SV1070: $i,SV152: $i > $o,SV1113: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1113 ) )
= $true )
| ( ( ~ ! [SY4260: $i] :
( ~ ( SV448 @ SY4260 )
| ( SV1113 = SY4260 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV152 @ ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5599]) ).
thf(5640,plain,
! [SV1070: $i,SV152: $i > $o,SV1106: $i,SV448: $i > $o] :
( ( ( SV448 @ SV1106 )
= $false )
| ( ( ~ ! [SY4253: $i] :
( ~ ( SV448 @ SY4253 )
| ( SV1106 = SY4253 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV1070
= ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5600]) ).
thf(5641,plain,
! [SV1065: $i,SV152: $i > $o,SV1107: $i,SV448: $i > $o] :
( ( ( SV448 @ SV1107 )
= $false )
| ( ( ~ ! [SY4254: $i] :
( ~ ( SV448 @ SY4254 )
| ( SV1107 = SY4254 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV152 @ ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5601]) ).
thf(5642,plain,
! [SV1065: $i,SV152: $i > $o,SV1104: $i,SV448: $i > $o] :
( ( ( ! [SY4251: $i] :
( ~ ( SV448 @ SY4251 )
| ( SV1104 = SY4251 ) ) )
= $false )
| ( ( SV448 @ SV1104 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV1065
= ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5602]) ).
thf(5643,plain,
! [SV197: $i > $o,SV1097: $i,SV491: $i > $o] :
( ( ( ~ ( ~ ( SV491 @ ( sK185_SY3519 @ SV1097 @ SV197 @ SV491 ) )
| ~ ! [SY4275: $i] :
( ~ ( SV491 @ SY4275 )
| ( ( sK185_SY3519 @ SV1097 @ SV197 @ SV491 )
= SY4275 ) ) ) )
= $true )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV197 @ ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5607]) ).
thf(5644,plain,
! [SV197: $i > $o,SV1097: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK179_SY3519 @ SV1097 @ SV197 @ SV491 ) )
| ~ ! [SY4269: $i] :
( ~ ( SV491 @ SY4269 )
| ( ( sK179_SY3519 @ SV1097 @ SV197 @ SV491 )
= SY4269 ) ) )
= $false )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5608]) ).
thf(5645,plain,
! [SV491: $i > $o,SV1098: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ ( sK186_SY2866 @ SV1098 @ SV491 @ SV197 ) )
| ~ ! [SY4276: $i] :
( ~ ( SV197 @ SY4276 )
| ( ( sK186_SY2866 @ SV1098 @ SV491 @ SV197 )
= SY4276 ) ) ) )
= $true )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV491 @ ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5609]) ).
thf(5646,plain,
! [SV491: $i > $o,SV1098: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK180_SY2866 @ SV1098 @ SV491 @ SV197 ) )
| ~ ! [SY4270: $i] :
( ~ ( SV197 @ SY4270 )
| ( ( sK180_SY2866 @ SV1098 @ SV491 @ SV197 )
= SY4270 ) ) )
= $false )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5610]) ).
thf(5647,plain,
! [SV197: $i > $o,SV1092: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK181_SY3519 @ SV1092 @ SV197 @ SV491 ) )
| ~ ! [SY4271: $i] :
( ~ ( SV491 @ SY4271 )
| ( ( sK181_SY3519 @ SV1092 @ SV197 @ SV491 )
= SY4271 ) ) )
= $false )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV197 @ ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5611]) ).
thf(5648,plain,
! [SV197: $i > $o,SV1092: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK173_SY3519 @ SV1092 @ SV197 @ SV491 ) ) )
= $false )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV1092
= ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5612]) ).
thf(5649,plain,
! [SV197: $i > $o,SV1092: $i,SV491: $i > $o] :
( ( ( ~ ! [SY4261: $i] :
( ~ ( SV491 @ SY4261 )
| ( ( sK173_SY3519 @ SV1092 @ SV197 @ SV491 )
= SY4261 ) ) )
= $false )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV1092
= ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5612]) ).
thf(5650,plain,
! [SV491: $i > $o,SV1093: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK182_SY2866 @ SV1093 @ SV491 @ SV197 ) )
| ~ ! [SY4272: $i] :
( ~ ( SV197 @ SY4272 )
| ( ( sK182_SY2866 @ SV1093 @ SV491 @ SV197 )
= SY4272 ) ) )
= $false )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV491 @ ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5613]) ).
thf(5651,plain,
! [SV491: $i > $o,SV1093: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK174_SY2866 @ SV1093 @ SV491 @ SV197 ) ) )
= $false )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV1093
= ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5614]) ).
thf(5652,plain,
! [SV491: $i > $o,SV1093: $i,SV197: $i > $o] :
( ( ( ~ ! [SY4262: $i] :
( ~ ( SV197 @ SY4262 )
| ( ( sK174_SY2866 @ SV1093 @ SV491 @ SV197 )
= SY4262 ) ) )
= $false )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV1093
= ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5614]) ).
thf(5653,plain,
! [SV197: $i > $o,SV1094: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK183_SY3519 @ SV1094 @ SV197 @ SV491 ) )
| ~ ! [SY4273: $i] :
( ~ ( SV491 @ SY4273 )
| ( ( sK183_SY3519 @ SV1094 @ SV197 @ SV491 )
= SY4273 ) ) )
= $false )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV197 @ ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5615]) ).
thf(5654,plain,
! [SV197: $i > $o,SV1094: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK175_SY3519 @ SV1094 @ SV197 @ SV491 ) ) )
= $false )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV1094
= ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5616]) ).
thf(5655,plain,
! [SV197: $i > $o,SV1094: $i,SV491: $i > $o] :
( ( ( ~ ! [SY4263: $i] :
( ~ ( SV491 @ SY4263 )
| ( ( sK175_SY3519 @ SV1094 @ SV197 @ SV491 )
= SY4263 ) ) )
= $false )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV1094
= ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5616]) ).
thf(5656,plain,
! [SV491: $i > $o,SV1095: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK184_SY2866 @ SV1095 @ SV491 @ SV197 ) )
| ~ ! [SY4274: $i] :
( ~ ( SV197 @ SY4274 )
| ( ( sK184_SY2866 @ SV1095 @ SV491 @ SV197 )
= SY4274 ) ) )
= $false )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV491 @ ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5617]) ).
thf(5657,plain,
! [SV491: $i > $o,SV1095: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK176_SY2866 @ SV1095 @ SV491 @ SV197 ) ) )
= $false )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV1095
= ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5618]) ).
thf(5658,plain,
! [SV491: $i > $o,SV1095: $i,SV197: $i > $o] :
( ( ( ~ ! [SY4264: $i] :
( ~ ( SV197 @ SY4264 )
| ( ( sK176_SY2866 @ SV1095 @ SV491 @ SV197 )
= SY4264 ) ) )
= $false )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV1095
= ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5618]) ).
thf(5659,plain,
! [SV197: $i > $o,SV1086: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK177_SY3519 @ SV1086 @ SV197 @ SV491 ) ) )
= $false )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV197 @ ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5619]) ).
thf(5660,plain,
! [SV197: $i > $o,SV1086: $i,SV491: $i > $o] :
( ( ( ~ ! [SY4265: $i] :
( ~ ( SV491 @ SY4265 )
| ( ( sK177_SY3519 @ SV1086 @ SV197 @ SV491 )
= SY4265 ) ) )
= $false )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV197 @ ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5619]) ).
thf(5661,plain,
! [SV197: $i > $o,SV1086: $i,SV491: $i > $o] :
( ( ( SV491 @ ( sK170_SY3519 @ SV1086 @ SV197 @ SV491 ) )
= $true )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV1086
= ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5620]) ).
thf(5662,plain,
! [SV197: $i > $o,SV1086: $i,SV491: $i > $o] :
( ( ( ! [SY4255: $i] :
( ~ ( SV491 @ SY4255 )
| ( ( sK170_SY3519 @ SV1086 @ SV197 @ SV491 )
= SY4255 ) ) )
= $true )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV1086
= ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5621]) ).
thf(5663,plain,
! [SV491: $i > $o,SV1087: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK178_SY2866 @ SV1087 @ SV491 @ SV197 ) ) )
= $false )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV491 @ ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5622]) ).
thf(5664,plain,
! [SV491: $i > $o,SV1087: $i,SV197: $i > $o] :
( ( ( ~ ! [SY4266: $i] :
( ~ ( SV197 @ SY4266 )
| ( ( sK178_SY2866 @ SV1087 @ SV491 @ SV197 )
= SY4266 ) ) )
= $false )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV491 @ ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5622]) ).
thf(5665,plain,
! [SV491: $i > $o,SV1087: $i,SV197: $i > $o] :
( ( ( SV197 @ ( sK171_SY2866 @ SV1087 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5623]) ).
thf(5666,plain,
! [SV491: $i > $o,SV1087: $i,SV197: $i > $o] :
( ( ( ! [SY4256: $i] :
( ~ ( SV197 @ SY4256 )
| ( ( sK171_SY2866 @ SV1087 @ SV491 @ SV197 )
= SY4256 ) ) )
= $true )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5624]) ).
thf(5667,plain,
! [SV226: $i,SV1041: $i,SV1056: $i] :
( ( ( in @ SV1056 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
= $true )
| ( ( in @ SV1041 @ ( sK152_SY4193 @ SV1056 @ SV1041 @ SV226 ) )
= $true )
| ( ( SV1041 = SV1056 )
= $true )
| ( ( in @ SV1041 @ SV226 )
= $false )
| ( ( in @ SV1056 @ SV226 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5625]) ).
thf(5668,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( ~ ( in @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
| ~ ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SV955 ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5628]) ).
thf(5669,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( ~ ! [SY4236: $i] :
~ ~ ( ~ ( in @ SY4236 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
| ~ ( in @ SY4236 @ SV955 ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5629]) ).
thf(5670,plain,
! [SV226: $i,SV955: $i,SV1079: $i,SV1116: $i] :
( ( ( ! [SY4267: $i] :
( ~ ( in @ SY4267 @ SV1116 )
| ( in @ SY4267 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) ) ) )
= $true )
| ( ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SV1116 )
= $true )
| ( ( in @ SV1116 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5630]) ).
thf(5671,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( ~ ( in @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5631]) ).
thf(5672,plain,
! [SV1072: $i,SV955: $i,SV226: $i] :
( ( ( ~ ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SV955 ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5631]) ).
thf(5673,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( ! [SY4230: $i] :
~ ~ ( ~ ( in @ SY4230 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
| ~ ( in @ SY4230 @ SV955 ) ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5632]) ).
thf(5674,plain,
! [SV226: $i,SV955: $i,SV1072: $i,SV1110: $i,SV1118: $i] :
( ( ( ~ ( in @ SV1118 @ SV1110 )
| ( in @ SV1118 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) ) )
= $true )
| ( ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SV1110 )
= $true )
| ( ( in @ SV1110 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5633]) ).
thf(5675,plain,
! [SV1077: $i,SV152: $i > $o,SV1117: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ SV1117 ) )
= $true )
| ( ( ~ ! [SY4268: $i] :
( ~ ( SV448 @ SY4268 )
| ( SV1117 = SY4268 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV152 @ ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5635]) ).
thf(5676,plain,
! [SV1077: $i,SV152: $i > $o,SV1111: $i,SV448: $i > $o] :
( ( ( SV448 @ SV1111 )
= $false )
| ( ( ~ ! [SY4258: $i] :
( ~ ( SV448 @ SY4258 )
| ( SV1111 = SY4258 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV1077
= ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5636]) ).
thf(5677,plain,
! [SV1069: $i,SV152: $i > $o,SV1112: $i,SV448: $i > $o] :
( ( ( SV448 @ SV1112 )
= $false )
| ( ( ~ ! [SY4259: $i] :
( ~ ( SV448 @ SY4259 )
| ( SV1112 = SY4259 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV152 @ ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5637]) ).
thf(5678,plain,
! [SV1069: $i,SV152: $i > $o,SV1105: $i,SV448: $i > $o] :
( ( ( ! [SY4252: $i] :
( ~ ( SV448 @ SY4252 )
| ( SV1105 = SY4252 ) ) )
= $false )
| ( ( SV448 @ SV1105 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV1069
= ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5638]) ).
thf(5679,plain,
! [SV1070: $i,SV152: $i > $o,SV1113: $i,SV448: $i > $o] :
( ( ( SV448 @ SV1113 )
= $false )
| ( ( ~ ! [SY4260: $i] :
( ~ ( SV448 @ SY4260 )
| ( SV1113 = SY4260 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV152 @ ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5639]) ).
thf(5680,plain,
! [SV1070: $i,SV152: $i > $o,SV1106: $i,SV448: $i > $o] :
( ( ( ! [SY4253: $i] :
( ~ ( SV448 @ SY4253 )
| ( SV1106 = SY4253 ) ) )
= $false )
| ( ( SV448 @ SV1106 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV1070
= ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5640]) ).
thf(5681,plain,
! [SV1065: $i,SV152: $i > $o,SV1107: $i,SV448: $i > $o] :
( ( ( ! [SY4254: $i] :
( ~ ( SV448 @ SY4254 )
| ( SV1107 = SY4254 ) ) )
= $false )
| ( ( SV448 @ SV1107 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV152 @ ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5641]) ).
thf(5682,plain,
! [SV1104: $i,SV152: $i > $o,SV1065: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK187_SY4251 @ SV1065 @ SV152 @ SV1104 @ SV448 ) )
| ( SV1104
= ( sK187_SY4251 @ SV1065 @ SV152 @ SV1104 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1104 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV1065
= ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5642]) ).
thf(5683,plain,
! [SV197: $i > $o,SV1097: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK185_SY3519 @ SV1097 @ SV197 @ SV491 ) )
| ~ ! [SY4275: $i] :
( ~ ( SV491 @ SY4275 )
| ( ( sK185_SY3519 @ SV1097 @ SV197 @ SV491 )
= SY4275 ) ) )
= $false )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV197 @ ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5643]) ).
thf(5684,plain,
! [SV197: $i > $o,SV1097: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK179_SY3519 @ SV1097 @ SV197 @ SV491 ) ) )
= $false )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5644]) ).
thf(5685,plain,
! [SV197: $i > $o,SV1097: $i,SV491: $i > $o] :
( ( ( ~ ! [SY4269: $i] :
( ~ ( SV491 @ SY4269 )
| ( ( sK179_SY3519 @ SV1097 @ SV197 @ SV491 )
= SY4269 ) ) )
= $false )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5644]) ).
thf(5686,plain,
! [SV491: $i > $o,SV1098: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK186_SY2866 @ SV1098 @ SV491 @ SV197 ) )
| ~ ! [SY4276: $i] :
( ~ ( SV197 @ SY4276 )
| ( ( sK186_SY2866 @ SV1098 @ SV491 @ SV197 )
= SY4276 ) ) )
= $false )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV491 @ ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5645]) ).
thf(5687,plain,
! [SV491: $i > $o,SV1098: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK180_SY2866 @ SV1098 @ SV491 @ SV197 ) ) )
= $false )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5646]) ).
thf(5688,plain,
! [SV491: $i > $o,SV1098: $i,SV197: $i > $o] :
( ( ( ~ ! [SY4270: $i] :
( ~ ( SV197 @ SY4270 )
| ( ( sK180_SY2866 @ SV1098 @ SV491 @ SV197 )
= SY4270 ) ) )
= $false )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5646]) ).
thf(5689,plain,
! [SV197: $i > $o,SV1092: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK181_SY3519 @ SV1092 @ SV197 @ SV491 ) ) )
= $false )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV197 @ ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5647]) ).
thf(5690,plain,
! [SV197: $i > $o,SV1092: $i,SV491: $i > $o] :
( ( ( ~ ! [SY4271: $i] :
( ~ ( SV491 @ SY4271 )
| ( ( sK181_SY3519 @ SV1092 @ SV197 @ SV491 )
= SY4271 ) ) )
= $false )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV197 @ ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5647]) ).
thf(5691,plain,
! [SV197: $i > $o,SV1092: $i,SV491: $i > $o] :
( ( ( SV491 @ ( sK173_SY3519 @ SV1092 @ SV197 @ SV491 ) )
= $true )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV1092
= ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5648]) ).
thf(5692,plain,
! [SV197: $i > $o,SV1092: $i,SV491: $i > $o] :
( ( ( ! [SY4261: $i] :
( ~ ( SV491 @ SY4261 )
| ( ( sK173_SY3519 @ SV1092 @ SV197 @ SV491 )
= SY4261 ) ) )
= $true )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV1092
= ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5649]) ).
thf(5693,plain,
! [SV491: $i > $o,SV1093: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK182_SY2866 @ SV1093 @ SV491 @ SV197 ) ) )
= $false )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV491 @ ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5650]) ).
thf(5694,plain,
! [SV491: $i > $o,SV1093: $i,SV197: $i > $o] :
( ( ( ~ ! [SY4272: $i] :
( ~ ( SV197 @ SY4272 )
| ( ( sK182_SY2866 @ SV1093 @ SV491 @ SV197 )
= SY4272 ) ) )
= $false )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV491 @ ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5650]) ).
thf(5695,plain,
! [SV491: $i > $o,SV1093: $i,SV197: $i > $o] :
( ( ( SV197 @ ( sK174_SY2866 @ SV1093 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV1093
= ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5651]) ).
thf(5696,plain,
! [SV491: $i > $o,SV1093: $i,SV197: $i > $o] :
( ( ( ! [SY4262: $i] :
( ~ ( SV197 @ SY4262 )
| ( ( sK174_SY2866 @ SV1093 @ SV491 @ SV197 )
= SY4262 ) ) )
= $true )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV1093
= ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5652]) ).
thf(5697,plain,
! [SV197: $i > $o,SV1094: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK183_SY3519 @ SV1094 @ SV197 @ SV491 ) ) )
= $false )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV197 @ ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5653]) ).
thf(5698,plain,
! [SV197: $i > $o,SV1094: $i,SV491: $i > $o] :
( ( ( ~ ! [SY4273: $i] :
( ~ ( SV491 @ SY4273 )
| ( ( sK183_SY3519 @ SV1094 @ SV197 @ SV491 )
= SY4273 ) ) )
= $false )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV197 @ ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5653]) ).
thf(5699,plain,
! [SV197: $i > $o,SV1094: $i,SV491: $i > $o] :
( ( ( SV491 @ ( sK175_SY3519 @ SV1094 @ SV197 @ SV491 ) )
= $true )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV1094
= ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5654]) ).
thf(5700,plain,
! [SV197: $i > $o,SV1094: $i,SV491: $i > $o] :
( ( ( ! [SY4263: $i] :
( ~ ( SV491 @ SY4263 )
| ( ( sK175_SY3519 @ SV1094 @ SV197 @ SV491 )
= SY4263 ) ) )
= $true )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV1094
= ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5655]) ).
thf(5701,plain,
! [SV491: $i > $o,SV1095: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK184_SY2866 @ SV1095 @ SV491 @ SV197 ) ) )
= $false )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV491 @ ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5656]) ).
thf(5702,plain,
! [SV491: $i > $o,SV1095: $i,SV197: $i > $o] :
( ( ( ~ ! [SY4274: $i] :
( ~ ( SV197 @ SY4274 )
| ( ( sK184_SY2866 @ SV1095 @ SV491 @ SV197 )
= SY4274 ) ) )
= $false )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV491 @ ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5656]) ).
thf(5703,plain,
! [SV491: $i > $o,SV1095: $i,SV197: $i > $o] :
( ( ( SV197 @ ( sK176_SY2866 @ SV1095 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV1095
= ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5657]) ).
thf(5704,plain,
! [SV491: $i > $o,SV1095: $i,SV197: $i > $o] :
( ( ( ! [SY4264: $i] :
( ~ ( SV197 @ SY4264 )
| ( ( sK176_SY2866 @ SV1095 @ SV491 @ SV197 )
= SY4264 ) ) )
= $true )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV1095
= ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5658]) ).
thf(5705,plain,
! [SV197: $i > $o,SV1086: $i,SV491: $i > $o] :
( ( ( SV491 @ ( sK177_SY3519 @ SV1086 @ SV197 @ SV491 ) )
= $true )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV197 @ ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5659]) ).
thf(5706,plain,
! [SV197: $i > $o,SV1086: $i,SV491: $i > $o] :
( ( ( ! [SY4265: $i] :
( ~ ( SV491 @ SY4265 )
| ( ( sK177_SY3519 @ SV1086 @ SV197 @ SV491 )
= SY4265 ) ) )
= $true )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV197 @ ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5660]) ).
thf(5707,plain,
! [SV197: $i > $o,SV1086: $i,SV1119: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1119 )
| ( ( sK170_SY3519 @ SV1086 @ SV197 @ SV491 )
= SV1119 ) )
= $true )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV1086
= ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5662]) ).
thf(5708,plain,
! [SV491: $i > $o,SV1087: $i,SV197: $i > $o] :
( ( ( SV197 @ ( sK178_SY2866 @ SV1087 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV491 @ ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5663]) ).
thf(5709,plain,
! [SV491: $i > $o,SV1087: $i,SV197: $i > $o] :
( ( ( ! [SY4266: $i] :
( ~ ( SV197 @ SY4266 )
| ( ( sK178_SY2866 @ SV1087 @ SV491 @ SV197 )
= SY4266 ) ) )
= $true )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV491 @ ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5664]) ).
thf(5710,plain,
! [SV491: $i > $o,SV1087: $i,SV1120: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1120 )
| ( ( sK171_SY2866 @ SV1087 @ SV491 @ SV197 )
= SV1120 ) )
= $true )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5666]) ).
thf(5711,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( ~ ( in @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5668]) ).
thf(5712,plain,
! [SV1079: $i,SV955: $i,SV226: $i] :
( ( ( ~ ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SV955 ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5668]) ).
thf(5713,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( ! [SY4236: $i] :
~ ~ ( ~ ( in @ SY4236 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
| ~ ( in @ SY4236 @ SV955 ) ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5669]) ).
thf(5714,plain,
! [SV226: $i,SV955: $i,SV1079: $i,SV1116: $i,SV1121: $i] :
( ( ( ~ ( in @ SV1121 @ SV1116 )
| ( in @ SV1121 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) ) )
= $true )
| ( ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SV1116 )
= $true )
| ( ( in @ SV1116 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5670]) ).
thf(5715,plain,
! [SV226: $i,SV955: $i,SV1072: $i] :
( ( ( in @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5671]) ).
thf(5716,plain,
! [SV1072: $i,SV955: $i,SV226: $i] :
( ( ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SV955 )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5672]) ).
thf(5717,plain,
! [SV226: $i,SV955: $i,SV1072: $i,SV1122: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1122 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
| ~ ( in @ SV1122 @ SV955 ) ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5673]) ).
thf(5718,plain,
! [SV226: $i,SV955: $i,SV1072: $i,SV1110: $i,SV1118: $i] :
( ( ( ~ ( in @ SV1118 @ SV1110 ) )
= $true )
| ( ( in @ SV1118 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
= $true )
| ( ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SV1110 )
= $true )
| ( ( in @ SV1110 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5674]) ).
thf(5719,plain,
! [SV1077: $i,SV152: $i > $o,SV1117: $i,SV448: $i > $o] :
( ( ( SV448 @ SV1117 )
= $false )
| ( ( ~ ! [SY4268: $i] :
( ~ ( SV448 @ SY4268 )
| ( SV1117 = SY4268 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV152 @ ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5675]) ).
thf(5720,plain,
! [SV1077: $i,SV152: $i > $o,SV1111: $i,SV448: $i > $o] :
( ( ( ! [SY4258: $i] :
( ~ ( SV448 @ SY4258 )
| ( SV1111 = SY4258 ) ) )
= $false )
| ( ( SV448 @ SV1111 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV1077
= ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5676]) ).
thf(5721,plain,
! [SV1069: $i,SV152: $i > $o,SV1112: $i,SV448: $i > $o] :
( ( ( ! [SY4259: $i] :
( ~ ( SV448 @ SY4259 )
| ( SV1112 = SY4259 ) ) )
= $false )
| ( ( SV448 @ SV1112 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV152 @ ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5677]) ).
thf(5722,plain,
! [SV1105: $i,SV152: $i > $o,SV1069: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK188_SY4252 @ SV1069 @ SV152 @ SV1105 @ SV448 ) )
| ( SV1105
= ( sK188_SY4252 @ SV1069 @ SV152 @ SV1105 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1105 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV1069
= ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5678]) ).
thf(5723,plain,
! [SV1070: $i,SV152: $i > $o,SV1113: $i,SV448: $i > $o] :
( ( ( ! [SY4260: $i] :
( ~ ( SV448 @ SY4260 )
| ( SV1113 = SY4260 ) ) )
= $false )
| ( ( SV448 @ SV1113 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV152 @ ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5679]) ).
thf(5724,plain,
! [SV1106: $i,SV152: $i > $o,SV1070: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK189_SY4253 @ SV1070 @ SV152 @ SV1106 @ SV448 ) )
| ( SV1106
= ( sK189_SY4253 @ SV1070 @ SV152 @ SV1106 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1106 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV1070
= ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5680]) ).
thf(5725,plain,
! [SV1107: $i,SV152: $i > $o,SV1065: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK190_SY4254 @ SV1065 @ SV152 @ SV1107 @ SV448 ) )
| ( SV1107
= ( sK190_SY4254 @ SV1065 @ SV152 @ SV1107 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1107 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV152 @ ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5681]) ).
thf(5726,plain,
! [SV1104: $i,SV152: $i > $o,SV1065: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK187_SY4251 @ SV1065 @ SV152 @ SV1104 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1104 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV1065
= ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5682]) ).
thf(5727,plain,
! [SV448: $i > $o,SV152: $i > $o,SV1065: $i,SV1104: $i] :
( ( ( SV1104
= ( sK187_SY4251 @ SV1065 @ SV152 @ SV1104 @ SV448 ) )
= $false )
| ( ( SV448 @ SV1104 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV1065
= ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5682]) ).
thf(5728,plain,
! [SV197: $i > $o,SV1097: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ ( sK185_SY3519 @ SV1097 @ SV197 @ SV491 ) ) )
= $false )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV197 @ ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5683]) ).
thf(5729,plain,
! [SV197: $i > $o,SV1097: $i,SV491: $i > $o] :
( ( ( ~ ! [SY4275: $i] :
( ~ ( SV491 @ SY4275 )
| ( ( sK185_SY3519 @ SV1097 @ SV197 @ SV491 )
= SY4275 ) ) )
= $false )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV197 @ ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5683]) ).
thf(5730,plain,
! [SV197: $i > $o,SV1097: $i,SV491: $i > $o] :
( ( ( SV491 @ ( sK179_SY3519 @ SV1097 @ SV197 @ SV491 ) )
= $true )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5684]) ).
thf(5731,plain,
! [SV197: $i > $o,SV1097: $i,SV491: $i > $o] :
( ( ( ! [SY4269: $i] :
( ~ ( SV491 @ SY4269 )
| ( ( sK179_SY3519 @ SV1097 @ SV197 @ SV491 )
= SY4269 ) ) )
= $true )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5685]) ).
thf(5732,plain,
! [SV491: $i > $o,SV1098: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK186_SY2866 @ SV1098 @ SV491 @ SV197 ) ) )
= $false )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV491 @ ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5686]) ).
thf(5733,plain,
! [SV491: $i > $o,SV1098: $i,SV197: $i > $o] :
( ( ( ~ ! [SY4276: $i] :
( ~ ( SV197 @ SY4276 )
| ( ( sK186_SY2866 @ SV1098 @ SV491 @ SV197 )
= SY4276 ) ) )
= $false )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV491 @ ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5686]) ).
thf(5734,plain,
! [SV491: $i > $o,SV1098: $i,SV197: $i > $o] :
( ( ( SV197 @ ( sK180_SY2866 @ SV1098 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5687]) ).
thf(5735,plain,
! [SV491: $i > $o,SV1098: $i,SV197: $i > $o] :
( ( ( ! [SY4270: $i] :
( ~ ( SV197 @ SY4270 )
| ( ( sK180_SY2866 @ SV1098 @ SV491 @ SV197 )
= SY4270 ) ) )
= $true )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5688]) ).
thf(5736,plain,
! [SV197: $i > $o,SV1092: $i,SV491: $i > $o] :
( ( ( SV491 @ ( sK181_SY3519 @ SV1092 @ SV197 @ SV491 ) )
= $true )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV197 @ ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5689]) ).
thf(5737,plain,
! [SV197: $i > $o,SV1092: $i,SV491: $i > $o] :
( ( ( ! [SY4271: $i] :
( ~ ( SV491 @ SY4271 )
| ( ( sK181_SY3519 @ SV1092 @ SV197 @ SV491 )
= SY4271 ) ) )
= $true )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV197 @ ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5690]) ).
thf(5738,plain,
! [SV197: $i > $o,SV1092: $i,SV1123: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1123 )
| ( ( sK173_SY3519 @ SV1092 @ SV197 @ SV491 )
= SV1123 ) )
= $true )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV1092
= ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5692]) ).
thf(5739,plain,
! [SV491: $i > $o,SV1093: $i,SV197: $i > $o] :
( ( ( SV197 @ ( sK182_SY2866 @ SV1093 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV491 @ ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5693]) ).
thf(5740,plain,
! [SV491: $i > $o,SV1093: $i,SV197: $i > $o] :
( ( ( ! [SY4272: $i] :
( ~ ( SV197 @ SY4272 )
| ( ( sK182_SY2866 @ SV1093 @ SV491 @ SV197 )
= SY4272 ) ) )
= $true )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV491 @ ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5694]) ).
thf(5741,plain,
! [SV491: $i > $o,SV1093: $i,SV1124: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1124 )
| ( ( sK174_SY2866 @ SV1093 @ SV491 @ SV197 )
= SV1124 ) )
= $true )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV1093
= ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5696]) ).
thf(5742,plain,
! [SV197: $i > $o,SV1094: $i,SV491: $i > $o] :
( ( ( SV491 @ ( sK183_SY3519 @ SV1094 @ SV197 @ SV491 ) )
= $true )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV197 @ ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5697]) ).
thf(5743,plain,
! [SV197: $i > $o,SV1094: $i,SV491: $i > $o] :
( ( ( ! [SY4273: $i] :
( ~ ( SV491 @ SY4273 )
| ( ( sK183_SY3519 @ SV1094 @ SV197 @ SV491 )
= SY4273 ) ) )
= $true )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV197 @ ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5698]) ).
thf(5744,plain,
! [SV197: $i > $o,SV1094: $i,SV1125: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1125 )
| ( ( sK175_SY3519 @ SV1094 @ SV197 @ SV491 )
= SV1125 ) )
= $true )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV1094
= ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5700]) ).
thf(5745,plain,
! [SV491: $i > $o,SV1095: $i,SV197: $i > $o] :
( ( ( SV197 @ ( sK184_SY2866 @ SV1095 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV491 @ ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5701]) ).
thf(5746,plain,
! [SV491: $i > $o,SV1095: $i,SV197: $i > $o] :
( ( ( ! [SY4274: $i] :
( ~ ( SV197 @ SY4274 )
| ( ( sK184_SY2866 @ SV1095 @ SV491 @ SV197 )
= SY4274 ) ) )
= $true )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV491 @ ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5702]) ).
thf(5747,plain,
! [SV491: $i > $o,SV1095: $i,SV1126: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1126 )
| ( ( sK176_SY2866 @ SV1095 @ SV491 @ SV197 )
= SV1126 ) )
= $true )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV1095
= ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5704]) ).
thf(5748,plain,
! [SV197: $i > $o,SV1086: $i,SV1127: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1127 )
| ( ( sK177_SY3519 @ SV1086 @ SV197 @ SV491 )
= SV1127 ) )
= $true )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV197 @ ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5706]) ).
thf(5749,plain,
! [SV197: $i > $o,SV1086: $i,SV1119: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1119 ) )
= $true )
| ( ( ( sK170_SY3519 @ SV1086 @ SV197 @ SV491 )
= SV1119 )
= $true )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV1086
= ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5707]) ).
thf(5750,plain,
! [SV491: $i > $o,SV1087: $i,SV1128: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1128 )
| ( ( sK178_SY2866 @ SV1087 @ SV491 @ SV197 )
= SV1128 ) )
= $true )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV491 @ ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5709]) ).
thf(5751,plain,
! [SV491: $i > $o,SV1087: $i,SV1120: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1120 ) )
= $true )
| ( ( ( sK171_SY2866 @ SV1087 @ SV491 @ SV197 )
= SV1120 )
= $true )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5710]) ).
thf(5752,plain,
! [SV226: $i,SV955: $i,SV1079: $i] :
( ( ( in @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) @ ( sK2_SY2943 @ SV226 ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5711]) ).
thf(5753,plain,
! [SV1079: $i,SV955: $i,SV226: $i] :
( ( ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SV955 )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5712]) ).
thf(5754,plain,
! [SV226: $i,SV955: $i,SV1079: $i,SV1129: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1129 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
| ~ ( in @ SV1129 @ SV955 ) ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5713]) ).
thf(5755,plain,
! [SV226: $i,SV955: $i,SV1079: $i,SV1116: $i,SV1121: $i] :
( ( ( ~ ( in @ SV1121 @ SV1116 ) )
= $true )
| ( ( in @ SV1121 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
= $true )
| ( ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SV1116 )
= $true )
| ( ( in @ SV1116 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5714]) ).
thf(5756,plain,
! [SV226: $i,SV955: $i,SV1072: $i,SV1122: $i] :
( ( ( ~ ( ~ ( in @ SV1122 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
| ~ ( in @ SV1122 @ SV955 ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5717]) ).
thf(5757,plain,
! [SV226: $i,SV955: $i,SV1072: $i,SV1110: $i,SV1118: $i] :
( ( ( in @ SV1118 @ SV1110 )
= $false )
| ( ( in @ SV1118 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
= $true )
| ( ( in @ ( sK153_SY4229 @ SV226 @ SV955 @ SV1072 ) @ SV1110 )
= $true )
| ( ( in @ SV1110 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5718]) ).
thf(5758,plain,
! [SV1077: $i,SV152: $i > $o,SV1117: $i,SV448: $i > $o] :
( ( ( ! [SY4268: $i] :
( ~ ( SV448 @ SY4268 )
| ( SV1117 = SY4268 ) ) )
= $false )
| ( ( SV448 @ SV1117 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV152 @ ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5719]) ).
thf(5759,plain,
! [SV1111: $i,SV152: $i > $o,SV1077: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK191_SY4258 @ SV1077 @ SV152 @ SV1111 @ SV448 ) )
| ( SV1111
= ( sK191_SY4258 @ SV1077 @ SV152 @ SV1111 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1111 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV1077
= ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5720]) ).
thf(5760,plain,
! [SV1112: $i,SV152: $i > $o,SV1069: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK192_SY4259 @ SV1069 @ SV152 @ SV1112 @ SV448 ) )
| ( SV1112
= ( sK192_SY4259 @ SV1069 @ SV152 @ SV1112 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1112 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV152 @ ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5721]) ).
thf(5761,plain,
! [SV1105: $i,SV152: $i > $o,SV1069: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK188_SY4252 @ SV1069 @ SV152 @ SV1105 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1105 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV1069
= ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5722]) ).
thf(5762,plain,
! [SV448: $i > $o,SV152: $i > $o,SV1069: $i,SV1105: $i] :
( ( ( SV1105
= ( sK188_SY4252 @ SV1069 @ SV152 @ SV1105 @ SV448 ) )
= $false )
| ( ( SV448 @ SV1105 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV1069
= ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5722]) ).
thf(5763,plain,
! [SV1113: $i,SV152: $i > $o,SV1070: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK193_SY4260 @ SV1070 @ SV152 @ SV1113 @ SV448 ) )
| ( SV1113
= ( sK193_SY4260 @ SV1070 @ SV152 @ SV1113 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1113 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV152 @ ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5723]) ).
thf(5764,plain,
! [SV1106: $i,SV152: $i > $o,SV1070: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK189_SY4253 @ SV1070 @ SV152 @ SV1106 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1106 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV1070
= ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5724]) ).
thf(5765,plain,
! [SV448: $i > $o,SV152: $i > $o,SV1070: $i,SV1106: $i] :
( ( ( SV1106
= ( sK189_SY4253 @ SV1070 @ SV152 @ SV1106 @ SV448 ) )
= $false )
| ( ( SV448 @ SV1106 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV1070
= ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5724]) ).
thf(5766,plain,
! [SV1107: $i,SV152: $i > $o,SV1065: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK190_SY4254 @ SV1065 @ SV152 @ SV1107 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1107 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV152 @ ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5725]) ).
thf(5767,plain,
! [SV448: $i > $o,SV152: $i > $o,SV1065: $i,SV1107: $i] :
( ( ( SV1107
= ( sK190_SY4254 @ SV1065 @ SV152 @ SV1107 @ SV448 ) )
= $false )
| ( ( SV448 @ SV1107 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV152 @ ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5725]) ).
thf(5768,plain,
! [SV1104: $i,SV152: $i > $o,SV1065: $i,SV448: $i > $o] :
( ( ( SV448 @ ( sK187_SY4251 @ SV1065 @ SV152 @ SV1104 @ SV448 ) )
= $true )
| ( ( SV448 @ SV1104 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV1065
= ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5726]) ).
thf(5769,plain,
! [SV197: $i > $o,SV1097: $i,SV491: $i > $o] :
( ( ( SV491 @ ( sK185_SY3519 @ SV1097 @ SV197 @ SV491 ) )
= $true )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV197 @ ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5728]) ).
thf(5770,plain,
! [SV197: $i > $o,SV1097: $i,SV491: $i > $o] :
( ( ( ! [SY4275: $i] :
( ~ ( SV491 @ SY4275 )
| ( ( sK185_SY3519 @ SV1097 @ SV197 @ SV491 )
= SY4275 ) ) )
= $true )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV197 @ ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5729]) ).
thf(5771,plain,
! [SV197: $i > $o,SV1097: $i,SV1130: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1130 )
| ( ( sK179_SY3519 @ SV1097 @ SV197 @ SV491 )
= SV1130 ) )
= $true )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5731]) ).
thf(5772,plain,
! [SV491: $i > $o,SV1098: $i,SV197: $i > $o] :
( ( ( SV197 @ ( sK186_SY2866 @ SV1098 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV491 @ ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5732]) ).
thf(5773,plain,
! [SV491: $i > $o,SV1098: $i,SV197: $i > $o] :
( ( ( ! [SY4276: $i] :
( ~ ( SV197 @ SY4276 )
| ( ( sK186_SY2866 @ SV1098 @ SV491 @ SV197 )
= SY4276 ) ) )
= $true )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV491 @ ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5733]) ).
thf(5774,plain,
! [SV491: $i > $o,SV1098: $i,SV1131: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1131 )
| ( ( sK180_SY2866 @ SV1098 @ SV491 @ SV197 )
= SV1131 ) )
= $true )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5735]) ).
thf(5775,plain,
! [SV197: $i > $o,SV1092: $i,SV1132: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1132 )
| ( ( sK181_SY3519 @ SV1092 @ SV197 @ SV491 )
= SV1132 ) )
= $true )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV197 @ ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5737]) ).
thf(5776,plain,
! [SV197: $i > $o,SV1092: $i,SV1123: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1123 ) )
= $true )
| ( ( ( sK173_SY3519 @ SV1092 @ SV197 @ SV491 )
= SV1123 )
= $true )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV1092
= ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5738]) ).
thf(5777,plain,
! [SV491: $i > $o,SV1093: $i,SV1133: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1133 )
| ( ( sK182_SY2866 @ SV1093 @ SV491 @ SV197 )
= SV1133 ) )
= $true )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV491 @ ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5740]) ).
thf(5778,plain,
! [SV491: $i > $o,SV1093: $i,SV1124: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1124 ) )
= $true )
| ( ( ( sK174_SY2866 @ SV1093 @ SV491 @ SV197 )
= SV1124 )
= $true )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV1093
= ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5741]) ).
thf(5779,plain,
! [SV197: $i > $o,SV1094: $i,SV1134: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1134 )
| ( ( sK183_SY3519 @ SV1094 @ SV197 @ SV491 )
= SV1134 ) )
= $true )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV197 @ ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5743]) ).
thf(5780,plain,
! [SV197: $i > $o,SV1094: $i,SV1125: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1125 ) )
= $true )
| ( ( ( sK175_SY3519 @ SV1094 @ SV197 @ SV491 )
= SV1125 )
= $true )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV1094
= ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5744]) ).
thf(5781,plain,
! [SV491: $i > $o,SV1095: $i,SV1135: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1135 )
| ( ( sK184_SY2866 @ SV1095 @ SV491 @ SV197 )
= SV1135 ) )
= $true )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV491 @ ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5746]) ).
thf(5782,plain,
! [SV491: $i > $o,SV1095: $i,SV1126: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1126 ) )
= $true )
| ( ( ( sK176_SY2866 @ SV1095 @ SV491 @ SV197 )
= SV1126 )
= $true )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV1095
= ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5747]) ).
thf(5783,plain,
! [SV197: $i > $o,SV1086: $i,SV1127: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1127 ) )
= $true )
| ( ( ( sK177_SY3519 @ SV1086 @ SV197 @ SV491 )
= SV1127 )
= $true )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV197 @ ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5748]) ).
thf(5784,plain,
! [SV197: $i > $o,SV1086: $i,SV1119: $i,SV491: $i > $o] :
( ( ( SV491 @ SV1119 )
= $false )
| ( ( ( sK170_SY3519 @ SV1086 @ SV197 @ SV491 )
= SV1119 )
= $true )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV1086
= ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5749]) ).
thf(5785,plain,
! [SV491: $i > $o,SV1087: $i,SV1128: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1128 ) )
= $true )
| ( ( ( sK178_SY2866 @ SV1087 @ SV491 @ SV197 )
= SV1128 )
= $true )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV491 @ ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5750]) ).
thf(5786,plain,
! [SV491: $i > $o,SV1087: $i,SV1120: $i,SV197: $i > $o] :
( ( ( SV197 @ SV1120 )
= $false )
| ( ( ( sK171_SY2866 @ SV1087 @ SV491 @ SV197 )
= SV1120 )
= $true )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5751]) ).
thf(5787,plain,
! [SV226: $i,SV955: $i,SV1079: $i,SV1129: $i] :
( ( ( ~ ( ~ ( in @ SV1129 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
| ~ ( in @ SV1129 @ SV955 ) ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5754]) ).
thf(5788,plain,
! [SV226: $i,SV955: $i,SV1079: $i,SV1116: $i,SV1121: $i] :
( ( ( in @ SV1121 @ SV1116 )
= $false )
| ( ( in @ SV1121 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
= $true )
| ( ( in @ ( sK157_SY4235 @ SV226 @ SV955 @ SV1079 ) @ SV1116 )
= $true )
| ( ( in @ SV1116 @ ( sK2_SY2943 @ SV226 ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5755]) ).
thf(5789,plain,
! [SV226: $i,SV955: $i,SV1072: $i,SV1122: $i] :
( ( ( ~ ( in @ SV1122 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
| ~ ( in @ SV1122 @ SV955 ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5756]) ).
thf(5790,plain,
! [SV1117: $i,SV152: $i > $o,SV1077: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK194_SY4268 @ SV1077 @ SV152 @ SV1117 @ SV448 ) )
| ( SV1117
= ( sK194_SY4268 @ SV1077 @ SV152 @ SV1117 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1117 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV152 @ ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5758]) ).
thf(5791,plain,
! [SV1111: $i,SV152: $i > $o,SV1077: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK191_SY4258 @ SV1077 @ SV152 @ SV1111 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1111 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV1077
= ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5759]) ).
thf(5792,plain,
! [SV448: $i > $o,SV152: $i > $o,SV1077: $i,SV1111: $i] :
( ( ( SV1111
= ( sK191_SY4258 @ SV1077 @ SV152 @ SV1111 @ SV448 ) )
= $false )
| ( ( SV448 @ SV1111 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV1077
= ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5759]) ).
thf(5793,plain,
! [SV1112: $i,SV152: $i > $o,SV1069: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK192_SY4259 @ SV1069 @ SV152 @ SV1112 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1112 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV152 @ ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5760]) ).
thf(5794,plain,
! [SV448: $i > $o,SV152: $i > $o,SV1069: $i,SV1112: $i] :
( ( ( SV1112
= ( sK192_SY4259 @ SV1069 @ SV152 @ SV1112 @ SV448 ) )
= $false )
| ( ( SV448 @ SV1112 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV152 @ ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5760]) ).
thf(5795,plain,
! [SV1105: $i,SV152: $i > $o,SV1069: $i,SV448: $i > $o] :
( ( ( SV448 @ ( sK188_SY4252 @ SV1069 @ SV152 @ SV1105 @ SV448 ) )
= $true )
| ( ( SV448 @ SV1105 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV1069
= ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5761]) ).
thf(5796,plain,
! [SV1113: $i,SV152: $i > $o,SV1070: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK193_SY4260 @ SV1070 @ SV152 @ SV1113 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1113 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV152 @ ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5763]) ).
thf(5797,plain,
! [SV448: $i > $o,SV152: $i > $o,SV1070: $i,SV1113: $i] :
( ( ( SV1113
= ( sK193_SY4260 @ SV1070 @ SV152 @ SV1113 @ SV448 ) )
= $false )
| ( ( SV448 @ SV1113 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV152 @ ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5763]) ).
thf(5798,plain,
! [SV1106: $i,SV152: $i > $o,SV1070: $i,SV448: $i > $o] :
( ( ( SV448 @ ( sK189_SY4253 @ SV1070 @ SV152 @ SV1106 @ SV448 ) )
= $true )
| ( ( SV448 @ SV1106 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV1070
= ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5764]) ).
thf(5799,plain,
! [SV1107: $i,SV152: $i > $o,SV1065: $i,SV448: $i > $o] :
( ( ( SV448 @ ( sK190_SY4254 @ SV1065 @ SV152 @ SV1107 @ SV448 ) )
= $true )
| ( ( SV448 @ SV1107 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1065 )
= $false )
| ( ( SV152 @ ( sK147_SY4201 @ SV448 @ SV1065 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5766]) ).
thf(5800,plain,
! [SV197: $i > $o,SV1097: $i,SV1136: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1136 )
| ( ( sK185_SY3519 @ SV1097 @ SV197 @ SV491 )
= SV1136 ) )
= $true )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV197 @ ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5770]) ).
thf(5801,plain,
! [SV197: $i > $o,SV1097: $i,SV1130: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1130 ) )
= $true )
| ( ( ( sK179_SY3519 @ SV1097 @ SV197 @ SV491 )
= SV1130 )
= $true )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5771]) ).
thf(5802,plain,
! [SV491: $i > $o,SV1098: $i,SV1137: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1137 )
| ( ( sK186_SY2866 @ SV1098 @ SV491 @ SV197 )
= SV1137 ) )
= $true )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV491 @ ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5773]) ).
thf(5803,plain,
! [SV491: $i > $o,SV1098: $i,SV1131: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1131 ) )
= $true )
| ( ( ( sK180_SY2866 @ SV1098 @ SV491 @ SV197 )
= SV1131 )
= $true )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5774]) ).
thf(5804,plain,
! [SV197: $i > $o,SV1092: $i,SV1132: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1132 ) )
= $true )
| ( ( ( sK181_SY3519 @ SV1092 @ SV197 @ SV491 )
= SV1132 )
= $true )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV197 @ ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5775]) ).
thf(5805,plain,
! [SV197: $i > $o,SV1092: $i,SV1123: $i,SV491: $i > $o] :
( ( ( SV491 @ SV1123 )
= $false )
| ( ( ( sK173_SY3519 @ SV1092 @ SV197 @ SV491 )
= SV1123 )
= $true )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV1092
= ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5776]) ).
thf(5806,plain,
! [SV491: $i > $o,SV1093: $i,SV1133: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1133 ) )
= $true )
| ( ( ( sK182_SY2866 @ SV1093 @ SV491 @ SV197 )
= SV1133 )
= $true )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV491 @ ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5777]) ).
thf(5807,plain,
! [SV491: $i > $o,SV1093: $i,SV1124: $i,SV197: $i > $o] :
( ( ( SV197 @ SV1124 )
= $false )
| ( ( ( sK174_SY2866 @ SV1093 @ SV491 @ SV197 )
= SV1124 )
= $true )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV1093
= ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5778]) ).
thf(5808,plain,
! [SV197: $i > $o,SV1094: $i,SV1134: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1134 ) )
= $true )
| ( ( ( sK183_SY3519 @ SV1094 @ SV197 @ SV491 )
= SV1134 )
= $true )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV197 @ ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5779]) ).
thf(5809,plain,
! [SV197: $i > $o,SV1094: $i,SV1125: $i,SV491: $i > $o] :
( ( ( SV491 @ SV1125 )
= $false )
| ( ( ( sK175_SY3519 @ SV1094 @ SV197 @ SV491 )
= SV1125 )
= $true )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV1094
= ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5780]) ).
thf(5810,plain,
! [SV491: $i > $o,SV1095: $i,SV1135: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1135 ) )
= $true )
| ( ( ( sK184_SY2866 @ SV1095 @ SV491 @ SV197 )
= SV1135 )
= $true )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV491 @ ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5781]) ).
thf(5811,plain,
! [SV491: $i > $o,SV1095: $i,SV1126: $i,SV197: $i > $o] :
( ( ( SV197 @ SV1126 )
= $false )
| ( ( ( sK176_SY2866 @ SV1095 @ SV491 @ SV197 )
= SV1126 )
= $true )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV1095
= ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5782]) ).
thf(5812,plain,
! [SV197: $i > $o,SV1086: $i,SV1127: $i,SV491: $i > $o] :
( ( ( SV491 @ SV1127 )
= $false )
| ( ( ( sK177_SY3519 @ SV1086 @ SV197 @ SV491 )
= SV1127 )
= $true )
| ( ( SV197 @ SV1086 )
= $false )
| ( ( SV197 @ ( sK158_SY4221 @ SV491 @ SV1086 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5783]) ).
thf(5813,plain,
! [SV491: $i > $o,SV1087: $i,SV1128: $i,SV197: $i > $o] :
( ( ( SV197 @ SV1128 )
= $false )
| ( ( ( sK178_SY2866 @ SV1087 @ SV491 @ SV197 )
= SV1128 )
= $true )
| ( ( SV491 @ SV1087 )
= $false )
| ( ( SV491 @ ( sK159_SY4222 @ SV197 @ SV1087 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5785]) ).
thf(5814,plain,
! [SV226: $i,SV955: $i,SV1079: $i,SV1129: $i] :
( ( ( ~ ( in @ SV1129 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
| ~ ( in @ SV1129 @ SV955 ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5787]) ).
thf(5815,plain,
! [SV226: $i,SV955: $i,SV1072: $i,SV1122: $i] :
( ( ( ~ ( in @ SV1122 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) ) )
= $true )
| ( ( ~ ( in @ SV1122 @ SV955 ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5789]) ).
thf(5816,plain,
! [SV1117: $i,SV152: $i > $o,SV1077: $i,SV448: $i > $o] :
( ( ( ~ ( SV448 @ ( sK194_SY4268 @ SV1077 @ SV152 @ SV1117 @ SV448 ) ) )
= $false )
| ( ( SV448 @ SV1117 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV152 @ ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5790]) ).
thf(5817,plain,
! [SV448: $i > $o,SV152: $i > $o,SV1077: $i,SV1117: $i] :
( ( ( SV1117
= ( sK194_SY4268 @ SV1077 @ SV152 @ SV1117 @ SV448 ) )
= $false )
| ( ( SV448 @ SV1117 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV152 @ ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5790]) ).
thf(5818,plain,
! [SV1111: $i,SV152: $i > $o,SV1077: $i,SV448: $i > $o] :
( ( ( SV448 @ ( sK191_SY4258 @ SV1077 @ SV152 @ SV1111 @ SV448 ) )
= $true )
| ( ( SV448 @ SV1111 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV1077
= ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $false )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5791]) ).
thf(5819,plain,
! [SV1112: $i,SV152: $i > $o,SV1069: $i,SV448: $i > $o] :
( ( ( SV448 @ ( sK192_SY4259 @ SV1069 @ SV152 @ SV1112 @ SV448 ) )
= $true )
| ( ( SV448 @ SV1112 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1069 )
= $false )
| ( ( SV152 @ ( sK148_SY4209 @ SV448 @ SV1069 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5793]) ).
thf(5820,plain,
! [SV1113: $i,SV152: $i > $o,SV1070: $i,SV448: $i > $o] :
( ( ( SV448 @ ( sK193_SY4260 @ SV1070 @ SV152 @ SV1113 @ SV448 ) )
= $true )
| ( ( SV448 @ SV1113 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1070 )
= $false )
| ( ( SV152 @ ( sK149_SY4210 @ SV448 @ SV1070 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $false )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5796]) ).
thf(5821,plain,
! [SV197: $i > $o,SV1097: $i,SV1136: $i,SV491: $i > $o] :
( ( ( ~ ( SV491 @ SV1136 ) )
= $true )
| ( ( ( sK185_SY3519 @ SV1097 @ SV197 @ SV491 )
= SV1136 )
= $true )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV197 @ ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5800]) ).
thf(5822,plain,
! [SV197: $i > $o,SV1097: $i,SV1130: $i,SV491: $i > $o] :
( ( ( SV491 @ SV1130 )
= $false )
| ( ( ( sK179_SY3519 @ SV1097 @ SV197 @ SV491 )
= SV1130 )
= $true )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5801]) ).
thf(5823,plain,
! [SV491: $i > $o,SV1098: $i,SV1137: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV1137 ) )
= $true )
| ( ( ( sK186_SY2866 @ SV1098 @ SV491 @ SV197 )
= SV1137 )
= $true )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV491 @ ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5802]) ).
thf(5824,plain,
! [SV491: $i > $o,SV1098: $i,SV1131: $i,SV197: $i > $o] :
( ( ( SV197 @ SV1131 )
= $false )
| ( ( ( sK180_SY2866 @ SV1098 @ SV491 @ SV197 )
= SV1131 )
= $true )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $false )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5803]) ).
thf(5825,plain,
! [SV197: $i > $o,SV1092: $i,SV1132: $i,SV491: $i > $o] :
( ( ( SV491 @ SV1132 )
= $false )
| ( ( ( sK181_SY3519 @ SV1092 @ SV197 @ SV491 )
= SV1132 )
= $true )
| ( ( SV197 @ SV1092 )
= $false )
| ( ( SV197 @ ( sK161_SY4225 @ SV491 @ SV1092 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5804]) ).
thf(5826,plain,
! [SV491: $i > $o,SV1093: $i,SV1133: $i,SV197: $i > $o] :
( ( ( SV197 @ SV1133 )
= $false )
| ( ( ( sK182_SY2866 @ SV1093 @ SV491 @ SV197 )
= SV1133 )
= $true )
| ( ( SV491 @ SV1093 )
= $false )
| ( ( SV491 @ ( sK162_SY4226 @ SV197 @ SV1093 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5806]) ).
thf(5827,plain,
! [SV197: $i > $o,SV1094: $i,SV1134: $i,SV491: $i > $o] :
( ( ( SV491 @ SV1134 )
= $false )
| ( ( ( sK183_SY3519 @ SV1094 @ SV197 @ SV491 )
= SV1134 )
= $true )
| ( ( SV197 @ SV1094 )
= $false )
| ( ( SV197 @ ( sK163_SY4227 @ SV491 @ SV1094 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5808]) ).
thf(5828,plain,
! [SV491: $i > $o,SV1095: $i,SV1135: $i,SV197: $i > $o] :
( ( ( SV197 @ SV1135 )
= $false )
| ( ( ( sK184_SY2866 @ SV1095 @ SV491 @ SV197 )
= SV1135 )
= $true )
| ( ( SV491 @ SV1095 )
= $false )
| ( ( SV491 @ ( sK164_SY4228 @ SV197 @ SV1095 @ SV491 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $false )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5810]) ).
thf(5829,plain,
! [SV226: $i,SV955: $i,SV1079: $i,SV1129: $i] :
( ( ( ~ ( in @ SV1129 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) ) )
= $true )
| ( ( ~ ( in @ SV1129 @ SV955 ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5814]) ).
thf(5830,plain,
! [SV226: $i,SV955: $i,SV1072: $i,SV1122: $i] :
( ( ( in @ SV1122 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
= $false )
| ( ( ~ ( in @ SV1122 @ SV955 ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5815]) ).
thf(5831,plain,
! [SV1117: $i,SV152: $i > $o,SV1077: $i,SV448: $i > $o] :
( ( ( SV448 @ ( sK194_SY4268 @ SV1077 @ SV152 @ SV1117 @ SV448 ) )
= $true )
| ( ( SV448 @ SV1117 )
= $false )
| ( ( ( descr
@ ^ [SY2731: $i] : ( SV152 @ SY2731 ) )
= ( descr
@ ^ [SY3432: $i] : ( SV448 @ SY3432 ) ) )
= $true )
| ( ( SV152 @ SV1077 )
= $false )
| ( ( SV152 @ ( sK154_SY4216 @ SV448 @ SV1077 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK12_SY3425 @ SV448 @ SV152 ) )
= $true )
| ( ( SV448 @ ( sK28_SY3994 @ SV152 @ SV448 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5816]) ).
thf(5832,plain,
! [SV197: $i > $o,SV1097: $i,SV1136: $i,SV491: $i > $o] :
( ( ( SV491 @ SV1136 )
= $false )
| ( ( ( sK185_SY3519 @ SV1097 @ SV197 @ SV491 )
= SV1136 )
= $true )
| ( ( SV197 @ SV1097 )
= $false )
| ( ( SV197 @ ( sK167_SY4233 @ SV491 @ SV1097 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5821]) ).
thf(5833,plain,
! [SV491: $i > $o,SV1098: $i,SV1137: $i,SV197: $i > $o] :
( ( ( SV197 @ SV1137 )
= $false )
| ( ( ( sK186_SY2866 @ SV1098 @ SV491 @ SV197 )
= SV1137 )
= $true )
| ( ( SV491 @ SV1098 )
= $false )
| ( ( SV491 @ ( sK168_SY4234 @ SV197 @ SV1098 @ SV491 ) )
= $true )
| ( ( SV197 @ ( sK13_SY3515 @ SV491 @ SV197 ) )
= $true )
| ( ( SV491 @ ( sK32_SY4003 @ SV197 @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5823]) ).
thf(5834,plain,
! [SV226: $i,SV955: $i,SV1079: $i,SV1129: $i] :
( ( ( in @ SV1129 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
= $false )
| ( ( ~ ( in @ SV1129 @ SV955 ) )
= $true )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5829]) ).
thf(5835,plain,
! [SV226: $i,SV1072: $i,SV955: $i,SV1122: $i] :
( ( ( in @ SV1122 @ SV955 )
= $false )
| ( ( in @ SV1122 @ ( sK144_SY4116 @ SV1072 @ SV955 @ SV226 ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV226 )
= $false )
| ( ( in @ SV1072 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5830]) ).
thf(5836,plain,
! [SV226: $i,SV1079: $i,SV955: $i,SV1129: $i] :
( ( ( in @ SV1129 @ SV955 )
= $false )
| ( ( in @ SV1129 @ ( sK146_SY4116 @ SV1079 @ SV955 @ SV226 ) )
= $false )
| ( ( in @ ( sK102_SY4114 @ SV226 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1079 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5834]) ).
thf(5837,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[592,5836,5835,5833,5832,5831,5828,5827,5826,5825,5824,5822,5820,5819,5818,5817,5813,5812,5811,5809,5807,5805,5799,5798,5797,5795,5794,5792,5788,5786,5784,5772,5769,5768,5767,5765,5762,5757,5753,5752,5745,5742,5739,5736,5734,5730,5727,5716,5715,5708,5705,5703,5699,5695,5691,5667,5665,5661,5634,5627,5626,5606,5605,5604,5603,5594,5593,5591,5590,5583,5564,5562,5550,5549,5546,5545,5505,5473,5470,5434,5430,5374,5360,5359,5342,5327,5306,5305,5304,5282,5281,5280,5279,5278,5277,5276,5275,5270,5265,5264,5262,5261,5259,5258,5236,5235,5233,5232,5229,5228,5226,5225,5224,5222,5221,5219,5218,5216,5215,5214,5212,5211,5205,5204,5199,5196,5193,5178,5177,5168,5166,5163,5161,5160,5158,5157,5153,5152,5149,5146,5143,5140,5139,5137,5134,5132,5115,5114,5113,5102,5097,5087,5084,5083,5082,5080,5079,5077,5071,5070,5065,5054,5051,5036,5035,5033,5032,5030,5029,5011,5010,5003,5001,4997,4996,4994,4993,4992,4991,4980,4978,4975,4967,4966,4961,4957,4956,4954,4945,4938,4935,4932,4917,4914,4903,4901,4892,4887,4882,4880,4874,4873,4871,4864,4863,4861,4860,4859,4818,4815,4801,4796,4791,4787,4784,4776,4771,4769,4768,4763,4761,4758,4756,4746,4745,4732,4725,4724,4723,4722,4721,4720,4719,4718,4703,4702,4659,4657,4641,4640,4639,4632,4619,4617,4610,4607,4604,4584,4579,4569,4568,4561,4560,4559,4555,4554,4540,4539,4529,4525,4524,4520,4519,4518,4516,4509,4507,4490,4489,4488,4487,4484,4483,4482,4481,4478,4477,4476,4475,4472,4471,4458,4452,4450,4444,4438,4437,4431,4429,4425,4420,4418,4415,4414,4405,4399,4397,4392,4391,4387,4380,4379,4378,4355,4346,4340,4336,4333,4329,4326,4322,4319,4306,4305,4286,4280,4278,4275,4273,4272,4259,4258,4257,4256,4255,4254,4252,4243,4224,4222,4215,4214,4212,4211,4209,4208,4196,4191,4189,4185,4184,4139,4129,4123,4113,4112,4104,4103,4101,4086,4085,4083,4082,4080,4079,4076,4065,4064,4063,4061,4055,4050,4040,4038,4037,4036,4029,4026,4023,4015,4014,4002,3996,3987,3948,3947,3932,3928,3922,3920,3919,3917,3915,3914,3907,3901,3898,3897,3894,3891,3888,3886,3885,3871,3864,3857,3856,3855,3833,3829,3828,3826,3825,3803,3799,3798,3777,3768,3767,3766,3763,3754,3753,3752,3732,3731,3730,3726,3725,3695,3661,3643,3632,3631,3630,3626,3625,3624,3621,3620,3619,3606,3605,3604,3580,3576,3574,3573,3571,3570,3568,3566,3565,3563,3557,3556,3554,3546,3545,3544,3530,3529,3526,3525,3517,3515,3513,3506,3468,3467,3432,3422,3419,3402,3398,3378,3363,3362,3355,3334,3324,3297,3296,3295,3272,3251,3250,3234,3226,3225,3223,3219,3218,3213,3210,3206,3192,3191,3190,3177,3176,3175,3174,3170,3169,3168,3162,3145,3134,3117,3116,3107,3094,3091,3085,3084,3083,3065,3064,3055,3053,3052,3051,3045,3043,3042,3039,3034,3015,3013,3012,2997,2996,2993,2977,2976,2973,2964,2943,2930,2927,2924,2915,2907,2906,2905,2897,2895,2894,2892,2890,2884,2867,2863,2851,2850,2834,2831,2822,2818,2814,2803,2791,2786,2784,2779,2770,2757,2756,2749,2724,2713,2711,2697,2692,2688,2643,2637,2625,2601,2591,2539,2513,2508,2491,2486,2477,2476,2471,2450,2432,2427,2415,2407,2401,2384,2361,2350,2344,2341,2340,2328,2316,2311,2309,2305,2295,2292,2268,2263,2237,2231,2221,2216,2213,2208,2203,2189,2186,2185,2184,2183,2181,2179,2172,2162,2143,2140,2136,2117,2101,2086,2080,2076,2029,2012,2009,2005,2002,1997,1988,1984,1981,1980,1979,1975,1965,1955,1948,1923,1907,1889,1852,1823,1774,1707,1694,1693,1692,1689,1688,1687,1680,1663,1631,1630,1629,1313,1312,1311,1310,1309,1308,1307,1306,1305,1304,1303,1302,1301,1299,1298,1297,1296,1295,1294,1293,1292,1289,1288,987,986,985,982,981,979,964,963,962,658,634,596]) ).
thf(5838,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[5837]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU813^1 : 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
% 0.11/0.19 % Computer : n018.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Oct 6 15:37:52 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 159.46/26.85 ..
% 159.46/26.85
% 159.46/26.85 No.of.Axioms: 0
% 159.46/26.85
% 159.46/26.85 Length.of.Defs: 80414
% 159.46/26.85
% 159.46/26.85 Contains.Choice.Funs: true
% 159.46/26.85 .................................................................................................................................................................................................................................................................
% 159.46/26.85
% 159.46/26.85 ********************************
% 159.46/26.85 * All subproblems solved! *
% 159.46/26.85 ********************************
% 159.46/26.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:329,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:5837,loop_count:0,foatp_calls:1,translation:fof_full)
% 159.46/26.85
% 159.46/26.85 %**** Beginning of derivation protocol ****
% 159.46/26.85 % SZS output start CNFRefutation
% See solution above
% 159.46/26.89
% 159.46/26.89 %**** End of derivation protocol ****
% 159.46/26.89 %**** no. of clauses in derivation: 5838 ****
% 159.46/26.89 %**** clause counter: 5837 ****
% 159.46/26.89
% 159.46/26.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:329,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:5837,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------